A study of arterial blood noises (cervical bruits)
by Joel Morris Bowers
A thesis submitted to the Graduate Faculty in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE in Aerospace and Mechanical Engineering
Montana State University
© Copyright by Joel Morris Bowers (1969)
Abstract:
The purpose of this investigation, a mathematical analysis of the acoustical properties of cervical
bruits, was to differentiate the auscultatory signals of diseased neck arteries (stenotic bruits) from
similar sounding healthy artery signals (innocent bruits).
By studying the variation and first moment of *the acoustical signal distribution curve, no significant
difference was found between the stenotic and innocent bruit.
Significant difference between the innocent and stenotic bruit was evident from an examination of the
zero crossing frequency of the signal. The bandwidth, mean frequency, and number of peaks in the
energy spectrum of the signal also showed significant difference between the innocent and stenotic
bruit.
The average stenotic bruit studied was found to have 90% of its energy contained in a frequency band
width of 188 Hz. with a center frequency of 131 Hz. The frequency band containing 90% of the energy
of the average innocent bruit was 123 Hz. wide and centered at 82 Hz. Counting the number of spectral
peaks in the energy density spectrum proved to be the most reliable test for identifying the two types of
bruits. Stenosis was diagnosed correctly in 77% to 85% of the patients studied using the spectral peak
count. I
A STUDY OF ARTERIAL BLOOD NOISES
(CERVICAL BRUITS)
by
JOEL MORRIS BOWERS
A t h e s i s submitted to
f u l f i l l m e n t o f the
t he Gr a d u a t e F a c u l t y i n p a r t r a l
r e q u i r e m e n t s f o r t he d e gr e e
of
MASTER OF SCIENCE
in
A e r o s p a c e and Me c h a n i c a l
Engineering
Ap p r o v e d :
Head,
M a j o r De p a r t me n t
(vu ry iiY )
hai rmafhl,
E x a mi n i n g
Commi t t ee
Gr a (Xiace Dean
MONTANA STATE UNIVERSITY
Bozeman, Mont ana
March I 969
I
iii
ACKNOWLEDGMENT
The a u t h o r
for
granting
is
i n d e b t e d t o t h e Mont ana H e a r t A s s o c i a t i o n
financial
assistance
H a r r y W. Townes who d i r e c t e d
A.
Br aun,
M.D.
used i n t h i s
this
to t h i s
research;
who p r o v i d e d t h e c e r v i c a l
research.
project;
and t o
bruit
to
Dr .
Dr .
Har ol d
recordings
i v
TABLE OF CONTENTS
Chapter
I
Page
INTRODUCTION
....................................................................
E a r l y War n i n g & P r e v e n t i o n o f
The E x i s t i n g Pr obl em
. . . .
The Gener al Appr oac h
. . . . .
II
III
IV
V
VI
VII
VIII
Stroke . . .
.............................
.............................
REVIEW OF L I T E R A T U R E ................................................ V
B r u i t Res ear c h
.
R e l a t e d Resear ch
I
I
I
2
3
. ' .....................................................
.........................................................
3
4
NATURE OF THE BRUIT WA V E F O R M..............................
10
A P P R O A C H ......................................................................
13
DATA COLLECTION
15
DATA ANALYSIS
..........................................................
....................................... . . . . ' .
18
Dat a P l o t ............................................................................
S t a t i s t i c a l Analysis
................................................
Zer o C r o s s i n g A n a l y s i s
Spectral Analysis
. . . .......................................
Fr e q u e n c y L i m i t s
................................. -.
.. .
Mean F r e q u e n c y and Band Wi d t h
Test s . . . .
Peak Count
. . ■...................................... ' ......................
F i l t e r and Zer o C r o s s i n g A n a l y s i s ...................
18
18
20
21
22
24
2527
DISCUSSION OF RESULTS
29
.............................
P l o t s ................... ' ....................................■.........................
R e l a t i n g B r u i t C h a r a c t e r i s t i c s t o t he
I n n o c e n t o r S t e n o t i c P o p u l a t i o n ...................
P r o b l e m , A r e a s ■ ..............................................................
40.
51
CONCLUSIONS AND RECOMMENDATIONS
56
. . . . .
29
Summary o f R e s u l t s
................................................ ' 5 6
F u t u r e Work
.........................................................
57
V
Table of
Co n t e n t s
Conti nued
Chapter
page
A P P E N D I X .......................................................................
58
A p p e n d i x A, Revi ew o f S i g n a l T h e o r y
and F o u r i e r T e c h n i q u e s . . . ........................
59
Appendi x B , F o r t r a n
67
P r o g r a m s ......................
A p p e n d i x C, V o l t a g e L i m i t e r
.............................
92
A p p e n d i x D5 P o s s i b l e Mechani sm f o r
t h e B r u i t ....................................................
93
LITERATURE CONSULTED
97
.
......................................
vi
LI ST OF TABLES
Table
I
11
III
Page
Incidence
of B r u it
T Te s t o f Sever al
by A g e ...................................
Bruit
Characteristics
3
.
42
T T e s t s on t h e Number o f M a j o r Peaks
i n t h e B r u i t S p e c t r a ...........................................
45
#
IV
V
T T e s t s on t h e En e r g y - Ba n d Wi d t h o f
t h e B r u i t S p e c t r a .......................................:
.
.
47
T T e s t s on t h e Ener gy- Mean Fr equ enc y
o f t he B r u i t S p e c t r a ...........................................
48
T T e s t s on t h e Zer o C r o s s i n g
Fr e q u e n c y o f t h e B r u i t Sampl es
...................
49
VII
T T e s t A c c u r a c y ..........................................................
50
VIII
Ze r o C r o s s i n g , Ener gy- Mean Fr equ enc y
and Band Wi d t h Av er a ges f o r t he
Two P o p u l a t i o n s S t u d i e d
........................
51
VI
I
vi i
LI ST OF FIGURES
Fi g u r e
1
Page
a) . N o r m a l . P h o n o c a r d i og.ram
b)
C a r o t i d P r e s s u r e Pul s e
c)
Normal E l e c t r o c a r d i o g r a m
d)
Phonocardi ogram w i t h B r u i t
........................
11
..............................................................
19
2
Digital
3
A s s o c i a t e d H i s t o g r a m .............................
19
4
T y p i c a l D i g i t a l C o mp u t a t i o n o f t he
Spec t r um o f a Pure Tone
................................. ;
26
F i r s t and Second H e a r t Sound w i t h
B r u i t ....................................................
30
5
Wavef or m
-
6
Innocent
7
Hi stogram o f Heart
8
H i s t o g r a m o f an I n n o c e n t
9
Ener gy Sp e c t r u m o f an I n n o c e n t
10
Bruit
Sampl e
.
.
......................................
Beat Shown i n
Bruit
5
.- .
3 2.
Sampl e
.
.. .
33
Bruit . . . .
F i r s t and Second H e a r t Sound w i t h
Stenotic Bruit
................................. ■ .
B r u i t ..Sample
35
................................................
36
12
H i s t o g r a m o f H e a r t Beat Shown i n
14
15
Hfstogram of
/•
a .Stenotic
Bruit
. Ener gy Sp e c t r u m o f a S t e n o t i c
S c h e ma t i c o f t h e . V o l t a g e
.
Fig.
.
34
.
Stenotic
.
31
Fig.
11
'13
Innocent
10
.
.. .
Sampl e . . . .
37
38
B r u i t ......
39
L i m i t e r ............
92
*
16
Av e r a g e V e l o c i t y o v e r O b s t r u c t i o n vs
i t s S i z e . ■ . ........................................................................ ...
95
VI i i
ABSTRACT
The p u r p o s e o f t h i s i n v e s t i g a t i o n , a m a t h e m a t i c a l
a n a l y s i s o f the a c o u s t i c a l p r o p e r t i e s o f c e r v i c a l
b r u i t s , was t o d i f f e r e n t i a t e t he a u s c u l t a t o r y s i g n a l s
o f d i s e a s e d neck a r t e r i e s ( s t e n o t i c b r u i t s ) f r o m
s i m i l a r sounding h e a l t h y a r t e r y s i g n a l s ( i n n o c e n t
bruits).
By s t u d y i n g t h e v a r i a t i o n and f i r s t moment o f *the
a c o u s t i c a l s i g n a l d i s t r i b u t i o n c u r v e , no s i g n i f i c a n t
d i f f e r e n c e was f o u n d bet ween t h e s t e n o t i c and
innocent b r u i t .
S i g n i f i c a n t d i f f e r e n c e bet ween t he i n n o c e n t and
s t e n o t i c b r u i t was e v i d e n t f r o m an e x a m i n a t i o n o f t he
zero c r o s s i n g f r e q u e n c y o f the s i g n a l .
The b a n d ­
w i d t h , mean f r e q u e n c y , and number o f peaks i n t h e
e n e r g y s p e c t r u m o f t h e s i g n a l a l s o showed s i g n i f i c a n t
d i f f e r e n c e bet ween t h e i n n o c e n t and s t e n o t i c b r u i t .
The a v e r a g e s t e n o t i c b r u i t s t u d i e d was f o u n d t o have
90% o f i t s e n e r g y c o n t a i n e d i n a f r e q u e n c y band w i d t h
o f 188 Hz. w i t h a c e n t e r f r e q u e n c y o f 131' Hz.
The
f r e q u e n c y band c o n t a i n i n g 90% o f t h e en e r g y o f t h e
a v e r a g e i n n o c e n t b r u i t was 123 Hz. wi de and c e n t e r e d
a t 82 Hz.
C o u n t i n g t h e number o f s p e c t r a l peaks i n
t h e e n e r g y d e n s i t y s p e c t r u m p r o v e d t o be t he most
r e l i a b l e t e s t f o r i d e n t i f y i n g t h e t wo t y p e s o f b r u i t s .
S t e n o s i s was d i a g n o s e d c o r r e c t l y i n 77% t o . 85% o f
t h e p a t i e n t s s t u d i e d u s i n g t h e s p e c t r a l peak c o u n t .
I .
INTRODUCTION
E a r l y War ni ng and P r e v e n t i o n
Many s t r o k e s
o c c u r ! ng i n o l d e r
an o b s t r u c t i o n
or narrowing
artery
to
labeled
leading
stenosis
by p h y s i c i a n s ,
applied
to
this
The E x i s t i n g
abnor mal
people.
its
sound.is
This
existence
type of
this
wh i c h w i l l
allow
innocent
is
bruit,
The me d i c a l
t er m
bruit.
of
differentiation
bruit'.
Also,
to
of stenosis
in futu re
healthy
bruit,
and
frustrating
the e f f i c i e n c y
by a p p l y i n g
bruit
find
to
nor mal ,
an i n n o c e n t
the a c o u s t i c a l
is
in
increase
stenosis
investigation
referred
occur
called
-is " p o s s i b l e t o
met hods t o
purpose o f
the
may a l s o
bruit
of diagnosis
mat hemat i cal
sound).
and second h e a r t
the c e r v i c a l
can make the. d i a g n o s i s
and u n c e r t a i n . - I t
■ V1
to the
Pr obl em
as t h e b r u i t ,
reliability
first
stenosis.
U n f o r t u n a t e l y , the c e r v i c a l
references
o f the a r t e r y .
(listening
sound he ar d bet ween t h e
of
an a i l m e n t
can be d i a g n o s e d and r e p a i r e d
the a c c e s s i b i l i t y
sounds may be an i n d i c a t i o n
of
(carotid)
Such an o b s t r u c t i o n ,
i s made by a u s c u l t a t i o n
An abnor mal
p e o p l e ar e t h e r e s u l t
i n t h e m a j o r neck
the b r a i n .
by s u r g e r y because o f
Diagnosis
of Stroke
and
moder n
signal.
The
a met hod o f a n a l y s i s
o f the s t e n o t i c
any i d e n t i f y i n g
bruit
f r om
characteristics
I
-2wh i c h
hel p
to
The Gener al
explain
recorded
is
made t o s o l v e
sound f r o m t h e
o f whom have h e a l t h y
arteries.
In a l l
s t u d y an a t t e m p t
the
stenotic
spectral
bruit
ar e l a b e l e d .
Appr oac h
An a t t e m p t
the
t he mechani sm o f
analysis,
and s i x
studied,
i s made t o
bruit
neck a r t e r y
arteries
cases
by t h r e e
t h e p r o b l e m by a n a l y z i n g
of
the
techniques
and z e r o c r o s s i n g
seven
o f whom have d i s e a s e d
a bruit
separate
13 p a t i e n t s ,
--
exists.
In t h i s
innocent
bruit
statistical
analysis.
from
analysis,
II.
Bruit
REVIEW OF.THE LITERATURE
Resear ch
A st udy o f o v e r . 4,000 p a t i e n t s
(1966)
revealed
I summar i zes
his
that
the
bruit
type o f
made by B r a u n , et_ a I ,
occurance
variation
varies with
age.
Ta b l e
wh i c h was d i s c o v e r e d
in
study.
TABLE I
INCIDENCE OF BRUIT BY. AGE
Age i n
Year s
It. is
in
the
Bruit
Oc c ur anc e
Percentage
Number
Ex a mi ned
0- 9
20
30
10- 19
14
605
20- 29
6
1082
30 - 39
5
680
40-49
3
...685
50- 59
,3
' 566
60 - 69
4
387
70- 79
3
232
80-89
14
28
apparent
from t h i s
table
that
v e r y young and t h e v e r y o l d .
young can u s u a l l y
because t h e
be assumed t o
incidence
bruits
o c c u r most commonl y
Bruits
occuring
be o f an i n n o c e n t
of a r t e r i a l
di sease at
this
i n t he
nature
age i s
I
-4practically
innocent
nil.
bruit
of a shorter
B r a u n , e^t a_l_,
occuring
duration,
i n 20% o f a l l
appearing
sound t h a n t h e s t e n o t i c
true
for
the
A study
especially
lower
is
in
verify
found
into
The b r u i t
help
1954)
bruit.
( 1 964 )
bruit
while
found t h a t ,
originates
the s t e n o t i c
in t h i s
injected
is.used
type of
study,
p r o c e d u r e make i t
but
impracti­
may be i n n o c e n t .
has been done w h i c h woul d
research
bet ween t h e
nor.Rennie's
characteristics
stenosis
stenotic
studies
since
and i n n o c e n t
wer e c o n c l u s i v e
o f the
innocent
or
determine
1954,
bruit.
in
stenotic
must be f ound t o e n a b l e s i m p l e r
Re s e a r c h .
and t h e
to
and l i t t l e
In or der to
bruits
bruit
t h e neck o v e r t h e c a r o t i d
met hods o f d i a g n o s i s .
Related
hol d
people.
p e o p l e whose b r u i t s
the.characteristics
Some
necessarily
an a r t e r i o g r a m ,
of t h i s
heart
with
Braun's
identifying
of
is
has been i d e n t i f i e d
to d i f f e r e n t i a t e
Neither
does n o t
t he
peopl e
the f i r s t
o f an opaque s o l u t i o n
of a stenosis
and t r o u b l e
to
innocent
side,
t he b l o o d s t r e a m ,
use on h e a l t h y
(Fisher,
t he
found t h a t
young h e a l t h y
and McDowel l
near t he mi ddl e
the e x i s t a n c e
for
This
right
picture
also
closer
in old er
Ejrup
t h e neck on t h e
the discomfort
cal
bru.it
by R e n n i e ,
An X - r a y
locally
bruit.
i n young a d u l t s ,
normally
artery.
innocent
(1966)
and u n d e r s t a n d t h e o r i g i n
di agnosi s, o f s t e n o s i s
it
is
of
necessary to
-5search
related
topics
for
pertinent
i m p o r t a n t , because o f
their
four
the
such t o p i c s :
f l o w o f blood
and 4)
I)
of
relation
structure
in a r t e r i e s ,
t he d i a g n o s i s
close
3)
ment
vascular
is
lining
known t h a t
to
the a r t e r i e s ,
active
He e x p l a i n s
how h y d r a u l i c
form v a l v e s ,
blood v e s s e l s ,
in
forces
cushions,
besides
gr owi ng
during
( Si mpson and Nakagawa, 1960)
Bl ood
is
is
pulsatile,
surge
in
pressure,
t he boundary l a y e r ,
changes
along the axi s
gradient.
vessel
filtration
across
The r ed b l o o d c e l l s
o f a vessel
giving
1960)
of v a r i a t i o n
is
losing
o l d age.
very d i f f i c u l t
ter ms.
Bl ood f l o w
d i a m e t e r changes d u r i n g
the vessel
and t h e v i s c o s i t y
( Mc Do n a l d ,
latitude
vessel
any b u t q u a l i t a t i v e
of
It
is
i n both
wall
t he b l o o d
a n o m a l o u s l y f r o m moment t o mo ment . "
J o h n s o n , 1 96 2)
wi d e
the
flow
with
It
childhood,
( Rodbar d , 1 95 6)
compl ex medi a and i t s
"...
upon t h e
and s t e n o s i s .
elasticity
in
h e a r t mu r mu r s ,
can a c t
their
exactly,
the
and has shown by e x p e r i ­
and become t w i s t e d
to describe
2)
ar e
bl ood vessel
t end t o e l o n g a t e
a very
bruit,
h e a r t mur mur .
research.
(1956,1957,1959)
of
Especially
to the
t h e mechani sm o f
Rodbar d has been p a r t i c u l a r l y
and b l o o d f l o w
information.
each
disturbs
probably
( Rodbar d and
have a t e n d e n c y t o gr oup
rise
to a r a d i a l
apparent t h a t
the
bl ood f l o w
viscosity
there
is
a
and t he
structure.
Br uns
advances
a general
theory
of
t he causes o f murmur
-6(1959)
closely
wh i c h
also
related.
evidence,
applicable
to
bruits
Based on t h e o r e t i c a l
he d i s c o u n t s
turbulence
vortex
is
as n o i s e
the
in
high c a r d i a c
with
bruits
vortex
output
shedding
all
under t he
the form of
pa p e r c l i p
He showed t h a t
the vessel
the
g e o me t r y and t h e
be made s i m i l a r
Br uns
to
as s t e n o s i s
that
ar e a s s o c i a t e d
and o r i f i c e s
noise
rate
of
can cause
conditions.
by i n t r o d u c i n g
frequency of
t he
Anemi a o r o t h e r causes
appropriate
wire
that
cause o f
these c o n d i t i o n s
p r o d u c e d mur mur s a r t i f i c i a l l y
and
and a s s e r t s
ar e t h e more l i k e l y
as w e l l
and mu r mu r s ;
and e x p e r i m e n t a l
arteries
n o i s e we he ar as mur mur s o r b r u i t s .
of
t h e y ar e so
i mport ance of c a v i t a t i o n
generators
shedding or eddies
since
obstructions
into
in
rubber tubing.
pr odu c ed
flow,
Br uns
is
related
to
and t h e n o i s e can
o f mur mur s.
has shown t h a t
for
large
diameter o r i f i c e s
t u b e s , t h e f r e q u e n c y o f sound p r o d u c e d w i l l
in
be a p p r o x i m a t e d
by
v e l o c i t y o f f l u i d f l o w _______
6 . x - wi d t h o f o r i f i c e s h o u l d e r
FREQUENCY.
wher e t h e w i d t h
the d i f f e r e n c e
v e r y s ma l l
of the o r i f i c e
FREQUENCY
is
bet ween t h e t u b e and o r i f i c e
diameter o r i f i c e s ,
t on e p r o d u c e d
shoulder
by v o r t e x
h o we v e r ,
equal
one-half
diameters.
For
t he f r e q u e n c y o f t he
sheddi ng
is
appr oxi mat ed
' 0.6 x v e l o c i t y
of
flow
o r i f i c e di ameter.
to
by
i
-7" T h u s , as a c o n s t r i c t i o n
or s t e n o s i s
diameter
decreases)
one s h o u l d
at f i r s t
high,
become l o w e r and t h e n
(Bruns,
will
Jacobs,
Hor okoshi
an i n s t r u m e n t wh i c h
electrocardiogram
grossly
abnor mal
uses
signal
subject of
to separate
ones w i t h
frequency,
increase
once m o r e . "
f r e q u e n c y component s
hi gh
and a z e r o c r o s s i n g
on t h e number o f
amplifier
detector
t i me s
and s t o p p e d
gram s i g n a l .
a o r t i c - valves
a given
brass
f r o m s heep.
spectrum c h a r a c t e r i s t i c ,
p r o d u c e d a nor mal
boost
the
t h e l o w-
the f i l t e r
amplified
The c o u n t i n g
They f o u n d t h a t
stenosed
frequency spectra.
rate,
that
the
They
noise
but a d e f i n i t e
correlation
o f t he sheep h e a r t w i t h
t h e model
characteristic
Thi s
a b n o r m a l s based
pr oduced a s i m i l a r
while
from
on e x p e r i m e n t a l l y
h e a r t and v a l v e ,
orifice
plus the
from t he e l e c t r o c a r d i o ­
r an t e s t s
flow
hearts
t h e zer o' a x i s .
n o t be f o u n d . . A c o n c r e t e model
a triangular
have d e v i s e d
94% c e r t a i n t y .
beat t h a t
by t r i g g e r i n g
increases with
in recent
the phonocardiogram si gn al
identify
have c h a r a c t e r i s t i c
found,for
intensity
valves
to
crosses
These men a l s o
s t e nosed a o r t i c
nor mal
syst em t o
of
pe r h e a r t
phonocardiogram ampl i t ud e
started
study
( 1 968 )
approximately
level
could
basic
the phonocardi ogr am s i g n a l
uses a f i l t e r
also
the
active
and P e t r o v i c k
instrument
is
that
(orifice
1959)
Murmur s have been t h e
years.
find
becomes g r e a t e r
with
spect r um.
stenosed
no o b s t r u c t i o n
Jacobs,
et a l ,
-8deduced f r o m t h e i r
the s p e c t r a l
analysis
de gr e e o f s t e n o s i s
ascertain
they
did
by t h e
the
of t h i s
signals,
induced
conclude t h a t
t h e changes wh i c h o c c u r e d
n o i s e wer e r e l a t e d
in the
valve.
responsible
the noise
is
while
may n o t
unabl e to
the f r e q u e n c y changes,
not det ermi ned
of
uniquely
t h e s yst em
The z e r o c r o s s i n g
effective
separating
in
enough t o
in
t o the
as a w h o l e .
be s e n s i t i v e
bet ween two s i m i l a r
Wh i l e
for
b u t by t h e c o n d i t i o n s
conditions)
study,
that
of valve
paramet er s
stenosis
arterial
studies
--
the
innocent
Division
of
the Th i okol
analysis
grossly
detect
signals
( h e a r t and
different
differences
and s t e n o t i c
bruit.
The H u m e t r i c s
tion
d e v e l o p e d a more s o p h i s t i c a t e d
Ph o n oCar di oSc an
(Durin,
test, p r o j e c t s .
Specialized
not on l y
detects
the
ejt al_,
detector
1 965)
anal og
Chemi cal ' C o r p o r a ­
for
called
use i n
digital
the
school
circuitry
presence o f c o n g e n i t a l
heart
heart
whi ch
defects,
but
also
h e l p s t o i d e n t i f y t h e p a r t i c u l a r t y p e o f d e f e c t , was
.
devel oped. - , . The i n s t r u m e n t used s p e c t r a l a n a l y s i s da t a
acquired
f r o m known d i s e a s e d h e a r t s
and d i a g n o s i s .
recorded
The r a t h e r
simultaneously
elaborate
t h e sounds
ph o n e s ,
the e l e c t r o c a r d i o g r a m
signal,
and a v o i c e
requires
t wo i n p u t s ;
as a b a s i s
c o mp a r i s o n
da t a a c q u i s i t i o n
syst em
from f o u r . c h e s t m i c r o ­
s i g n a l , the
commen t ar y .
for
respiratory
The i n s t r u m e n t
itself
phase
only
an e l e c t r o c a r d i o g r a m and a c h e s t m i c r o -
-.9phone i n p u t .
regions
The mi c r o p h o n e
pl acement .
t h r e e mi nut es
toward
ar e v e r y
defects.
will
moved t o
and 10 t o 30 h e a r t c y c l e s
mi c r o p h o n e
taken
is
identifying
similar
It
reveal
and i n n o c e n t
instrument.
is
to
those
a significant
A similar
stenotic
hoped t h a t
bruit
ar e exami ned
The who l e t e s t i n g
per p a t i e n t .
each o f
process
since
sounds o r i g i n a t i n g
difference
whi ch c oul d
for
each
o n l y takes
ap p r o a c h c o u l d
bruits
spectral
t he f o u r
analysis
bruit
in
sounds
heart
of the
bet ween t h e
be d e t e c t e d
be
bruit
stenotic
by such an
III.
. Ausculation
to
tell
the
ability
has been empl oyed f o r many y e a r s
condition
of
and l i m i t a t i o n s
have l e d t o
magnet i c
to
NATURE OF THE BRUIT WAVEFORM
recording
tapes.
This
the
heart
record of
as a p h o n o c a r d i o g r a m .
gram ap p e a r s
as i n
sounds
ar e q u i t e
fairly
silent.
major a r t e r i e s
listening
during
h e a r t , but v a r i a t i o n
i mposed by t h e
the
Fig.
la.
hearing
the h e a r t
of
sound i s
t he nor mal
The r e m a i n d e r o f
hearing
charts
As s h o wn , t he f i r s t
These t wo sounds a r e
in
threshold
sounds on s t r i p
One c y c l e
distinct.
by d o c t o r s
referred
phonocardi
and second
the s i g n a l
transmitted
examination
for
such as o v e r t h e
cervical
carotid
is
through
and a s i m i l a r wav e f or m can be o b t a i n e d
o v e r an a r t e r y
and
t he
by
artery
bruits.
The f i r s t h e a r t sound o c c u r s w i t h t h e o n s e t o f
ven tricula r contraction.
B e f o r e t he v e n t r i c l e s
c o n t r a c t , t h e m i t r a l and t r i c u s p i d v a l v e s c l o s e
by a t r i a l c o n t r a c t i o n .
The c l o s u r e o f t h e s e
v a l v e s , is- t h e p r i n c i p l e s o u r c e o f s ound, a l t h o u g h
an a d d i t i o n a l component may come f r o m v i b r a t i o n s
o f t h e chamber- w a l l s . . . The second h e a r t sound i s
g e n e r a t e d by c l o s u r e o f t h e a o r t i c , and p u l mo n a r y
v a l v e s : .'. The i n t e n s i t y o f t h e sound i s depen den t
on t h e r a p i d i t y w i t h wh i c h t h e v a l u e c l o s e s and
t h e c o n d i t i o n o f t h e v a l v e . (Jacobs- , e_t aj_, 1 9 68)
It
obtained
sensing
lb.
is
instructive
t o exami ne s i m u l t a n e o u s
f r o m an e l e c t r o c a r d i o g r a p h
d e v i c e on t h e c a r o t i d
and Tc.
The t wo h e a r t
artery
sounds
in
signals
and f r o m a p r e s s u r e
such as shown i n
Fig.,la.
mar k t h e
Figs,
beginning
and e n d i n g
the c a r o t i d
pulse,
of
Fig.
systole
(contraction)
as seen f r om
lb.
The f i r s t sound s t a r t s a f t e r t h e QRS wave o f t he
e l e c t r o c a r d i o g r a p h and b e f o r e t he o n s e t o f t h e
a n a c r o t i c l i mb o f the c a r o t i d p u l s e .
The second
sound b e g i n s j u s t a f t e r t h e end o f t h e T- wave o f
t h e e l e c t r o c a r d i o g r a m and j u s t b e f o r e t h e
d i a c r o t i c notch o f the c a r o t i d p u l s a t i o n .
( Gr e e n ,
1 957 )
SECOND
FIRST
SOUND
ANACROTIC
DIACROTIC
NOTCH
LIMB
ORS
f\
T
-------------- / " " V
BRUIT
D-
,V f ’ 'I
Figure
Note:
I .
a)
b)
c)
d)
These s k e t c h e s
Norma I p h o n o c a r d i o g r a m
C a r o t i d p r e s s u r e p u l se
Norma I e l e c t r o c a r d i o g r a m
Phonocardi ogram w i t h b r u i t .
ar e t a k e n
f r o m Green
(1957).
t
-12The same r e l a t i o n s h i p s
shown i n
Fig.
I should
bet ween t h e p h y s i o l o g i c a l
hold t r u e
o f t h e sound o v e r t h e
carotid
a p p e a r as s k e t c h e d
Fig.
t h e wav e f or m w i l l
noise
bei ng
in
be t h a t
observed
and i n
appear s i m i l a r
both
Ia.,
persons.
i n a nor mal
b u t wher e b r u i t
sketched
in
first
Fig.
Id.,
that
of
position
Fig.
the
Id.
bruit
on t h e a r t e r y
up arid down s t r e a m f r o m t h e
but
present
an a d d i t i o n a l
through
the
t h e neck c o u l d
be caused by a mur mur .
ap p e a r s
with
person w i l l
and second sound.
some cases- t h e sound o b s e r v e d a t
to
The d i a g r a m
is
sounds may be t r a n s m i t t e d
But u n l i k e mur mur sounds
particular
artery
bet ween t h e
Murmur s o r o t h e r
artery
in a l l
signals
loudest
at a
a diminishing
location
of
t he
intensity
bruit.
I V.
Hypothesizing
bruit
bel ong
study
has as i t s
objective
innocent
the
When t h e
more p r a c t i c a l
bruit
families
of
stenotic
of waveforms, t h i s
of
the
differentiate
differences
met hod
and t h e
identification
w h i c h may be used t o
t wo w a v e f o r m s .
reliable,
the
t o t wo d i f f e r e n t
characteristics
the
that
APPROACH
ar e
bet ween
known a
diagnosing
stenosis
can
be d e v i s e d .
Since onl y the c h a r a c t e r i s t i c s
exami ned
the
is
natural
to
from the
analysis.
t h e wa v e f o r m i s
utilization
comput er .
of
such as. t h e o p e n i n g
and c l o s i n g
record
because i t
speed and f l e x i b i l i t y
rate
is
fast
wh i c h can be f o r m u l a t e d ,
record
allows
of
A c o mp u t e r can be pr ogr ammed t o n e a r l y
any t y p e o f a n a l y s i s
sampl i ng
a r e b e i ng
The most u s e a b l e t ype' o f
a digital
the g r e a t
bruit
e x c l u d e the. o t h e r component s o f
phonocardiogram s i g n a l ,
sounds,
of
it
o f the
t he
the d i g i t a l
duplicate
provided
enough t o c o m p l e t e l y d e s c r i b e
t he
the
signal.
. Wo r k i n g w i t h
gr oup o f s t e n o t i c
find
criteria
by f a m i l y .
type
t h e sound r e c o r d i n g s
t a k e n f r o m a l ar ge,
and i n n o c e n t
the o b j e c t i v e
whi ch w i l l
Previous
bruits,
enabl e t he
investigations
have been s u c c e s s f u l
using
separation
of
is
to
the b r u i t s
o f t h e wa v e f o r m a n a l y s i s
one o f
three types
of
signal
-14analysis:
on t h e
I)
statistical
random n o i s e
wh i c h
aI , I 968);
met hods
This
3)
used most
t y p e s i g n a l ; 2)
has p r o v e d t o
speech a n a l y s i s
analysis,
be a s i m p l e ,
(Scarr,
1968)
spectral
as used i n t h e
zero c r o s s i n g
highly
using
three
(Jacobs,
ejt
Fourier transform
d e v e l o p me n t o f t h e
all
analysis,
a c c u r a t e met hod o f
and mur mur a n a l y s i s
analysis
investigation, includes
successfully
of
PhonoCar di oScan.
t h e s e met hods o f
analysis.
The s t a t i s t i c a l
tion
o f the f i r s t
met hods
used her e
include
moment and t h e v a r i a t i o n
the
o f the
determina­
bruit
hi st ogram.
A zero c r o s s i n g
spectral
analysis,
analysis,
usually
filters
whose o u t p u t s
But f o r
this
bruit
signal
study,
includes
ar e a l l
is
actually
a series
analyzed
the zero c r o s s i n g s
for
of
a f or m o f
br oad band
zero c r o s s i n g s .
of the
unfiltered
wer e c o u n t e d .
A spectral
analysis
spectrum ob t a i n e d
record.
wh i c h
was made o f
from a F o u r i e r
Recent advances
t he e n e r g y d e n s i t y
transform of
i n c o mp u t i n g
t r a n s f o r m on a d i g i t a l
record f e a s i b l e
t r a n s f o r m code,
efficient
a very
transform c o e ffic ie n t s .
science
using
the si gnal
have made t h i s
the f a s t
met hod o f o b t a i n i n g
Fourier
the
i
V.
The r e c o r d i n g s
wer e made a t
Harol d
of a r t e r i a l
noise
used i n
t h e Wes t er n Mont ana C l i n i c
Br aun u s i n g
a Sanbor n s u r f a c e
over the b r u i t
silicon
DATA COLLECTION
a Crown Model
lubricated,
neck a r t e r y
one-fourth
in Missoula
Model
of
b a c k i n g was used f o r
Duri ng
recording
process,
let
it
a f ew s e c o n d s .
used f o r
voice
a r t e r i aI
noise.
out,
o f the
controller,a
digital
Model
specifically
di g i t aI
circuitry
at
a rate
the a n a l o g - t o - d i g i t a l
IBM 1620 c o mp u t e r and c a r d
a fairly
obviously
wer e i n s t r u c t e d
without
"clean"
punch.
s p o t on t h e t a p e ,
obliterated
by s k i n
protect
for
r e c o r d t he
usi ng
a
a Model
limiter
the a n a l o g - t o -
sampl e
o f 4, 000' sampl es
e q u i p me n t
to take
r e c o r d i n g was
and a v o l t a g e
The f i r s t
a 1.5
breathing
EECO 765 m u l t i p l e x e r ,
from ov e r l o a d .
202
recordings.
sampl es wer e t a k e n
(See A p p e n d i x C) t o
wer e made d i g i t i z i n g
with
the
two-track
EECO 761 a n a l o g - t o - d i g i t a T c o n v e r t e r ,
built
Sc o t c h
t ape w i t h
c o m me n t a r y ; t h e o t h e r was used t o
From the- r e c o r d i n g s ,
digital
patients
and r e ma i n s t i l l
One c ha nne l
5 7 2 - M', p l a c e d
i nch magnet i c
polyester
a breath,
by Dr .
the p a t i e n t s .
millimeter
the
research
SS800-S t a p e r e c o r d e r and
c o n t a c t mi cr ophone,
in the
this
records
p e r second
coupled d i r e c t l y
to the
The s a mp l i n g was. done a t
wher e t h e s i g n a l
wasn't '
n o i s e made by mi c r o p h o n e
slippage
o r by v o i c e o r b r e a t h i n g
sampl e r e c o r d s
of
hand s e l e c t e d
h e a r t sounds.
in
Fig.
Id.
Fairly
long
t w o - s e c o n d o r t h r e e - s e c o n d ' d u r a t i o n were
t a k e n and punched d i r e c t l y
t hen
interference.
on c a r d s .
by r e mo v i n g
On l y t h e
r e ma i n s
in
the
portion
the
The b r u i t
r e c o r d was
unwant ed f i r s t
of
the si gn al
and second
labeled
bruit
record.
The r e m a i n d e r o f t h e s a m p l i n g was done on t h e H e w l e t t Pac k ar d 2116A c o mp u t e r u t i l i z i n g
process
and a f a s t e r
second.
A trigger
selection
nix
of
digitizing
records
A trigger
a one-kilohertz
channel
rate
was e s t a b l i s h e d
signal
with
from t he
portion
the t ape.
from t h i s
the a r t e r i a l
sound on t h e d i s p l a y
The p r o p e r t i m e
controller,
signal,
thus
to the b e g i n n i n g
initiating
type
I A4 p l u g - i n
output
--
screen,
Triggering
the
a t t h e wavef or m o f
time
d e l a y s wer e
and end o f t h e b r u i t
p a r t o f t he
d e l a y s wer e t he n s e t on t h e d i g i t a l
at
the c o r r e c t
r e c o r d e r was s t a r t e d
t he d i g i t i z i n g
pr ogr am a c c e p t e d t wo l i n e s
after
and l o o k i n g
t h e t a p e was p o s i t i o n e d
and t h e t a p e
hand
was r e c o r d e d on t h e v o i c e
of
signal
the
u s i n g a t y p e '549 T e k t r o ­
scope c a l i b r a t i o n
oscilloscope
signal .
I O 9OOO sampl es per
a four-channel
s q u a r e wave - -
near a c l ea n
calculated
--
selection
and d e l a y s y s t em wh i c h e l i m i n a t e d
storage o sci llos co pe
unit.
an i mp r o v e d r e c o r d
process.
of d e s c rip tio n
for
trigger
each sampl e;
The H e w l e t t - P a c k a r d
from the
each sampl e and punched t h e d e s c r i p t i o n
and
teletype
digital
I
-17r e c o r d on p a p e r t a p e .
Hewlett-Packard
punched on c a r d s
Sy s t e ms ,
t i me
and t h e
for
IBM c o mp u t e r s
later
of
the
analysis
133 sampl es
different
phase o f
on t h e S c i e n t i f i c
be
Data
individuals;
project.
At t h a t
of
seven o f whom had i n n o c e n t
o f whom had s t e n o t i c
bruits.
this
c a r d punch c u t
had been g a t h e r e d f r o m a t o t a l
a b o u t 55% ar e f r o m i n n o c e n t
stenotic
bet ween t he
al l owed t he data to
IBM 1620 and i t s
the data c o l l e c t i o n
and s i x
interface
Si gma 7 c o mp u t e r .
The r emoval
short
A high-speed
bruits.
bruits.
Of t h e t o t a l
13
bruits,
s a mp l e s ,
The r e m a i n d e r ar e f r o m
I
VI.
DATA ANALYSIS
Dat a P l o t
Partly
process
ities
as a c hec k on t he a n a l o g
and p a r t l y
as a v i s u a l
or d i f f e r e n c e s
digital
Usi ng t h e
plotter,
i n a sampl e was p l o t t e d
that
the t i me a x i s . o f
the p l o t s
r e c o r d was 1 , 0 0 0 m i l l i v o l t s .
exampl es o f
these p l o t s . )
Statistical
Analysis
t h e wav e f or ms
characteristic
the s t e n o t i c
in
bruit
t han
histogram frequency
in
is
different
length.
5,
bruit
6,
so
The
i n each
10 and 11 f o r
family
have a
f r o m t h e wav ef or ms o f
t h e d i f f e r e n c e may be more e v i d e n t
t h e wa v e f o r ms - t h e m s e l v e s .
curve,
had any d i r e c t
and w h i c h was a m p l i t u d e
normalized.
the s i g n a l
by a m p l i t u d e
brackets,
t i me s
the s i gn a l
that
and
t h e maximum a m p l i t u d e
(See F i g s .
distribution
wav e f or m wh i c h
was made o f
each d a t a p o i n t
was o f c o n s t a n t
innocent
family,
similar­
The t i me Was s c a l e d
the
shape t h a t
the hi st ograms
digital
of
a plot
IBM 1620 c o mp u t e r
time.
so t h a t
s a mp l i n g
outstanding
t h e ma g n i t u d e o f
against
a m p l i t u d e was n o r m a l i z e d
If
c hec k f o r
bet ween t h e f a m i l i e s ,
each sampl ed w a v e f o r m .
associated
to d i g i t a l
was d e v e l o p e d f r om t h e
current
It
An
bias
removed
was made by s o r t i n g
counting
t h e number of .
falls
within
each b r a c k e t
and p l o t t i n g
the f r e q u e n c y of oc c u r r e n c e
versus
the a mp l i t u d e .
For e x a mp l e .
-19t he wa v e f o r m shown i n
different
points
in
time,
r e n c e a t +1 i s p l o t t e d
/
etc.
The b r u i t s i g n a l
m illivolts
Fig.
2 has a ma g n i t u d e o f +1 a t
therefore
and each d a t a
p o i n t was r e c o r d e d
Ch o os i ng a b r a c k e t w i d t h
a 100 p o i n t
histogram.
information
the c o n f u s i o n
Figure
3.
Thi s
of
t o show any d i f f e r e n c e s
Wavef or m
3)
as t h r e e ,
to the
t o +1 , 0 0 0
nearest
20 m i l l i v o l t s
bracket width
o f a more d e t a i l e d ,
Digital
(Fig.
r anged f r o m - 1 , 0 0 0
m illivolt.
enough
t he f r e q u e n c y o f o c c u r ­
on t h e h i s t o g r a m
ma g n i t u d e
three
smaller
F i g u r e 4.
seems t o
that
gives
preserve
exist without
bracket,
histogram.
Associated
Hi stogram
-20The common met hod f o r
a histogram,
indicating
the c h a r a c t e r i s t i c s
or f r e que nc y d i s t r i b u t i o n
variation
and s t a n d a r d
variation
is
simply
the
deviation
of
curve,
is
to f i n d
the d i s t r i b u t i o n .
second moment o f
of
t he
The
t he h i s t o g r a m a b o u t
the average a m p l i t u d e ;
Variation
wher e f .
is
and N i s
the
=
N .
o
Z f. (a.-aJ^/N,
i =1
1 . 1
the f r e que ncy of o c c u r r e n c e ,
number o f
The mean a m p l i t u d e ,
a,
N
Z
i =I
a . f./N.
1 1
The s t a n d a r d
deviation
a =
variation.
positive
of
in
histogram.
'
is
given
by t h e s qu ar e r o o t
and s t a n d a r d
the f i r s t
o f t he
deviation
a r e al ways
moment o f
the
t he h i s t o g r a m w i l l
h i s t o g r a m,
a plot
become e v i d e n t .
statistical
was made o f t h e
and an a t t e m p t was. made t o f i n d
characteristic
the
by
e x a mi n i n g t h e s e
each h i s t o g r a m ,
each s a mp l e ,
ting
to
the ampl i t ud e,
N
Z f . ( a . -a)/N ,
i =1 1
1
symmet r y o f
In a d d i t i o n
or amplitudes
given
By t a k i n g
moment =
any l a c k o f
tics
is
The v a r i a t i o n
number s.
First
points
a^ is
characteris­
histogram of
some d i f f e r e n t i a ­
visually.
Zer o C r o s s i n g A n a l y s i s
The z e r o c r o s s i n g
analysis
used her e c o n s i s t e d
of counting
-21 the
number o f
t i mes t h a t
average v a l u e .
was a d j u s t e d
signal
passed t h r o u g h
The a v e r a g e m a g n i t u d e f o r
to z e r o .
by t h e p e r i o d
a bruit
The number o f c r o s s i n g s
o f t h e sampl e t o
zero c r o s s i n g .
It
each b r u i t
was t h i s
give
its
record
was d i v i d e d
a pseudo f r e q u e n c y o f
pseudo f r e q u e n c y
t h a t was exami ned
1X
to
see i f
the
innocent
stenotic.
This
signal , in
effect,
component s
of
Spectral
type of
the b r u i t
zero c r o s s i n g
disregards
the b r u i t
Fourier
signal
functions
energy d e n s i t y
This
description
in
c o mp u t i n g
an e f f i c i e n t
digital
f r o m the.
o f an u n f i l t e r e d
low-level
can be r e p r e s e n t e d
hi gher frequency
o r as a s e r i e s
of
a wav e f or m such as
as a s e r i e s
s p e c t r u m can t he n be o b t a i n e d
have p r o v i d e d
records.
tool
The f a s t
the d i s c r e t e
in
signal
Fourier
analysis
and i n
t r a n s f o r m changes t h e
filter
discrete
a review of
Fourier
analysis
transform
is
transform,
o f smal l ,
an a l g o r i t h m
transform c o e f f ic ie n t s
steps.
simulation.
ti me
Fourier
Recent advances
the f a s t
Fourier
The
a v er y compl et e
characteristics.
and p o w e r f u l
s i n e and
f r o m t he
(See A p p e n d i x A f o r
energy spectrum p r o v i d e s
science
of
compl ex e x p o n e n t i a l s .
a mi ni mum number o f c o m p u t a t i o n a l
spectral
test
transform techniques,
o f the s i gn a l
w h i c h comput es
with
the
significantly
signal.
transform c o e f f ic ie n t s .
theory.)
differed
Analysis
Us i ng
cosine
bruit
series
It
is
useful
The f a s t
in
Fourier
representation
of
a
-22wav e f or m t o a d i s c r e t e
representation
analysis,
evident
in
in
the
certain
spectrum,
the f r equency
f r o m two b r u i t
f r e q u e n c y d o ma i n ,
do mai n.
frequency constructed
in
series.
By e x a mi n i n g t he
called
spectral
c h a r a c t e r ! ' s i t c s may ap p e a r wh i c h ar e no t
t he t i me
energy d e n s i t y
frequency
is
a function
from the
do mai n .
sampl es
The p e r i o d o g r a m, a f o r m o f t he
of amplitude
representation
Exampl es o f
a r e shown i n
of
versus
t h e wavef or m
p e r i o d o g r a ms
constructed
the r e s u l t s
(Figs.
9 and
t he s a mp l i n g
period
has
14).
Neither
t he sampl i ng
been h e l d c o n s t a n t
rate
in t h i s
nor
study,
so
different
sized periodoQ
grams
have been
generated
Ther e a r e s e v e r a l
whose s i z e s
ways t o o b t a i n
simplified
p e r i o d o g r a m.
information
of
t h e p e r i o d o g r a m wer e d e v i s e d and t h r e e were used i n an
Frequency L i m i t s
In using
necessary
the
innocent
signal
four
tests
from the s t e n o t i c
■
discrete
t o assume t h a t
Ol de r sampl i ng t h e o r y
no f r e q u e n c i e s
the
study
whi c h
available
to d i f f e r e n t i a t e
In t h i s
to 2
is
attempt
from t he
Ip
r ange f r o m 2
finite
t he
Fourier
bruit
signal
transform
is
it
band l i m i t e d .
( C o c h r a n , et. aj_,. 1 967 )' d i c t a t e s
h i g h e r t h a n to, g i v e n
is
that
by
to = i r / A t ,
be p r e s e n t
in the
s i g n a l , wher e At
is
t h e t i me
bet ween sampl es
-23On t h e o t h e r
Doughert y
hand, a t h e o r e t i c a l
(1966)
using
ideal
gence o f
the
obtained
o n l y when t h e r e
content
of
numerically
the
signal
exampl es
calculated
is
has shown t h a t
Fourier
an u p p e r
given
s t u d y by Lees and
lim it
conver­
transform
is
of the frequency
by
9
This
co = O . l i r / A t
radians/second,
f
cycles/second.
= 0.05/At
lim it
theory
is
one-tenth
previously
used.
Dat a used i n t h i s
1 0 , 0 0 0 sampl es
giving
that
given
investigation
up p e r f r e q u e n c y
of
rate
p e r second a t
and 200 c y c l e s
c o mp u t e r code f o r
t o an i n t e g r a l
points
in
l ower ed the
frequency
t he f a s t
the
points
in
transform
To a d j u s t
sampl i ng
rate
by
the f a s t e r
rate.
The
used r e q u i r e d
each sampl e r e c o r d
an i n t e r p o l a t i o n
effective
as s u g g e s t e d
slower
at
p e r second
p e r second a t
Fourier
power o f t wo .
each r e c o r d
limits
500 c y c l e s
number o f d a t a
s a mp l i n g
was d i g i t i z e d - b o t h
p e r second and a t 4 , 0 0 0 sampl es
allowable
the
by c o n v e n t i o n a l
(See A p p e n d i x A)
Lees and D o u g h e r t y ,
that
or
be equal
t he number o f t o t a l
scheme was used whi c h
and w i t h
it
t h e upper
lim it.
The l o w e r
by d i s c r e t e
lim it
finite
of
t h e f r e q u e n c y whi c h w i l l
F o u r i e r met hods
Wq = 2 tt/ T r a d i a n s
p e r sec o nd:
is
given
by
be d e t e c t e d
-24Be i n g
interested
only
in the
sampl ed o v e r t h e e n t i r e
any f r e q u e n c i e s
of
the b r u i t
and i s
t h e Wq l i m i t
at
limitations
So,
in t h i s
60 Hz.
this
and 200 Hz.
it
with
can be assumed t h a t
the l onger
in
be i g n o r e d
and r e c o r d e r
(depending
wh i c h
the
is
f requency bias
Any f r e q u e n c y component s
l e s s must
is
period of
the b r u i t
show up as a z e r o
analysis.
study
and h a v i n g
are not uni que c h a r a c t e r i s t i c s
present
will
in a m p l i f i e r
in general,
60 Hz.
or
characteristics
period,
l o we r t han w
Any f r e q u e n c y
ignored
appearing
bruit
b u t ar e a s s o c i a t e d
heart cycle.
l ower than
bruit
because o f
response
limited
in
this
to frequenci es
on t h e s a m p l i n g
t he
range.
bet ween
rate).
Mean F r e q u e n c y and Band Wi d t h T e s t s
If
t h e t wo b r u i t
families
f r e q u e n c y band and t h e
different
for
by l o o k i n g
band o f
at
each f a m i l y ,
the
half.
then
the d i s t i n c t i o n
f r e q u e n c y wh i c h
divides
the
above t h e mean and h a l f
energy-band wi dth
is
signal
90% en er g y
is
the s i g n a l
is
present
bel ow t h e mean.
d e f i n e d her e t o
be t h a t
ar e
may show up
The e n e r g y - me a n f r e q u e n c y
H a l f o f the energy i n
frequencies
o f one
f r e q u e n c y o r t h e band w i d t h
e n er g y - me an f r e q u e n c y and t h e
each s p e c t r u m .
her e t o mean t h a t
in
center
ar e composed s t r o n g l y
defined
en er g y
in
The 90%
f r equency band,
c e n t e r e d on t h e mean e n e r g y f r e q u e n c y , enc omp as s i ng 9 0% o f
t he energy o f
find
this
the s i g n a l .
A c o mp u t e r
en e r g y - me a n and e n e r g y - b a n d .
pr ogr am was w r i t t e n
to
I
-25Peak Count
The f a s t
Fourier
transform
generates
ar e p o i n t s
transform
coefficients
as t h e r e
When t h i s
is
to
converted
including
points
i n t h e wa v e f o r m r e c o r d .
it
the z e r o t h
as many p o i n t s
came,
as ar e
t er m Where N i s
ar e some v e r y
is' n o t e d f r o m e x a m i n i n g
f r e q u e n c y component s
50 s p e c t r a l
confined
to t he maj or
magni t ude
is
greater
gives
records
lengthy
these
dr ops
the f i r s t
This
in the d i g i t a l
and s i n c e t h e d i g i t a l
t o 4096 t h e r e
spectra
in
the
10% o f t h a t
simplification
reduces
sampl es
t h e c o mp u t i n g
of
r ange
that
in
size
f r o m 256
to a n a l y z e .
It •
t h e ma g n i t u d e o f
o f ma g n i t u d e
if
in
interest
is
say t h o s e whose
of the g r e a t e s t
peak,
need be exami ne d.
Thi s
t i me c o n s i d e r a b l y .
t he e n e r g y s p e c t r u m compar es t he
by the. number o f d i f f e r e n t
wh i c h make up t h e w a v e f o r m , .
up as a peak i n t h e
a r e N/ 2
r e c o r d f r o m whi c h
spect rum,
50 s p e c t r u m component s
test
there
Therefore
onl y the f i r s t
The peak c o u n t
record.
a spectrum w i t h
a b o u t t wo o r d e r s
peaks
the
t h e number o f
spectra
coefficients.
than
in
p e r i o d o g ram f o r m ,
points
half
as many compl ex
since
spect r um.
major f requency
component s
each m a j o r component shows
For e x a mp l e ,
look
at
a t i me
function,
f
wh i c h
= s i n( o) t ) ,
is
a pu r e t o n e
having
one f r e q u e n c y component - namel y
-
co.
If
The p e r i o d
the
t on e
of
is
this
t one
sampl ed f o r
p e r i odograrn w i l l
given
a period,
at
equal
bet ween t wo o f
similar
T5 , t he a s s o c i a t e d
frequencies
t o one o f
have o n l y one n o n - z e r o
wher e co f a l l s
by
given
by
k = 1,2,3,...
For t h e case wher e co i s
appear
-
is
have p o i n t s
GO^ = 2mk/ T s ,
gram w i l l
26
to t h a t
point
a t co.
the c o ^ ' s ,
shown i n
Fig.
t he c o ^ ' s ,
the p e r i o d o -
But f o r
t he case
t he p e r i odograrn w i l l
4.
In e i t h e r
case a
30 «
3
O CD
20 -
.
.
U- ^
O
IO - • * “ *
LU
Q
%b
Ii
0
I
I
500
I i
i
l
I
l
1000
2000
I
—I---5000
FREQUENCY (HZ)
Figure
4.
T y p i c a l d i g i t a l c o m p u t a t i o n o f t he s p e c t r u m
o f a pur e t o n e a t 1021 Hz, wher e t h e F o u r i e r
c o e f f i c i e n t s have a f r e q u e n c y s p a c i n g o f
4 5 . 4 Hz.
( M a l i n g , ejt aj [, 1 967 )
-27single
t one
is
shown t o y i e l d
whose w i d t h
is
roughly
u and t h e n e a r e s t oo^.
o u r more c o m p l i c a t e d
originating
of
spectrum, i t
is
Now f o r
analysis
spectra
this
can be i n t e r p r e t e d
the
that
the
first
that
innocent
of
in
as each
of
t he c r e s t
number o f m a j o r peaks
i n each
family
of bruits
tones
t ha n
bruits.
A c o mp u t e r code was w r i t t e n
i n the
is
bet ween
t h e peaks
be composed o f more o r l e s s m a j o r
family
p e r i odogr am
t o t he d i f f e r e n c e
postulated
to
the
proportional
By c o u n t i n g
be f o u n d
the s t e n o t i c
peak i n
f r o m a t o n e whose f r e q u e n c y
t h e peak.
will
a single
50 s p e c t r a l
t h e maxi mum a m p l i t u d e .
to
c o u n t t h e number o f peaks
coefficients
whi c h wer e above 10% o f
See A p p e n d i x B f o r
the l i s t i n g
of t h i s
p r o g r a m.
Filter
and Zer o C r o s s i n g
■ As s t a t e d
distinguishing
previously
nor mal
br oad band f i l t e r
digital
Analysis
some s u c c e s s
f r o m abnor mal
amplification
signal
as a g a t e t o
sampl e t h r o u g h
very
counters
amplifier
heart
The r e a s o n f o r
f r e q u e n c y component s was t o
by u s i n g
analog-to(Jacobs,
et aI ,
beat
the
the a m p l i f i c a t i o n
boost
and r ah t he
s e r i e s wh i c h e l i m i n a t e d
l ow f r e q u e n c y component s and a m p l i f i e d
c o mp o n e n t s .
in
used t h e e l e c t r o c a r d i o g r a p h
sampl e an e n t i r e
a filte r
p h o n o c a r d i o g r a ms
together with
c o n v e r s i o n "knd, . zer o c r o s s i n g
1 9 6 8 ) . ' I n - 1Iii s s t u d y , Jacobs
has been r e a l i z e d
this
part of
the
high f r equency
of
hi gh
the
I
-28phonocardiogram s i gn al
counters.
bruit
This
signal,
met hod o f
but
it
advent o f the f a s t
perform t h i s
enough t o
test
Fourier
applicable
of
its
convolution
ficients
to
width,
simulation
but on l y
t h e same i n f o r m a t i o n
or pa r t
o f ma t c h i n g
to
bruit
the
more r e a d a b l e
t he
signal.
in t h i s
to t h a t
a met hod f o r
section
f o r m.
in
obtaining
same i n f o r m a t i o n
and i d e n t i f i a b l e
band­
contained
'
simplified,
• .
give
t h e mean f r e q u e n c y ,
supply
operation
c o u n t can be .made much
addition
of
because
transform coef­
transform
tests
to
transform
A filtering
unfiltered
and z e r o c r o s s i n g
the energy spect r um,
The
practical
filte r
the d i s c r e t e
be empha s i z ed t h a t
in
study.
has made i t
characteristics
the
be used on t h e
Fourier
an i n v e r s e
information
could
The f a s t
Then a z e r o c r o s s i n g
peak c o u n t ,
do n o t p r o v i d e
ideal
by z e r o c r o s s i n g
in th is
relationship.
t h e same as was done w i t h
should
transform
filte r
f r e q u e n c y and p e r f o r m i n g
It
pursued
by m u l t i p l y i n g
by d i s c r e t e
s yst em o u t p u t .
testing
analytically.
especially
can be s i m u l a t e d
signal
was n o t
is
si mpl e
be d e t e c t e d
in a
VII.
DISCUSSION OF RESULTS
Plots
Figs.
for
5 through
each i n n o c e n t
of
the h e a r t
of
this
peak i s
contains
is
called
level
three
5 shows
the n o i s y p a r t
heart
This
bruit.
An e n v e l o p e
#
The f i r s t e n v e l o p e
peaks.
and t h e
heart
or
t h a t wer e made
an i n n o c e n t
bruit,
sound.
plots
s o u n d ; t h e second peak
third
plot
peak i n
actually
beat c y c l e ,
silent.
Fig.
subset
Fig.
heart
5.
of
the
previous
As can be s e e n ,
sound was n o t c o m p l e t e l y
7 and 8 ar e t h e h i s t o g r a m s
Fig.
the
9 is
a plot
innocent
Fi gs..
Fig.
first
10,
of
for
attempt
6 shows
50 c o e f f i c i e n t s
bruit
of
Fig.
5 through
9,
b u t ar e f o r
the noi sy
part
heart
sound i s
of
s a mp l e .
6.
Figs.
not e a s i l y
It
of
is
to exclude
the f i r s t
in t h i s
10 t h r o u g h
bruit
case.
Figs.
respectively.
t he e n e r g y
a stenotic
a stenotic
part
indicated
5 and 6,
in
that
is
successful
Figs.
only
the o t h e r h a l f
p l o t whose p o s i t i o n
the
the envel ope
covers
but
h e a r t c y c l e wh i c h was chosen as a b r u i t
that
to
Fig.
the f i r s t
o f t h e nor mal
comparatively
the
in
is
for
contain
t he c e r v i c a l
half
s ampl e.
beat c y c l e
t h e second h e a r t
about
is
bruit
c u r v e woul d
what
9 show t h e t y p e o f
spectrum f o r
14 ar e s i m i l a r
b r u i t . . Not e i n
beat,
distinguished
that
t he
f r o m t he b r u i t .
BRUIT SAMPLE
-30-
- I
- V -
0.0
------------1---------------------------------- 1----------------------------------1----------------------- —-------- ,
0.1
0.2
0.5
0.4
TIME
FIGURE 5.
(SEC.)
FIRST AND SECOND HEART SOUND W ITH
(l2376G-5!2-HE)
INNOCENT B R U IT
0. 05
TIME (SEC.)
FIG U R E 6.
IN N O C ENT BRUIT S A M P LE ( I2 9 76 8- 5 I2 -H )
0.1
-32-
FIGURE 7.
HISTOGRAM
OF HEART BEAT SHOWN IN FIGURE 5
(129760-512-HE)
NORMALIZED FREQUENCY
-33-
AMPLITUDE
FIGURE 8.
HISTOGRAM OF AN INNOCENT BRUIT SAMPLE 029763-512-H)
NORMALIZED ENERGY
-34-
0.8
-
0.6 0.4 -I
0.2
-
-Q -O
FR E Q U E N C Y
FIGURE 9.
Q -cp-'O <»■« ■
(C Y C L E S PER SECOND)
ENERGY SPECTRUM OF AN INNOCENT BRUIT
(129763-512-H )
BRUIT SAMPLE
TIME (S E C .)
F IG U R E
10.
FIRST AND SECOND H E A R T S O U N D WITH S T E N O T IC B R U IT
( 12937 9-4 -AA)
TIME (S E C .)
FIGURE
II.
S T E N O T IC BRUIT S A M P LE
(1 293 79-4-A )
-37-
AMPLITUDE
FIGURE
12
HISTOGRAM OF HEART BEAT SHOWN IN
FIGURE IO
( 1 2 9 3 7 9 - 4 - AA)
NORMALIZED FR E Q U E N C Y
AM PLITU D E
FIGURE 13.
HISTOGRAM OF A STENOTIC BRUIT SAMPLE
(1 2 9 3 7 9 -4 -A )
-39-
300
FREQUENCY
FIGURE
14.
ENERGY SPECTRUM
•
(C Y C L E S PER SECOND)
OF A STENOTiC BRUIT
(1 2 9 3 7 9 - 4 -A )
I
-40|
A visual
examination
sampl ed p o p u l a t i o n s
ences
their
failed
bet ween t h e s t e n o t i c
Wh i l e t h e
variation
bet ween
but also
sampl e l e n g t h ,
conclusions
any o u t s t a n d i n g
innocent
t he
differ­
i n n o c e n t wavef or m.
patients
is
about
as much as
patient.
hi stograms
,
is
bet ween any t wo h e a r t
and by t he d i f f e r e n c e s
help
of
f r o m one p a t i e n t may be s i m i l a r ,
by t h e d i f f e r e n c e s
w h i c h wo u l d
could
wavef or m p l o t s
wav e f or m and t h e
the b r u i t
by t h e d i f f e r e n c e s
individual
reveal
and a s t e n o t i c
The a p p e a r a n c e o f
families
to
i n n o c e n t wav ef or ms
bet ween an i n n o c e n t
only
of the b r u i t
beats
not
o f an
i n sampl e p o s i t i o n ,
bet ween
to separate
be dr awn f r o m a v i s u a l
affected
individuals.
No
t he two b r u i t
examination
of
t he
hi s t ogr ani pi o t s .
Plots
information
of
the energy s p e c t r a ,
as t h e
signal
or h i s t o g r a m
simpler
visual
spectra
t o have more peaks t h a n t he
suggesting
the
form.
while
i dea
Visual
containing
plots,
examination
appear
shows t h e
innocent
as much
in a
stenotic
spect ra- . ,
o f a m a j o r peak c o u n t f o r
t hus
identification
purposes.
Relating B r u it C ha racte ristics
Population
To d e m o n s t r a t e
such as t h e
it
the
to
suc c es s o f
the
using
number o f m a j o r s p e c t r a l
must be shown t h a t
this
Innocent
a bruit
p e ak s ,
characteristic
or S t e n o t i c
is
to
characteristic,
predict
disease,
d e p e n d e n t on t h e
I
-41 population,
taken.
bruit
either
In or der
innocent
to t e s t
characteristic,
difference
or s t e n o t i c ,
the
a t
i ndependence o f
test
for
the s i g n i f i c a n c e
to
is
t h e mean o f
teristic;
this
assumpt i on
t
t h e peak c o u n t c h a r a c t e r i s t i c
is
called
The t
t he
innocent
the n u l l
all
the
innocent
peak r e s u l t s
with
variation
of a l l
the
stenotic
peak r e s u l t s
to
tions.
The t
allow
rejection
v a l u e and i t s
t h e t wo f a m i l y
from a s i n g l e
the s t e n o t i c
population
of
the
population.
population
p e ak s .
probability
level
spectral
to
in
of
of
if
For e x a mp l e ,
of
This
difference
look at
versus
t i s
be i n d e p e n d e n t w i t h
the
will
in
by random s a mp l i n g
a t
the
test
of
innocent
comput ed w i t h
population's
come f r o m a random s a m p l i n g o f t h e
11 g i v e s
t wo p o p u l a ­
woul d mean t h a t
the s t e n o t i c
A
probability
the
be o b t a i n e d
peaks
charac­
show how w e l l
f r e e d o m wh i c h c o r r e s p o n d s
peak p o p u l a t i o n .
Table
hypothesis
not
test
t h e mean and
the
al pha
spectral
0.05.
20 t h a t
separate
associated
Suppose a v a l u e
de g r e e s
peaks c o u l d
null
means c o u l d
appropriate
one chance
can be used t o
o f t he
compar es t h e mean and
of
characteristic
or
hypothesis.
variation
that
is
t h e mean o f t h e s t e n o t i c
characteristic
of
equal
that
it
the v a r i a b l e
bet ween t wo sampl e means was u s e d .
i n v o l v e s maki ng t h e a s s u mp t i o n
test
f r o m wh i c h
The t wo p o p u l a t i o n s
to
an a l p h a
there
is
only
mean number o f
innocent
bruit,
could
be . sai d
the t
test
95% c e r t a i n t y .
results
obtained
usi ng
to
-42TABLE I I
T TEST OF SEVERAL BRUIT CHARACTERISTICS DETERMINING THE
VALI DI TY OF USING THE CHARACTERISTIC AS A METHOD OF SEPARATING
THE STENOTIC AND INNOCENT BRUI T.
Characteristic
Innocent
Mean
Stenotic
Mean
31 5. 7
324.0
T 31
0.782
.5
105090. 0
I 07580.0
I 31
0.315
.8
-707.5
-565.0
131
0.952
.4
175.3
273.5
131
9.000
1 2 3. 3
• 188.4
11 5
7.732
—
82.0
13 0. 7
. 115
7.604
—
112
5. 5 77
Degr ees
Freedom
T
Test
Al pha
Prob.
Hi s t o g r a m
Standard d e v .
Variation
First
moment
Zero-Crossing
Frequency
Spectral
*
Analysis
En e r g y - Ba n d w i d t h
Ener gy- Mean
frequency
Number o f m a j o r
peaks
5. 2 3
7.55
"
*
Probability
of
a larger
t
is
less
t ha n
. 001.
-43test
the s i g n i f i c a n c e
and s t e n o t i c
standard
mean o f
deviation,
frequency,
o f the d i f f e r e n c e
each c h a r a c t e r i s t i c
variation,
number o f m a j o r s p e c t r a l
tant
reliably
to mini mi ze
hypothesis,
mar gi nal
reasonable
peaks.
the t ype
so t h a t
t i me
hypothesis.
be r e j e c t e d
tests.
but
is
several
quite
u s e a b l e sampl es
with
i n d , i v i d u ;al
II,
and a t h i r d
innocent
bruit
stenotic,
in
wh i c h
each t y p e
a b o u t 70% o f
influenced
mean o f
each i n d i v i d u a l
o f the n u l l
as t h e
of
the n u l l
hypothesis
t h e r e ar e sampl es
of
bruit,
can
by t he
furnishes
values
t h e number o f
stenotic
bruit
One
sampl es;
the i n n o c e n t
bruit
about
t he
two means,
tabulated
f r om
considerably.
50% o f
Because t h e
the t e s t s
greatly
i mpor­
has been used i n t h i s
the
about
individual
s a mp l e s .
each o f
is
wou l d be
o f 0. 01
the n u l l
Although
furnishes
s a mp l e s ;
rejection
and a c c e p t a n c e
f r o m each p e r s o n v a r i e s
individual- furnishes
another
false
it
the hi st ogr am c h a r a c t e r i s t i c s .
irregular.
individuals
families
probability
The sampl e c r o s s - s e c t i o n
study
bruit
and
a characteristic
Therefore, i t
As seen f r o m T a b l e
all
study —
and money ar e n o t wa s t e d w o r k i n g w i t h
bet ween r e j e c t i o n
for
this
moment , z e r o c r o s s i n g
In l o c a t i n g
I error,
t o chose an a l p h a
line
used i n
innocent
ener g y - me an f r e q u e n c y ,
separ at e the
characteristic
dividing
first
energy-band w i d t h ,
wh i c h w i l l
bet ween t h e
25% o f
i n n o c e n t and
in Table
from t hr ee
11 ar e so
individuals,
sampl ed must be checked t o
insure
the
S
-44that
he. can be c o n s i d e r e d
mean he h e l p s
t
test
to
establish.
bet ween t h e
In a t
a member o f t h e p o p u l a t i o n
test
individual's
the
rejection
point
In the
t
tion
the type
level
should
words,
null
test
should
be s e t
judged h e a l t h y
is
the
low;
and t h e
high;
least
say a t
falsely
11 e r r o r ,
say a t t h e
so the,
0.05
popula­
and t h e r e j e c t i o n
level.
In o t h e r
a diseased a r t e r y
of
level.
and t he s t e n o t i c
t h e 0. 01
so t h a t
innocent
of
desirable
mean.
classifying
is
no t
some h e a l t h y
as d i s e a s e d .
i n Table
III.
stenotic
patient
o f t he maj or
0.05 p r o b a b i l i t y
with
we see t h a t
level
at
in a l l
cases
same p a t i e n t s
patient's
with
mean w i t h
hypothesis
peaks f o r
each
population
it
at, t h e
b u t one.
the s t e n o t i c
the n u l l
this
a r e shown
wou l d be r e j e c t e d
with
level
test
innocent
Al I o f t h e s t e n o t i c
identified
the n u l l
the
hypothesis
t h e 0. 01
no case be r e j e c t e d .
each i n n o c e n t
t h e mean o f
null
Compar i ng t h e s e
been c o r r e c t l y
peak c o u n t i n g
Compar i ng t h e mean number o f
can be seen t h a t t h e
we r e j e c t
a type
even a t t h e r i s k
The r e s u l t s
tion
be s e t
by a
mean and each f a m i l y ' s
bet ween an i n d i v i d u a l
I error
determined
t he p o s s i b i l i t y
hypothesis,
c a r e must be t a k e n
arteries
c he c k i s
bet ween an i n d i v i d u a l
p o p u l a t i o n one must m i n i m i z e
accepting
This
whose
hypothesis
bruit
criteria.
the
popula­
inhocent
f or . .one p a t i e n t
can i n
patients
have
Now c o mpar i n g
p o p u l a t i o n mean,
only, . id e n tify -
-45TABLE I I I
T TESTS ON THE NUMBER-OF MAJOR PEAKS OF THE BRUlT SPECTRA
P a t i e n t Tested
Wi t h
Innocent
Population
Wi t h
Stenotic
Population
E
LO
CL
C
E
O
•f—
CO
(Z )
4 -)
4 O
U
•r-
C
(V3 fO
CD CU
Z
CL.
0)
E
Z3
Z
-p
C
O
•1
4—
• r - S-P
CU
C JO
—
-P CU E
rd " O =3
CL. n
Z
1/5 4 O
-P
C
SCU CU
•r ~ J D
CO
132323
I 29768
122252
1 33441 .
50268
1 1 6971
131824
4-
-P
O
•1—
C
O
- P •1—
C
-P
CU CO
CO O r—
Z5
CU O
S= C L
C
O
JD
O
SQ-
O-
=C
5
CO
CU
CU
SCD
.E
=3
CU
Q
O - Z
4.94
5. 87
4.86
7.60
3.33
4.50
4.00
63
63
63
63
63
63
63
Stenotic
35
4
4
3
2
I
I 29379
IllllT
115,326
222222
131921
124918
-Q
CO
Innocent
31
I5
77
5
3
2
2
-I
_c
-
-P
>5
-P
•1--I------
Li-
(0
S-
E
O
*a
CU
CU
S-
V)
Q)
7.11
7.50
8.50
10 . 33
7.50
11.00
98
67
67
66
65
64
-P
1—
t—
> ->
Bruit
0.62
I .07
0.44
2.34.
I .51
0. 4 8
0.80
Bruit
4.20
2. 0 4
2.88
4.08
I . 48
2.66
CO
-C
CL
O
-o
CU
CU
SU-
4O
>5
P
•r—
r—
•r—
JC
-p
•i—
S
CO
CU
CU
SCO
CU
a
u
*1
—P
-P -P
CO O
CU c
I -
C
O
•r—
OJ
-Q
CO
JD
O
SO-
cd
—
Cd
O
CL
CL
I
P O
t— (Z) Cl
<
Patients
0.60
0.30
0.70
0.05
0.20
0.70
0.50
78
62
54
52
50
49
49
5. 0 3
2. 6 7
3. 01
0.04
3.18
I . 88
2.20
0.01
0.01
0.90
0.01
0.10
0. 05
■ 47
47
47
47
47
47
0.89
0.04
0.79
2. 11
0.03
I .51
0.40
0.90
0.50
0. 05
0. 90
0.20
Patients
0. 0 5
0. 01
——
0.20
0. 01
-46i ng s i x
these
out o f
seven c o r r e c t l y
innocents
with
the s t e n o t i c
cases wher e t h e n u l l
only
hypothesis
57% a c c u r a c y w i t h
identifications,
this
is
bruit
innocent
The r e s u l t s
width,
in Tabl es
showed p r o mi s e
also
stenosis,
IV,
in Table
individual
V,
II.
patient
fied
as s t e n o t i c
that
these d i sc r e p a n c i es
u n i f o r m sampl i ng
ar e t h r e e
The a c c u r a c y o f
in
t he t
show t h a t
separating
t
tests
for
test
this
the
stenotic
energy-band
and z e r o c r o s s i n g
and VI
cases
is
f r e q u e n c y ar e
respectively;
Although
ar e s e v e r a l
wher e an i n n o c e n t
there
be r e j e c t e d , g i v i n g
in
shown t o
be most
character­
of
of
results
likely
i s made.
may d i s a p p e a r w i t h
three
prediction
each t a b l e
or the opposi t e mistake
p r o c e d u r e , and w i t h
all
these t h r e e
show some t r e n d ' t o w a r d c o r r e c t
there
Compar i ng
bruit.
en er g y - me a n f r e q u e n c y
tabulated
istics
the
criteria.
population
i n Ta bl e. V I I
very successful
of
this
cannot
test.
summar i zed
characteristic
from t he
with
classi­
is
felt
an a c c u r a t e ,
more
a large,
It
more b a l a n c e d
populationTabl e- VI ! . s u m m a r i z e s
Tabl es
III
through
VI.
It
our t e s t
to c o r r e c t l y
innocent
bruit,
and a l l
in the t
test
results
the s t e n o t i c
the accur acy o f t he
clearly
diagnose
four
the
shown i n
shows t h a t we have b i a s e d
stenotic
bruit
o v e r the.
characteristic
tests
show good
bet ween t h e
p o p u l a t i o n mean.
tests
stenotic
p a t i e n t mean and
The m a j o r peak c o u n t i n g
test
I
-47TABLE IV
T TESTS ON THE' ENERGY-BAND WIDTH OF THE BRUIT' SPECTRA
P a t i e n t Test ed
Wi t h
Innocent
Population
C
O
E
-o
CD
CD
S-
CD
CL
E
fd
OO
4O
SCD
-Q
E
23
Z
C
rd
CD
s:
Q
O
+->
rd
SZ
(/I
U
-
•r—
-P 4C T— SCD -P CD
T - . C _Q
-P CD E
CO - O
LU
'
23
CL. i— i Z
M-
-P
O
"O
-P T C 3
CD
•i— ~o
-P C
fd fd
CO
CD
'CD
SCO
CD.
Q
C u CO
Innocent
I6
33
7
3
2
5
2
129768
132323
122252
50268
I 66 971
133441
131824
130.
97 .
I 63.
89.
' 130.
200.
208.
66
66 •
66
66
66
66
66
Stenotic
35
4
4
3 .
2
I
- I-
O
(Z)
i—
129379
1 1 5326
111111
222222'.
131921
1 2491 8 ’
I 91 .
133.
228.
231 .
I 20.
180.
101
70
70
6 968
67
Wi t h
Stenotic
Population
-P
fd
>>
4->
'I—
I 1"
25
CL
-C
O
-P Cu
•t—
-P
C
-P CD
CO O
CD O
I— C
C
I—
Bruit
_Q
rd
_Q
O
So_
rd
SZ
CL
I
■
<
7.42
0.36
3. 97
3.59
0.10
I .01
MO
CO
CD
CD
SCO
CD
Q
S2
O
•r—
-P
fd
>3
-P
T-
r—
23
CL
SZ O
-P Q•r—
^
U
-P -P
CO O
CD £2
H CD
-P "
H- OO
S i
fd
_n
O
SCu
fd
SZ
CL
N—
<
Patients
0. 51 ■ 0. 7
2. 41
0.02
2. 0 2 ■ 0. 0 5
1.12
0.3
0.9
0. 1 9
3. 21
0. 01
0.05
2.29
Bruit
E
O
-o
CD
CD
SLu
63
80
54
50
49
52
49
6.38
10.09
I . 98
4.99
2.42
0. 71
0. 81
47
47
47
47
47
47
0.37
3. 31
2. 2 5
2.20
2.88
0.24
——
——
0.1
—
■—
0. 02
0. 5
0. 5
P a t i ents
0.8
——
——
0.9
0.3
0. 8
0.01
0. 0 5
0. 05
0.01
0.8 -
-48TABLE V
T TESTS ON THE ENERGY-MEAN FREQUENCY OF THE BRUIT SPECTRA
Patient
Test ed
CO
CD
i—
CO
CL
E
C
O
fd
OO
4->
CL
E
=3
s:
C
-p
C
T-
CD -P CD
T-
C
_Q
-P CD E
Cd " O =3
CL. t— I z :
E
O
XJ
CD
CD
S-
U_
c
cd
CO CD
- s:
U
♦ r-
O
SCD
CJ
cd •»— CD
C
CO
4—
JD
Wi t h
Innocent
Population
> )
CD CO
S-P CD
cd sz
CL LU
T-
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CD
CD
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CD.
Q
Innocent
16
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0.20
3.89
0.29
1. 19
3.32
Stenotic
Bruit
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0.9
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Wi t h
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0,1
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0.6
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-49. TABLE VI .
T TESTS ON THE ZERO-CROSSING FREQUENCY OF THE SAMPLES
Patient
Test ed
Wi t h
Innocent ■
Population
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181 .
212.
167 .
249.
322.
72
72
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72
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Stenotic
257 .
249.
465 .
I 99.
399.
263.
. 118
76
76
74
■ 74
73
Bruit
8.57
2. 51
9.86
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41
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Population
0.2
0. 5
— —
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0.8
TABLE V I I
T TEST ACCURACY*
Characteristic
used f o r T e s t
Innocent B ru i ts
Compared t o
Innocent
Stenotic
P o p u l a t i,dn P o p u l a t i o n
p=0 . 0 5 "
pr=0.Ql
Stenotic Bruits
Compared t o
Innocent
Population
p = 0 . 05
Stenotic
Population
p = 0 .01
Al I P a t i e n t s
Compared t o
Innocent
Population
p = 0 . 05
Stenotic
Population
p = 0.01
86%
57%
83%
100%
85%
77%
Zer o C r o s s i n g
Fr e q u e n c y
67%
50%
67%
83%
62%
62%
Ener gy- Mean
Fr e q u e n c y
43%
57%
50%
83%
46%
69%
43%
43%
50%
67%
46%
54%
90% Ener gy
Band Wi d t h
Gi ven
in
' -
percentage o f c o r r e c t
diagnosis.
-50-
M a j o r Peak
Count
-51 is
shown t o
accuracy
test
be t h e b e s t o v e r a l l
by t h e z e r o c r o s s i n g
and t h e
diagnostic
test,
90% e n e r g y band w i d t h
tool,
followed
t he en er g y - me an f r e q u e n c y
test
respectively.
The c e n t e r o r en e r g y - me a n f r e q u e n c y and band w i d t h
the
bruits
i n Tabl es
used i n t h i s
IV and V.
a r e shown f o r
the
s t u d y a r e shown f o r
The mean v a l u e s
t wo p o p u l a t i o n s
in
of a l l
studied
of
each i n d i v i d u a l
characteristics
(Table
VIII).
TABLE V I I I
ZERO CROSSING, ENERGY-MEAN FREQUENCY, BAND WIDTH AND PEAK
COUNT AVERAGES FOR THE TWO POPULATIONS STUDIED.
Innocent
Ener gy Spec t r um Mean Fr e q u e n c y
Stenotic
81 .96 Hz ■
1 3 0 . 7 Hz
Ener gy Sp e c t r u m 90% Band Wi dt h
12 3. 3
Hz
1 8 8. 4 Hz
Zer o C r o s s i n g
175. 3
Hz
2 7 3. 5 Hz
Frequency
Maj or S p e c t r a l
5. 23 Hz
Peaks
7 . 5 5 Hz
Pr obl em Ar eas
The a u t h o r was r e s p o n s i b l e
the a r t e r i a l
to
exclude
mitted
valves.
noise
the
through
to
first
the
for
be s ampl ed .
choosing
The p o l i c y
and second h e a r t
blood
and a r i s e
11 has been shown
(Braun,
t he' p e r i o d o f
e s t a b l i s h e d was
sounds w h i c h ar e t r a n s ­
from t he c l o s i n g
ejt aj_, 1 9 66)
that
of
heart
the
-52cervical
bruit
t he f i r s t
tion
sound t h a n
but the
istics
sampl es
destroyed
reasoning
short
of
to
the
sampl es
in t h i s
since
t h e end o f
why t h e band w i d t h
should
other
is
that, the
t han
the i n n o c e n t .
For a l l
having
study
don't
ejt aj_,
t h e band w i d t h
1 966)
necessarily
rather
t he
Thi s
If
bru.i t. n o i s e .
reflect
t he
shown i n T a b l e V I I I
is
band w i d t h .
Another p o s s i b l e
opposite
longer,
it
explana-
has a more c ompl ex s i g n a l
contributing
under the
sampl e
explain
bruit
bruit
the t r u e
t h a n on t r y i n g
could
is
But t he
the s t e n o t i c
studies
be
a w i d e r en e r g y band t h a n l ong
s t u d y a s a mp l i n g
u s e d , and band w i d t h
ar e w e l l
s o u n d s . mu s t
t he second s ou nd,
stenotic
patients
this
the c h a r a c t e r ­
l e n g t h may show up i n
difference
expected.
tion
present
in
of
and second s o u n d s ,
to f i n d
all
varia­
t o t h e second
the f i r s t
noise,
this
to
the s t e n o t i c
Any i d e n t i f i c a t i o n
by o m i t t i n g
haye t h e s h o r t e r
sampl es, t o
bruit.
since
closer
relative
that
emphasi s was p l a c e d on e n d i n g
bef ore onset o f
than t h a t
ma r k ,
extending
bruit
position
Br aun t h e o r i z e d
t h e same s i g n a l . ( Cochr an. ,
length
locate
and i n
used her e was t h a t
Differences
samples.taken
just
innocent
uni que to
--
bruit
be l o n g e r ,
the
is
r emoved.
test
length
may be an i d e n t i f y i n g
seems t o
position
in
and second s o u n d s .
itself
bruit
can v a r y
seven or more b r u i t
rate
show t h a t
o f 1 0 , 0 0 0 h e r t z was
t he up p e r f r e q u e n c i e s
suggested l i m i t
of
500 c y c l e s
per
-53second ..
earlier
For p a t i e n t s
with
studies
these b r u i t s
the l i m i t
showed t h a t
comput ed f o r
these
upper f r e q u e n c i e s
sampl i ng
theory,
function
of
these
well
spectra
the ac t u al
Thus, the
upper s i g n a l
lim it
will
controller.
controller
t i me
was s a m p l i n g
heart
of
This
cha nne l
The m a g n e t i c
is
error
settings
cases
it
earlier
could
rate
often
in the
repre­
is
slower
and t h e
Nevertheless,
be good a p p r o x i m a t i o n s .
present
in the
was n o t i c e d
on t h e d i g i t a l
that
t h a n was e x p e c t e d ,
possibly
the d i g i t a l
but onl y
include
t he
be caused by a n o i s e
n e a r t he t r i g g e r
deal
was n e c e s s a r y t o
ar ea o f t h e
s a mp l i n g
as me nt i on ed-
wer e d i a l e d
t a p e was h a n d l e d a g r e a t
It
s u g g e s t e d by
to a p pr o pr ia t e,
l o w e r e d some.
o f t he tape
t i me d e l a y s .
t he tape q u i t e
records
a second wh i c h was enough t o
sound.
voice
the proper
delay
above
interpolation
p e r i o d s wer e d e t e r m i n e d
In several
by a f r a c t i o n
on t h e
A pol ynomial
sampl i ng
Th e r e was some s y s t e m a t i c
and t h e p r o p e r
in
Therefore,
be an a p p r o x i m a t e
used s h o u l d s t i l l
The s a m p l i n g
( 19 6 6 ) .
under t he l i m i t
spectra.
effective
frequency
o f the s p e c t r a
process.
present
sampl es may n o t be c o r r e c t ,
has been used t o c o n v e r t o u r
lengths.
r a t e was u s e d .
the f r e q u e n c i e s
by Lees and D o u g h e r t y
but w i t h
sentation
s a mp l i n g
t he
e x t e n d e d , i n many c a s e s , 50 t o 100 h e r t z
suggested
the s p e c t r a
first
t h a n seven sampl es
s a m p l i n g met hod and s l o w e r
Band w i d t h
all
less
in
signal.
setting
s t o p and r e v e r s e
sampl ed b r u i t s ;
t he
-54del ays f o r
trigger
as many as t e n sampl es wer e measur ed f r o m t he
signal.
recordings,
the s i gn a l
tape
tape
bruit
this
p r o b l e ms
that
in
site
associated with
the
of
t o change w i t h
t he mi c r ophone.
that
study
on t he. c h e s t c a v i t y ,
theory
the v o r t e x , s h e d d i n g
f r e q u e n c y , but
signal
whi ch
is
lack of disease.
change in- t he
is
on t h e s i g n a l
individual
The
is
and w i t h
was c e n t e r e d
According
can o c c u r
but the
t o Bruns'
near.sound
hear d u p s t r e a m is- equal
the f r equency
to
hear d down­
l o w e r due t o v o r t e x c o a l e s c e n c e .
introduce
a function
a variable
of p o s i t i o n ,
The mi c r o p h o n e
bruit
different
process.
e t a l , 1957)
shift
The f r e q u e n c y
also
a stenotic
because o f
recording
n o t t h e neck a r e a .
(1959) a f r e q u e n c y
/
effect,will
mu s i c a l
a s p e a k e r down t h e e s o p h a g u s ,
producing 'o r if ic e s, -.
This
s t u d y was
Some wor k has been done on
(Lepeschkin,
stream from the o r i f i c e
in
may be q u i t e
the
on
t o most d o c t o r s .
originating
a s t u d y such as t h i s
p r o b l e m by l o w e r i n g
general
used i n t h i s
was a good q u a l i t y ,
signal
the
have had much e f f e c t
t h e s k i n may have as a f i l t e r
location
interest
it
production
used i n
unknown and s u b j e c t
the
but
accoustical
from t he s i g n a l
effect
not
r e c o r d e r w h i c h wo u l d be a v a i l a b l e
or ot h e r
several
should
t a p e was used f o r
The t ap e r e c o r d e r
accurate,
The a c t u a l
lesion
high q u a l i t y
handling
quality.
not e x t r e me l y
type,
Since
same
waveform.
Tt
in
the
recorded
no t o f d i s e a s e or
used her e i n t r o d u c e d
is
a special
another
type of m i c r o ­
-55phone, .used by t h e me d i c a l
signal
so t h a t
scope,
but
this
it
this
p r o f e s s i o n , whi c h f i l t e r s
duplicates
filtering
is
the
t he
sound hear d t h r o u g h a s t e t h o ­
n o t t h e most
important
effect
of
t y p e mi c r o p h o n e .
Even t h o u g h we may know what t h e c h a r a c t e r i s t i c s
o f t h e c o n t a c t mi c r o p h o n e i t s e l f ar e when p l a c e d
a g a i n s t the c h e s t , t he v a r i o u s c o n d i t i o n s or ’
v a r i a b l e s t h a t e x i s t , due t o t h e amount o f f a t
u n d e r l y i n g t he s k i n , t he t oneness o f the s k i n ,
how har d you p r e s s , and t h e s t i f f n e s s o f t he
m i c r o p h o n e . i t s e l f , ar e a l l v a r i a b l e s on wh i c h
I . c a n n o t g i v e you any d a t a .
They change f r o m
one s u b j e c t t o a n o t h e r and a r e j u s t a mass o f
unknowns.
( M. B . R a p p a p o r t , Sanbor n C o . ,
B o s t o n , Mass. 1 9 57 )
It- is
frequency
felt
the- p r o b l e ms w i t h
limitations,
due t o a r t e r y ,
of
that
tissue,
some s i g n i f i c a n c e
this
study.
consisted
bruit
but did
the
the
the
stenotic
upper
accuracy
r e s p o n s e wer e
results
investigation
of
was
f r o m t he
t h e most s u c c e s s f u l
the maj or s p e c t r a l
important
VIII).
invalidate
purpose o f
by f o u r me t h o d s ,
the
(Table
not
identifying
of counting
discovering
bruits
by ( I )
and r e c o r d i n g
mi c r o p h o n e and r e c o r d e r
The s t a t e d
accompl i shed
innocent
t ape h a n d l i n g
sampl e l o c a t i o n ,
p e ak s ,
f r e q u e n c y component s
and
found
o f whi c h
( 2)
in
I
VIII.
Summary o f
-
Result s
. The s t a t e d
stenotic
bruit
identifying
found t h a t
counting
CONCLUSIONS AND RECOMMENDATIONS
,
purpose
from the
features
0. 01
number o f m a j o r
of a t
level,
following:
bruits
zero
for
for
test,
(I)
crossing
innocent
innocent
Treating
and i n
tiating
definite
in
of
innocent
bruits
(175.3
each.
bruit.
the n u l l
bruits
bruits
the
for
(123.3
peaks - i n s t e n o t i c
innocent
conclusions
t h e mean
(273.5
bruits
Hz)
(130.7
( . 4 ) - t h e mean o f
bruits
and
Hz)
and
t h e en e r g y
(188.4
Hz)
and
Hz ) .
signal
histogram f o r
as random s t a t i o n a r y
differences
moment was f o u n d t o be u n s a t i s f a c t o r y
bet ween
a t t he
t he average energy
stenotic
accoustical
the
(3)
and
by
From t he
hypothesis
bruits
stenotic
( 82. 0 Hz);
was
separated
( 5 . 2 3 ) ; ( 2)
stenotic
for
It
possible
wer e f o u n d bet ween t he
bruits
Hz);
label
t he
a p e r i odogr am (a f or m
o f the
differences
frequency f o r
n o i s e and e x a mi n i n g
and f i r s t
and t o
t h e mean number o f s p e c t r a l
s p e c t r u m 90% band w i d t h
for
identify
be r e l i a b l y
peaks
rejecting
mean f r e q u e n c y
innocent
bruit,
could
spect r um)
significant
(7. -55)
spectrum,
innocent
t h e s e t wo f a m i l i e s
the
s t u d y was t o
or c h a r a c t e r i s t i c s
o f t he energy d e n s i t y
results
of t h i s
and s t e n o t i c
bruits.
a b o u t t h e mechani sm o f
in v a r ia t i o n
for
differen­
Although
bruit
can be
no-
-57dr awn f r o m t h e s e
results.
Appendi x D suggest s
some p o s s i b i l ­
ities.
F u t u r e Work
Some d i f f i c u l t y
section
of
of
the a u s c u l t a t o r y
the f i r s t
cardiograph
it
should
signal
signal
to
be p o s s i b l e
describe
digital
to
out
the
pick
filtering
studying
(1967)
sing
of
discrete
each s a mp l e ,
the
in
Fourier
spect rum.
is
the a u t h o r ' s
raw s i g n a l
analysis
has p r o v e d
analysis
to
is
by m e r i t
the
of
process,
portion
o f t he
coefficients
This
could
be used t o
having
compar ed
i n each p e r i o d o g r a m .
the f r e q u e n c y
s p e c t r u m by d i g i t a l
may be h e l p f u l
in
t e c h n i q u e was used by Mal i n g
convergence to
belief
that
since
case o f
t h e use o f e x p e n s i v e
theory.
zero c r o s s i n g
a band f i l t e r e d
wo u l d be as r e l i a b l e . i n
i nvolved .
bruit
electro­
a c o mp a r i s o n o f th.e p e r i o d o -
was so s u c c e s s f u l ,
be i n
sampl i ng
points
diagnosis
h e a r t mu r mu r s .
can be made by an e l e c t r i c a l
eliminating
testing
leakage
t he
including, parts
and r e l i a b l y .
to obtain' a c l o s e r
It
the
the
the b r u i t
By u s i n g t h e
the
t h e same f r e q u e n c y component s
Eliminating
sampl i ng
without
sounds.
grams woul d be more r e v e a l i n g
exactly
in
trigger
t h e same number o f
completely
signal
and second h e a r t
more q u i c k l y
If
was e n c o u n t e r e d
circuitry
of
z er o c r o s ­
studies
This
as i t
type o f
setup,
thus
c o mp u t e r t i me wher e e x t e n s i v e
APPENDIX
APPENDIX A
REVIEW OF SIGNAL THEORY AND FOURIER TECHNIQUES
Fourier
Series
. If
a function
f ( t)
f(.t)
= 2"^ + ^
^
n=l
a.n cos (
n
t hen t he c o e f f i c i e n t s
Euler formulas
for
can be expanded i n t h e
of
this
Fourier
i t ^)
1
t i me s e r i e s
+ b s i n ( --Il7r^ )
. n
1
series
can be f o u n d
(Al)
by t he
Coefficients:
- +T/ 2
2
: T
-
f(t)
cos
dt,
f(t)
sin
[ —n-j —] d t ,
n = 0,1,2,...
(A2)
n = 1,2,...'
( AS)
-T/2
■T/2
2
T
-T/2
For t h e
value
t i me s e r i e s
in
equation
of
t he f u n c t i o n , f ( t ) , t h e
1
D i r i c h i et. c o n d i t i o n s :
(I)
to converge to
signal
f (t)
t he t r u e
must s a t i s f y
the
W i t h i n t h e f i n i t e t i me i n t e r v a l , - T / 2 t o + T / 2 ,
f ( t ) must be s i n g l e v a l u e d ; must have a f i n i t e
number o f maxi ma and mi n i m a ; must possess a
; f i n i t e number o f d i s c o n t i n u i t i e s ; and must
s a t i s f y t he . i n e q u a l i t y :
'
rT/2 . .
| f(t)
| d t < 0°
- -T/2I
I
The a c t u a l t i me f u n c t i o n f ( t ) c o r r e s p o n d i n g t o any
p h y s i c a l s i g n a l w i l l s a t i s f y t h e s e c o n d i t i o n s a l t h o u g h some
common m a t h e m a t i c a l r e p r e s e n t a t i o n s do n o t . ( Co o p e r and
McGi H e m , 1 967 )
-60Wf t h a l i t t l e
equation
the
(Al)
manipulation,
can be e x p r e s s e d
in
Fourier
series
compl ex n o t a t i o n .
in
Usi ng
relationship
e 1" 9 = cos 0 + i
it
the
si n 6
(A4)
can be shown t h a t
cos
nx = 1 / 2
( e i n x + e™1 n x )
sin
nx = 1 / 2
( e inx
(AS)
and
Now u s i n g
f(x)
equations
= c
+
0
Z
n=l
(AS)
and
wher e i
(AG)
equation
=
.
(Al)
(A6)
becomes
(c e i n x + k e ' i n x )
n
n
c
wher e x = 2 i r t / T , c
The c o e f f i c i e n t s
- e~i n x ) ,
(A7)
( a n - i bn ) / 2 ,
2 ’ cn
can be f o u n d by t h e s e
and kn= ( a n+ i b n ) / 2 .
relations
' T/ 2
c.
'n
I
.T
f(x)
e ~ i n x dx
(A8)
-T/2
T/ 2
f ( x ) e 1- nx dx
( A 9)
T/ 2
But i t
can be seen t h a t
f (x) =
wher e c^ i s
Z
n = -.“
c ■e
k.
i nx
now e x p r e s s e d
c
- M
. so we can w r i t e
CO
Z
Yl=-CO c ne
in2nt/T
( Al O)
by
+T/ 2
I
T
f ( x ) B- ^ nx d x ;
-T/2
n
0,
I , 2,
(All)
-61Now l e t
us c a l l
recognizing
t h e f u n d a me n t a l
that
o r h a r mo n i c s
this
is
also
(oo0 = 2 i r / T ) .
component f r e q u e n c y Uq ,
t he s p a c i n g
Now t h e
bet ween component s
compl ex F o u r i e r
series
can
be w r i t t e n
f(t)
= E c
exp( i na) t )
n = - co
and t h e
.
• (Al 2)
0
coefficients
can be w r i t t e n
'T/2
« 0/271
f ( t)
e x p ( - i a ) Qn t )
dt
(Al 3)
-T/2
F o u ri e r Transform
The F o u r i e r
compl ex F o u r i e r
approaches
nu0
integral
series
infinity.
relation
by t a k i n g
Letting
can be d e r i v e d
the l i m i t
I -> «>, w
m, t h e summat i on can be w r i t t e n
as t h e
dm,
n
f r o m t he
period,
I,
=0 , and
as an i n t e g r a l
r+'
f(tj.
_ 00
■exp ( i m t ) [ dm/ 2tt
f(t)
exp(-imt)dt]
( Al 4)
or
Z +
f(t)
Z +
CO
= 1 / 2 tt
CO
f ( t)
C
exp(-iwt)
dt]
exp(iwt)
dm.
( Al 5)
Equation
inner
( Al 5') i s
integral
is
the
Fourier
called
t he
' +
& [f(t)]
integral
relation,
F o u r i e r Transform of
and t he
f (t ) ,
CO
f(.t)
= F( i M)
— CO
exp( - i Mt )
dt.
(Al 6)
-
The f u n c t i o n
( Al 5 ) .
f (t)
f ( t)
-
can be o b t a i n e d
We a c t u a l l y
function:
62
from F( i w)
have t wo c o m p l e t e
in the
using
equation
representations
t i me domai n and F(ioo)
o f the
in the frequency
domai n.
In r e p r e s en t i n g
the
value of
period;
this
bruit
the f u n c t i o n
since
this
particular
f ( t )=0;
the
t<T/2,
part
is
of
signal
it
can be assumed t h a t
zero o u t s i d e
the
signal
investigation.
doesn't
So w i t h
t > T / 2 , the t r a n s f o r m
of the
s a mp l i n g
interest
us i n
the s t i p u l a t i o n
limits
that
can be c h a n g e d , and
fT/2
F ( i a)) =
f (t ) exp(-iwt)
dt.
(Al 7)
-T/2
Notice
the s i m i l a r i t y
bet ween e q u a t i o n
series
c o e f f i c i e n t s , and e q u a t i o n
( Al 3)
(Al 7 ) ,
the
Fourier
the F o u r i e r
transform
coefficients.
Finite
Discrete Analysis
"If
digital
analyzing
the
of
data
time)
analysis
a continuous
be sampl ed
in order
to
represents
the
(usually
provided t h a t
at
into
et r ad_. , 1 966)
continuous
the
it
equally
pr oduce a t i me
f r e q u e n c y b a n d r l i mi t e d
ar e t o be used f o r
wav e f or m t h e n
sampl es wh i c h can be f e d
known ( C o c h r a n ,
techniques
is
spaced
series
a digital
necessary t h a t
of discrete
comput er .
such a t i m e s e r i e s
waveform, provided
..."
(Cochran,
upper l i m i t
intervals
in
this
As i s w e l l
completely
wavef or m i s
ejt a]_. , 1 9 6 7 ) ,
frequency
is
given
and
by w , and
-6303 ^
0 . 1i r / A t
wher e A t
radions
is
per s e c o n d ,
the t i me
periodic
T
T
~2 — * — 2" ( wher e T = NAt )
j
function
x(jAt)
= 0 ,1 ,2 ,...N-I.
= x(jl)
=
function
be r e p r e s e n t e d
consisting
To r e p r e s e n t
we can use t h e d i s c r e t e
x(jAt)
1 966)
bet ween sampl ed p o i n t s .
Let the c o n t i n u o u s
discrete
( Lees and D o u g h e r t y ,
Fourier
x(t)
in
by t h e f i n i t e
of N total
this
t he r ange
discrete
sampl es w i t h
function,
series,
2i ri n j
c ( n) e x p (^ " ' " J )
Z
x(jAt)
(Al 8)
n = -co
wher e
, N- I
c ( n) = ^
Z
9 Tn i
x ( j At ) exp ( ~ 1TNnj ) , n = 0 ,+ 1 , . . . ±=o
(Cooley,
The f i n i t e
discrete
represent x ( jA t )
Fourier
over the
ert aj_, I 9 67 )
t r a n s f o r m can a l s o
interval
of
( Al 9)
be used, t o
interest
in
the f o l l o w ­
i n g manner :
,
x ( j At ) = I
N- I
Z
n=0
c ( n)
- . .
exp. ( ^ 1 ^ ) , j = 0 , l , 2 , . . . N - I
( A20)
wher e
' c p (n)
=
N- I
Z
x(jAt)
e x p ( ~-2] | i n j ) , n = 0 , I ,2 , . . . N- I . ' (A21 )
( Cochr an,
The f o l l o w i n g
Fourier
d e v e l o p me n t o f
series
from Cool ey,
and t h e f i n i t e
ejt aj_,
the
relationship
Fourier
et^ aj_, 1 967)
bet ween t he
transform
1967.
is
qu ot e d.
j
RELATIONSHIP BETWEEN THE FOURIER SERIES AND THE FI NI TE
FOURIER TRANSFORM
Supp os e ,
we have a f u n c t i o n
x(t)
whi c h
is
periodic
-64of period I .
expansion
x(t)
=
Then x ( t )
has a F o u r i e r
series
Z ■ c ( n ) e - 2,n' ( n t / T )
( A22)
n = -oo
wher e t h e c ( n )
-T
c ( n) = J
ar e g i v e n
by
x(t)e-2m(nt/T)
^
( A23)
Now, i f we sampl e x ( t ) a t N e q u a l l y spaced p o i n t s
bet ween O and T , we g e n e r a t e t h e sequence x- ( j At ' )
wher e t = T / N. T h i s sequence i s p e r i o d i c o f p e r i o d
N ; s u b s t i t u t i n g i n ( A22) , we o b t a i n
x(j'At)
= x(jT/N)
2 TTi ( n j / N)
2in' ( n j ' / N)
( A24)
O
Ii
C
CO
N- I
= E [ 2
A= n=0
N- I
= E c n (n
P
c ( n)e
Thus , we see t h a t
transform of
C ri (
P
n) =
Thi s' i s
E
c ( n + N ji)
A=-GO
summar i zed by Theor em 2.
Theor em 2
I f the p e r i o d f u n c t i o n x ( t ) w i t h
F o u r i e r s e r i e s expansion c ( n ) ,
x(t)
p e r i o d T has t he
c(n)
t h e n t h e p e r i o d i c sequence x ( j A t ) o f p e r i o d N,
wher e t = T / N , has t h e f i n i t e . F o u r i e r t r a n s f o r m
c p ( n' ) :
CO
x (j A t)
c ( n)
p
=
E
c ( n + AN)
A =-=
-65From t h i s we see t h a t i n u s i n g t h e a l g o r i t h m f o r
h a r mo n i c a n a l y s i s we s h o u l d p i c k an N such t h a t t h e
e r r o r due t o a l i a s i n g i n t he a p p r o x i m a t i o n o f c ( n )
by E ^ ooC ( n + £N ) ■i s a c c e p t a b l e .
Then l e t At = T/ N
f Ormxy x ( j A t ) , and t a k e i t s f i n i t e F o u r i e r t r a n s f o r m .
A g a i n , as w i t h t h e F o u r i e r t r a n s f o r m , i f we l e t
c (n)
F
E c ( n+£N)
H=-oo
t h e n c ( n ) - c ( n ) f o r n = O , I ,2 , . . . , N-/2
Cp ( N-n “ - c ( - n ) f o r n = - l , - 2, . . . , - N/ 2 ( C o o l e y ,
If
nents
we p i c k N l a r g e
for
Jn I
band l i m i t e d
enough so t h a t
N / 2 ar e n e g l i g i b l e
function
the a p p r o x i ma t i o n s
with
e_t aj_,
1 9 67)
t h e f r e q u e n c y compo­
as woul d be t r u e
no component s
above
go
for
a
= ir/At,
t hen
i n Theor em 2 above s h o u l d become e x a c t
equalities:
c ( n) =
P
S1= -C O
E
c ( n + JlN) = c ( n ) , n = O , + I , + 2 , . . . + N/ 2
Cp( N- n)
= c (-n) , n = - 1 , - 2 , . ..-N/2.
and
As has been shown by Lees and D o u g h e r t y
mat i ons
i n Theor em 2 can be q u i t e
limited
functions
for
frequencies
second.
a c c u r a t e even f o r
p r o v i d e d we l o o k
lower
( 1 966) , t h e a p p r o x i ­
t han o r equal
o n l y at the
t o O. I n / A t
non-band
coefficients
radi a' n-s per
Ener gy Spec t r um
The e n e r g y s p e c t r u m , P ( T ) 5 i s
transform c o e ffic ie n t s
T
P( f ) = Tim
T->oo
Thi s
but
definition
t he usual
positive
and i s
f T/ 2
1
by
reference
positive
to the
referring
and n e g a t i v e
-T/2 < t
P(f)
< T/2,
to
2P(f)
over the
our spectrum i s
given
to
is fo r
r ange 0 < f .
have z e r o v a l u e
by
= (I / T ) F(iw)2
We ar e o n l y
interested
the s p e c t r a l
values
her e
in the r e l a t i v e
so t h e c o n s t a n t
s p e c t r u m can be e x p r e s s e d as
2P(f)
frequencies,
energy spectrum
S i n c e we have c o n s i d e r e d o u r s i g n a l
for
Fourier
-T/2
includes
frequencies
defined
from t h e
• ,
0
x ( t ) e _1wt d t | 2
I
j
obtained
= An2 + Bn 2 .
ma g n i t u d e s
of
can be d r o p p e d and t he
APPENDIX B
FORTRAN PROGRAMS
Content s
■
H i s t o g r a m Check
Peak Count
.
Page
...
.
............................. . ' .
. • ...................................... ....
.
o f Two Means
Subroutines:
FRT
.
.'
68
............................. • f
Ener gy Mean F r e q u e n c y and Band Wi d t h
T-Test
.
71
...................
75
..........................................................
78
.............................................................'.
81
ZCROS
......................................
83
GNRATE
.
84
CHECK
.............................
PLOT 2
............................. ....
85
TAPER
.
. ■ ........................"■....................
87
DATAID
.
.
RTAPE
. .......................................................
89
T TEST
.
.
90
PEAK
................... . ' .................................
91
............................
".
85
. '........................................................ 88
. ; ...........................................
n nn
HISTOGRAM CHECK
THIS p r o g r a m c h e c k s t h e
mome nt VALUE, VARI ATI ON,
H i s t o r a m f or f i r s t
AND STANDARD DEVIATION,
AND. FI NDS THE PSEUDO-FREQUENCY OR ZERO-CROSS FREQUENCY
C
.OF THE BRUIT SIGNAL
C
INTEGER BLANK, CLEAR, REM
COMMON I X ( D O l O ) , N P f S , D T , LERR
DIMENSION
R E M ( I S ) , D IS C (6)
LOGICAL L I T / B R U I T
i
DATA B L A N K / ' ■ ■ ' /
L I T=-. TRUE.WR I TE ( I OS, 153') '
153 FORMAT( I X , ' S T E N 0 T l C ' T 1 6 ; ' S A M P L E ' T 3 2 , ' M A X
MEAN MOMENT NCROS' T 6 0 ,
I 'CROSS FREQ' T 7 7 , ' V A R I A T I O N ' T 9 1 , ' S T A N D A R D D E v ' )
WR I T E ( 1 0 8 , 6 )
39 CONTINUE
TREAD=I
REa D ( 1 0 5 , 1 5 0 , END=DDD,ERR=170) CLEAR
150 F O R M A T ( I X , A A )
I F ( CL F A R . N E * B L A NK ) GO TO 170
98 CALL. C HE C K ( L I T )
.
I F ( , N O T , L I T ) GO TO 170"
''
LFRR=O'
'
TREAD = P
■
,
REa D ( N D S K ( I ) , 5 , END=DSD,ERR- 8 8 8 )
CALL C HEC K( L I T )
I F ( , N O T , L I T ) GO TO 170
' '
I READ = 3
■
REa DO-IDSK ( I ) , 7 , E N D = 9 9 9, ERR = 8 8 8 ) BRUI T, DI SCCALL c h e c k ( L i t )'
\
•
’ 1 ■ '
J F ( L I T ) GO TO 170
IREA-D = A
' .
READ( NDSK( I ) , 2 , END=DSD,ERR=888) NPTS
CALL CHECK( L I T)
I E ( L I T ) G6 TO 170
IREAD=B
READ( NDSK( I ) , A , ERRdSSS) NREC
.
. •.
I
O sI
CO
I
Z
DT=•OOOl
FORMAT(1415)
4 FORMAT( 1 5 )
5 'FORMAT (80H
I
6 FORMAT( / / 5
7 FORMAT ( L 6 , 6 A4 )
IF (NPTS)170, 170/ 175
175 TPI=6.P831852
)
1
-69-
• -3 XniPTS =NPTS
PRD=( X N P T S - 1 .> *DT
FST=TPIZPRD
Fl NC=FST
Nl = I
I NI 4 = I 4
N 14 = I NI 4
NCARD=( NPTSZI NI 4)
CRD=NCARO
CDS=XNPTSZI N14
I F ( COS, EQ. CRD) GO T8 51
NCARD=( NP TS ZI N1 4 ) + !
51 DO' 60 L = IzNCARD
CALL CHEC K( L I T )
IF ( L I T ) G G TB 170
' IREAD=A
REa D ( NDSK( I ) , 2, ERR = 8 8 8 ? ( I X ( I ) , I = N l , N 14)
42 FORMAT( 1 5 1 5 )
. DO 43 I L = M l , N14
43 CONTINUE
NI I = NI + I NI 4
N 14 - N 14 + I N14
60 CONTINUE
.
’
TL=O
DB 41 I = I z N P T S
TL = TL+IX.( I )
41 C&NTINUE
MFAN=TLZNPTS
KMAX=O
DB 40 • I = V NPTS
C
40
I
155
154
c
REMOVE THE DC COMPONENT OF. THE SIGNAL
I X ( D = T X d 5"MEAN
IF(IABsnX(I)D LT-KM AX)
GO TO 40
KMAX=IABSfIX(I))'
•
IMAX= I X ( I )
CONTINUE
. '
CALL ZCROS(NCROSZXHZ)
CALL• ■
D A T A I D ( MEAN, KMAX, MOMENT,VARI A N , STDEV)
WR I T E d 0 6 , 7 ) BRU I T , D I SC
WR I T E ( 1 0 6 , 1 5 5 ) BRU I T , ( DI SC( 1 1 ) , 1 1 = 1 , 3 ) , I MAX,MOMENT,NCR0S,X H Z , VARI AN
, STDEV
FORMATi 1,X, L I , I X , 3 A4 , I X, I 4 d X > I 5 , I X , I 5 , 3 < I X, E 14 • 5 ) )
WR I T E ( 1 0 0 , 1 5 4 ) BRUI T , DT S C , I MAX,MEAN,MOMENT,NCRQS , X H Z , VAR I A N , STDEV.
FORMAT ( L 4 , I X , 6A..4', I X , 14, I 6 , 2 X , 16, 2X, I 5 / 3 ( 2 X , E 1 4 . 5 ) )
GP TO 99
error
routine
70-
170 CONTINUE
VJR I TE ( 1 0 8 , 151 )
838 WR I T E ( 1 0 8 , 2 5 ! R E A D , LERR
151 FORMAT(' ERROR IN READING THI S SAMPLED
171 READ( 1 0 5 , 1 5 0 , E N D = 9 9 9 , ERR=SSS) CLEAR
■ I F ( C L E A R - N E - BLANK) Ge TB 171 :
GO TO 98
999 CALL E XI T
,
END
■^
,
' D "
•
D n. Cl Cl Tl
PROGRAM
PEAK
THI S PR9 GRAM PLQTS THE ENERGY SPECTRUM,
PRI NTS THp FI RST 5Q COEFFI CI ENTS, .
AND COUNTS THE MAJOR PEAKS
D I MENS I QN RM ( 8 4 0 0 ) , RN ( 4 2 qo >, DAT A ( . 2 , 4 2 0 0 ) ' TABLE ( 4 2 0 0 )
DIMENSION I X ( R4 0 0 )
D I MENS'! QN D I S C I ( 2 0 )
DIMENSION D I S C ( 6 )
DIMENSION PDS( 5 0 )
COMMON Mj Nj RMj RN'
LOGICAL L I T j BRUI T
DATA BL ANK/ !
'/
LIT='TRUE.
TPT=6 . 2 8 3 1 8 5 3
I S =O
REWIND I
99 CONTINUE
READ( 1 0 5 / 1 5 0 j END=999, ERR=170> CLEAR
I F ( C L E A R , N E * BLANK) GO TO 170
'98 CALL CHECK ( L I T )
I F ( . N O T , L I T ) GO TQ 170
■.
■READ(MDSK( 1 ) , 1 5 2 j END=999 j ERR=8 8 8 ) D I S C 1
152 FORMAT(20A4)
WR I T E ( 1 0 8 , 1 5 2 ) DI SCI
CALL CHECK( L I T)
I F ( . N Q T , L I T ) GO TO 170
RFAD(.NDSK-( I > , 7 ' E N D = 9 9 9 j ERR = 8 8 8 ) BRUI T j D LSC
WR I T E ( 1 0 8 j 7 ) BRUI T j D I SC
1
CALL CHECK( L I T)
J F ( L I T ) . GO TO 170
READ( NDSK( I ) J 3> END = 9 9 9 j ERR = SSS) M
MD I M= 8399
■IF(M»GT«MDIM) GO TO 170
CALL CHECK(LIT.)
I E ( L l T ) GO TO 170
READ( NDSK( I ) j I / END= 9 9 9 / ERR=SSS) DT
I F O R M A T ( 1 X / F 1 4 , 3)
' .
y
_ '
'I
2
3
- '4
6
' 7
12
8
5
'
I
HO
I
115
120
125
131
150
C
42
38
C
'
24
25
32
C
F O R M A T ( I X , 14)
FORMAT( 1 5 )
FORMAT( i X , 15)
FO.RMAT( I X , / / )
FORMAK 1 X , L 5 , 6 A 4 ) : •
'- ,
F 0 R M A T ( 4 ( 16 , SE 1 4 * 6 ) )
'
K
F 0 R M AT ( 4 ( 2X ^ I 4>2 ( I X , E1 3 « 6 ) ) )
FORMAT{ 80H
)
FORMAT ( 8QH
'
. )
F O R M A K I X , • ■ .MEAN? ' I R )
FORM AT ( I X , 9 F l 2 > 3 ) ..
■• ■ '
FORMAT( ' I ' )
FORMAT( 14 F5 t O)
FORMAT( I X , A 4 )
READ .IN DATA
'
'
READ( 1 0 5 , 4 2 , END =9 9 9 , ERR = 8 8 8 ) ( R M ( I ) , I = 1, M)
FORMAT( 1 5 F5 « 0 )
DO 38 1 = 1 , MIX(I)=R M (I)
find
POWER OF TWO OR n e x t SMALLER
RDn Gs =M
MPTS=M
P T =ALPG(RDNGS)ZALOG( 2 . 0 )
IT=IFIX(PT) ■
Ni = R * * I T
RMAX=ABS( RM( I ) )
DO 25 J = I , M
IF(ADS(RM(J))-RMAX) 2 5 , 2 5 , 2 4
RMAX= ABS ( RM( J ) )
CONTINUE
XMa X=RMAX
DO 32 1 = 1 , M
RM( I ) = 1 0 0 0 . * R M ( I ) / RMAX
CONTINUE
CALL GNRATE
WE HAVE GENERATED RN(N) FROM R M( M) , MUST ADD IMAGINARY PART
DO 20 • 1 = 1 , N
' DATA(Ij I ) - R N ( I )
DATA( 2 , I ) = 0 , 0
20 CONTINUE
• CALL TAPER( DI SC V D I SC j NPt S j D I j I X j B R U I T )
CALL -FRT
( DATA, T ABL E, I S , N , - I )
I S = -I
NR I T E ( 1 0 8 , 36)
36 FORMAT( / '
HZ
PDS
IBN
XLAM
' /)
• MPAN= I F I X ( DATA( I , 1 ) / F L 0 A T ( N ) )
U:R I TE ( I OS, 115} MEAN
MF=NXZ- I
MFT=MF
' WR I T E ( 1 0 8 , 3 7 ) MF
37 FORMAT( I X , 'NUMBER OF COEFFI CI ENTS = ' 15)
I F ( MFT »GT -50') MFT = 5o
WR I T E ( 1 0 6 , 7 ) B R U I T , D I S C
D" 111 K=1, MFT
HZ=K/(DT*(M-D)
XL AM=TPDHZ ■
AN=2 - * D A T A ( I , K + I ) / F L O A T ( N )
112
Ill
170
888
151
RN = S - V D A T A ( 2 , K + l ) / FLOAT (N)
P0S(K)=AN**2+BN**2WR I T E ( 1 0 8 , 1 1 2 ) K , H Z , P D S ( K ) , A N > B N , X L A M
Iv1R I T E ( I- O6 > 112) K, H Z, P DS ( K ) , AN, BN, X'L AM
FORMAT( I X , 1 3 , 7 ( 2 X , E 1 3 - 6 ) ) .
CONTINUE
W R I T E ( I D S , 125)
WRI TE( 1 0 8 , 7 ) B R U I T , D I S C
WR I TE ( 10-8, 6)
CALL PEAK(MFT,PDS) '
CALL P L B T 2 ( P D S , M F T , , TRUE. )
WR I T E ( 1 0 8 , 125)
GO TO g,9
ERROR ROUTINE
CONTINUE
WR I T E ( 1 0 8 , 1 5 1 )
W-RI TE ( 1 0 8 , 6 )
FORMAT!' ERROR IN READING THI S SAMPLED
171 R E A D ( 1 0 5 , 1 5 0 , E N D = 9 9 9 , E R R s g 8 8 )
I r (CLEAReNEoBLANK) Sfr TQ 171
GS TS 98
999 • ENiD F I L E I
REWI ND. I
END
CLEAR
n n
C
C
' BRUI T PROGRAM 10
J M BOWERS
CALCULATION OF THE MpAN FREQUENCY AND THE
WIDTH OF THE FREQUENCY B a n D (ABOUT THE MEAN)
'WHICH CONTAINS 90% OF THe SIGNAL ENERGY
logical
C
C
C
bruit
D I MENS ION R M ( S l O O ) , RN( 42Q0) , DATA ( 2 , 4 2 0 0 )
DIMENSION T A B L E ( 8 4 0 0 ) / D I S C I ( 2 0 )
D I MENS'! ON D I SC ( 6 ) / PDS ( 2 IQO >/ HZ ( 2100 )
COMMON M, N, RM, RN
■ REWIND I
LINE=I
10 CALL RTAPE ( DI SC I , D I S C , D T , BRUI T , & 9 9 } .
FI ND POWER OF 2 FOR INTERPOLATION SCHEME
FM = M
PT=ALOG( F M) / A L 0 G ( 2 , 0 - )
• It=IFIX(PT)
M= 2 # * I T
NORMALIZE SIGNAL : MAX=IOOO
RMAX=ABS( R M ( I ) )
DO 25 J = I z M
TF(RM(J)-RMAX) 2 5 , 2 5 , 2 0
20 RMAX=ABSf RM( U) )
;
25 CONTINUE
DO 30 1 = 1 , M
30 R M ( I ) = 1000»* RM( I-) XRMAX
GENERATE INTERPOLATED SAMPLE RN(N) '
CALL GNRATE
DO 35 1 = 1 , N
,
•
DATA( I , I ) = R N ( I )
35 DATA ( 2 , D = O - O
IS =O
IFRD=-I
CALL F R T ( D A T A , T A B L E , I S , N , I F R D )
MI DF = N/ 2 - I
HAE = O
DO 40 K = D M I D F
HZ(K)=K /(D T*(M -1))
AN = 2 . ^ D A T A f D K + 1 ) / FLO AT (N)
40
45
50
55
65
70
75
SO
85
90
I
HO
115
120
I
100
101
-76-
60
5 N = 2 » * D A T A ( Z , K + 1 ) / F L B A I (N)
PDS( K) =AN* * 2+BN* * 2
HAF=HAF+PDS(K)
HALF=O
ne 45 I = I z M l D F
P I NC = PDS( i>
h a l f =h a l f + p i n c
HAF
=HAF
-PINC
I F ( H A L f -HAF) 4 5 , 5 0 , 5 0
CONTINUE
FMf a n =HZ( I )
MFEN
=I
‘ .
PMEAN = P D S ( I )
PTCiT
=0,0
DO 55 J = I z M I D F •
PTOT
= p TBT + p DS( U )
1
P9=0.9*PTBT
PSUB
=PMEAN
DB 85 J = I z M I D F
I F ( MEEN - J ) 7 0 , 7 0 / 6 5
PGljB = p SUB + PDS ( MEEN- J) •
■
ILOW =MEEN-J
I F ( MI D F - ME E N - J ) 8 0 , 7 5 , 7 5
. . .
PSUB
=PSUB-S-PDS (MEEN + J )
' ■
I H I f i H s J+MEEN
• .
I F ( PSUBrPS) 3 5 , 9 0 , 9 0
CONTINUE
WOAND =HZ ( IHIGH-)-MZ ( ILQW )
. -J
WR I TE ( I OS,-100 5 BRUI T, DI SC/ FMEAN, W' BAND,
H Z d L n W),. HZ ( I H I G H )
IF (L IN E -I) 115,115,110
IF(LTNE-37)120,.llb,115
'
WR I TE ( 1 0 8 , 1 0 1 ' ) ■
'
LI NE=S
WR I T E ( ! O S , 100) B R U I T , D I S C , FMEANzWBAND,
Hf(ILOW),HZ(IHIGH)
L INE = L I NE +1
FORMAT(L6,6A4,4 ( 2 X , F 1 0 . 4 ) )
FORMAT( IH I , i STEN I , T 9 , ' D I ScR I PT I BN’ , T 3 3 , ' ME A N FREQ
BAND WIDTH f
HIGH FREQt / . )
.
\
~ LL~
'
LDW FREO
Ge T9 10
99 REWIND I
END
I
n o
T TEST SE TW6 MEANS
THI S PRGGRAM WILL ACCEPT TWB SETS SF SUBGRSUPq
C
c
c
b e l o n g i n g to tws d i f f e r e n t p o p u l a t i o n s
A^o p e r f o r m a t t e s t on t h e g r o u p ' s sr p o p u l a t i o n s
C
C
ALSO CHECKING EACH SUBGROUP BY A. T' TEST
WITH
THE TWO p o p u l a t i o n s
DIMENSION E ( 1 0 0 / 2 ) / T R ( 1 0 0 V e ) / N F S ( 1 0 ) / N T S ( 10)
;
DIMENSION A l ( 1 0 ) , A 2 ( 1 0 ) , T ( 1 0 ) , T I ( 1 6 ) , T S ( 10)
LOGICAL B R U I T , I N , ST
115
40
.45
50
60
65
70
'
-78-
30
35
• 105
IN = .f a ls e .
ST=-TRUE*
READ ( 1 0 5 , 1 1 5 )
FORMAT( 1
II= I
I =I
NR=I
IJ =I
J =I
CONTINUE
READt 1 0 5 , 1Q5,END = 6 0 ) . . B R U I T , ! D I S C , XHZ
FORMAT(5X,Ll,I6,20X,F10»4)
GO TS "(AO, 6 5 ) NR
I F ( B R U I T ) GO TS 50
F ( j , 2) = I DI SC
F ( J , I ) =XHZ
J = U+ I
GO TO 30
,
NFSt I D = J - I
JI = I D l
GO TO 30
.
NR=NR+I
I F ( N R . E Q , 3 ) GS TO 85
GS TO 35
I F ( f NST * BRUI T ) GO TO 30
T R{ 1 , 2 ) = I D I S C
T P ( I , I ) =XHZ
I =I +I
■■
.
'
. .
.'x
'
4
- -
.
'
1
•
12 = 1
CALL T T F S H F H R H N H n I 2 H F H i F 2 n , A ' n A 2 )
PRI NT 115
. . . . .
PRI NT I O U A l ( I H N F S ( I I - I ) , A 2 ( l ) / N T S ( I J - I ) , T ( I ) .
104 FORMAT(
.
.
/ / , ' INNOCENT POPUL
I A T I ON MEAN = r , 2 X , E l 4 . 5 / t
pOR’ / I S H
S A M P L E S ' , / , ' STENOTIC POPULATI
29N M E A N = ' , ? X , E 1 4 , 5 , ' . F S R i , 15, '
S A M P L E S ' , / / / , ' T TEST OF INNOCENT
3 POPULATION VERSUS STENOj i C POPULATION Y I E L D S ' , F 7 * 3 , / / / ) PRINT 107
107 FORMAT ( ' if SAMPLES I T TEsT OF I
MEAN
I
VS INNOC SAMPLE POP
I I
VS STEN SAMPLE POP
' )
103 FORMAT ( 4 X , 1 4 , 3X, ' | ' , 3 X , 16 , 2X, ' I ' , I X , F 8’«3, I X , ' T ' , 5 X , F 8 * 3 , 10X, » I ' , 5X
I
, F8 . 3
)
1
' PRI NT 109
...
.............................
109 FORMAT ( ' .................. _ _ _ _ _ _ _ _ _ _ _ ................. ........................................................................ —
I )
PRI NT H O
12 = 1
-79-
G? TO. 3 5 ...................................
80 NTS ( U 1) = I - I
TJ=IJ+!
GO TQ 35
85 CONTINUE '
IE l=J-I
1
IEE=I-I .
,
PRINT 1 0 6 , ( ( F ( L ' M ) , M = i , 2 ) } C = l ' I F l )
PPJNT n o
PRINT 10 6 1 (.( TR C UN ) , M = l ; 2 ) , l _ T l , I F 2 )
10-6 FORMAT ( 1 X , F 1 0 . ' 3 , 1 X , F 1 0 , Q )
PRI NT H O
H O FORMAT ( I X , / )
■ :
_
JR =II-I
.
.
PRINT " 1 1 2 / (NFS ( IP')-/ I P = V l G )
IC =IJ-I
PRINT H P H N T S ( I P ) H P = H I Q )
112 FORMAT( H ( I X , 1 7 ) )
PRINT 125
125 FORMAT ( 1H )
Tl = I
C
.
.
.
-
. ■
-T
80
IFE=I-I
... . ;
’
CALL TT EST( T R / T R / S T / 1 1 / I 2 , I F l / I F 2 / T S / A I / A 2 )
I FB = J - I
.........................................,
.
CALL T T E S T . ( T R / F / I N / 1 1 / 1 2 / I F l / I F 2 / T I / A 1 / A 2 )
PRINT 10 3/ - NUMB/ I DN/ A l ( I ) / T I ( I ) / TS ( I )
PRINT H O
I F t I U G T - I ) GQ TQ 97
PRINT 125
END
-
-L = O
94 L aL * l
...
,
....
TI TS 0NE MQRE THAN p. QF MEANS/ I S J ARE QN1E- MQRE THAN # QF SAMPLES
TF ( I I - L - I t E Q t O ) GB TB 95
NUMB =NFS ( I I - U - N F S ( I i - L - I )
I I = NFSt I I - L - D + l
•
r,0 TB 96'
55 I l = T •'
NUMB =NFS( I )
56 I F l = N F S ( I I - L )
IDN =Ft H / 2 )
IFB = J - I
.......
CALL T T E S T ( F , F , S T / 1 1 / 1 2 / IF I / I F 2 , T I / A l / A 2 >
IFB=I-I
...
CALL TTEST( F / T R / I N / I l / 1 2 , I F l / I F 2 / T S / A l / A S )
>
PRI NT 1 0 3 , NUMB, I D N / A l ( 1 ' ) / T I ( I ) / T S ( I ) ■
PRINT H O
.
'
I F ( I l . G T . l ). GQ TB 94
L =O
97 L =L + 1
I F ( I J - L - I * EQ. O) GB TB 98
NUMB =N T S t I J - L ) - N T S ( I J - L - 1)
'
.
"
' Il=NTSt I J - L - I ) + !
'
'
•
no TO 99
98 I l = I
NUMB=NTS( I )
’
S3 I F l = N T S ( I J - L )
'
. v
I DN=TR( 1 1 / 2 )
CALL
STATEMENTiCALL F K T ( A , T A B L E ' I S , N C P L X , ! S I G N )
PARAMETERS:
A=TH e a r r a y of n c p l x COMPLEX n u m b e r s TB BE TRANSFORMED,( '
WHERE'. NCPLX = E * * (SOME I N T E G E R ) ) , DIMENSION OF A IS g*NCPLX
THE-ARRAY A STORES COMPLEX NUMBERS AS ORDERED PAIRS
OF’ REAL NUMBERS WITH THE REAL PART OF THE WORD IN ODD
ADDRESS STORAGE LOCATIONS AND THE IMAGINARY PART OF THE
NUMBER IN THE .IMMEDIATELY ADJACENT NEXT EVEN ADDRESS
STORAGE LOCATI ON,
■
TABLE=AN ARRAY Qp TABULATED VALUES Op SI N p AND COSINE.
a f t e r an i n i t i a l c a l l s e t t i n g i s = o , t h e s u b r o u t i n e
MAY BE SUBSEQUENTLY CALLED a n y NUMBER Op TIMES '
WI T h IS = I WITH AN EXECUTION TIME SAVING OF ' APPROXIMATELY
1 / 3 . DIMENSION OF TABLE IS 2 * < NCPL X- I K AND- MUST
BE SQ DIMENSIONED IN THE CALLING PROGRAM?'- '
■Is i g m = f i x e d
p o i n t ' v a r ia b l e g i v i n g the d i r e c t i o n of- t h e .
TRANSFORMATION, SETTING I S I G N = - I
GIVES THE FOURIER
SPECTRUM*'NCPL.X;SETTING I S I GN =.+1 GIVES THE INVERSE
I RANsFORM»
,
...
■ J
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
SUBROUTINE FRT ( A, TABLE, I S , NCPLX, I SI GN) '
DIMENSION A ( I ) , TABL E( I ) ■
M=2*NCPLX
J=I
DO 11 I = I , N , 2
JPl=J+!
I P l = I +1
-81-
NCPLX=NUMBER QF COMPLEX NUMBERS TB Be TRANSFORMED.
A MUST BE DIMENSIONED AS TWICE THI S NUMBER IN THE
' CALLI NG PROGRAM.
no no no on n o n o n
n n n n n n n n n n n n n n
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
O T H I S SUBROUTINE PERFORMS t h e f a s t FOURIER TRANSFORM, a l g o r i t h m OF
C OF CORLEY-TUKEY
IF (I-J)2 ,4 ,4
2 TR = A ( J ) '
• TI=A(JPl)
A(U)-A(I)
A(U P l)=A (IP l)
A ( I ) =TR •
A(IP l)=TI
4
M = M /P
.r
'
5 IF ( M - U ) 6 , 1 1 , 1 1
6 U=U-M
M= M/ 2
IF (M -Z )11,5,5
11 U=U+M
MMAX=Z
MCBS=- I
13 I F ( MMAX-M) 1 4 , 9 9 , 9 9
14 iNCRs2*MMAX
P l M l = 3 . 14159265/ FUt i AT(MMAX)
DB 21 M= 1 , MMA X , 2
MCG3=Nc:0S+ 2
MS i N=MCBS+ I
I F ( I S ) 16,16,17
16 AMG = PIM I * F L B A T ( M - I )
TABLF(MCBS)=COS(ANG)
TABLE(MSIN)=SIN(ANG)
17 WI =TABLE( MSI N)
IF( ! S I G N ) 1 8 , 9 9 , 1 9
15 WI =-WI
19 DB 21 I = M, N , INCR
U = I + MMAX
UPl=U+ I
I P l = I +I
TP = T ABL E( MCBS) * A ( U ) - WI * A ( U P l )
T I = T A B L E ( M C B S ) * A ( U P 1 ) + W I * A (U)
A(U)=A(I)-TR
A (U P l)=A (IP l)-TI
A ( J ) = A ( I ) + TR
21 A ( I P 1 ) = A ( I P l ) + TI
MMa X=INCR
■I
CO
no
i
\
n D
OP TR 13.
99 RETURN
EMD
THI S subroutine computes the number of zerq- crqssings IN
SAMPLE ( NCR6S1) AND THE PS e UDOFREGUENCY OF CROSSING (XHZ)
SUBROUTINE ZCROS(NCROS^XHZ)
COMMON I X ( 9 0 1 0 ) /-NPTSz DT^ LERR
' NCROS = O
NPl = N P T S - I
■■■Dr? 10 J = ?. j NPl
I F ( IX (J ),E Q ,I X ( J - I ) ) GO
Te 10
-83-
2 I F ( I X ( J ) ) 4,10,5
THE
4 I F ( I X( J +1 ) >10,9,9
5 I F ( I X( J+1 ) ) 9 ,9 ,1 0
9 NCROS=NCROS+I
■10 CONTINUE
. . '
XHZ = FLB-AT ( NCROS) / ( DT*FLOAT ( NPTS) )
20 RETURN .
END
- ^
• •
X'
■
n n o o n n n o n n n n n n
SUBROUTINE GNRATE
D I MENS I ON R M ( 8 4 0 0 ) , R N ( 4200)
COMMON M,N,RM,RN
SUBROUTINE GNRATE PRODUCES THE ARRAY R N ( I ) .HAVING N TOTAL ELEMENTS
FROM THE ARRAY- RM( I ) HAVING M TOTAL ELEMENTS BY USE OF A FOUR TERM
LEGRANG I AN INTERPOLATION SCHEME (NOTE R M ( I ) = R 1
N ( I ) / RM( M) =RN( N) ) ,
V A R I A B L E S , .»
. ' .
RM
GIVEN ARRAY
RN
ARRAY TO. BE GENERATED
M
TOTAL NUMBER OF
ELEMENTS IN RM
N
TOTAL NUMBER OF
ELEMENTS IN RN
IN
ELEMENT NUMBER OF RN BEING COMPUTED
iM
n e a r e s t l o w e r e l e m e n t . o f rm l e s s o n e T
EXACT FLOATING POINT' LOCATION IN THE ARRAY RM OF IN
■
’ X
T-IM H .
'
.
on ■ . ( M - D Z ( N - I ) /
r a t i o of t h e d i s t a n c e b e t w e e n i n d i c i e s o f
RM TO RN,
A= M - I
B= N - I
DN= AZB
R N (I)= R M (I)
R N ( N ) = RM(M)
N Ll= N - I
''
,
do 40 IN-=B.! N L i
'
T= I N - I
T= T * 0 N + 1 *
IM =
T-I
V
..
CHECK FOR PROXIMITY OF LOWER BOUND.
•
.
C
IM -I >32/38/34
3 2
TM =I
GO TB 3,8 .
CHECK FOR PROXIMITY OF UPPER BOUND
'
I F ( IM + 3-M > 3 8 / 3 8 / 3 6
IM= M-3
A= IM
X= T - A
RN (IN )=
(X-l")*(X "2')*(X"3,)*R M (lM )Z(-6,)
C'
34
36
38
'
I
+(X)*
(X -2 ')*(X -3.,)*R M (IM +l ) Z ( + 2 . )
..
1 -
■>
'''
I
OD
-Pa.
I
+ ( X > * ( X - 1 . >*■
( X - 3 ,)*RM(IM+2 ) / ( - 2 , >
+(X)*(X.-1 ?) M X - 2 0 *
RM(IM + 3 ) / ( + 6 , )
40 CONTINUE'
RETURN
- END
.
2
3
C
C
- 85-
CARO 'CHECKING SUBROUTINE
READS A CARD AND STORES I T ON THE
c
' disk
TH e v a l u e of li t is s e t " t r u e f or a LI TERAL' STRING
FALSE'
C
FOR A NUMERIC STRING
'
.
SUBROUTINE C HECK( L I T ) .
COMMON I X ( 9 0 1 0 ) , N E T S , DTfLERR
DIMENSION CARD(SO)
LOGICAL L I T
INTEGER. CARD, B L f N E G , D E C f L Q , L9
DATA L O , L 9 , D E C , B L , N E G / ' O ' , t 9 I , ' , I , ' ' , I - , ' /
LERR=LERR+!
L I T = 'FALSE.
'
•
. READ( 1 0 5 , 1 5 2 , E N D = 9 9 9 , E R R = H ) CARD
152 FORMAT ( S OA l )
WR I T E ( NDSK( I ) , 1 5 2 ) CARD
■ .'
DO 10 TCH = I , 72
■.
I F ( CARD ( I C h ) . G E . L O. AND' CARD( I C h ) »LE' L9. ) GO TO 10
I F ( ( CARDf ICH) .EQ »DEC) . 0 « . ( CARD ( ICH ) , EQ. BL ) . OR« ( CARD ( ICH.) .EQoNEG ) )
I
GO TO 10
...
L I T = * TRUE»
T .
’
10 CONTINUE
60 RETURN
■ 4 FORMAT( 1 5 )
11 WRI TE( 1 0 8 , 4 ) LERR
STOP I
999 STOP 2
END
'^
C
SUBROUTINE P U e i 2 ( X , N , B A R ) .
GROUP; BASIC
REAL X ( N ) , H E A D ( I O ) ' ^
INTEGER
L I NE( 1 0 0 ) , b l a n k , STAR
LOGICAL BAR •
DATA B L A N K , S T A R / ' ' , I * ' /
I F ( N f LT » J ) G0 -JO 25
WRI TE( 1 0 8 , 5 0 2 )
■
DR I 1 = 1 , 1 0 0
■ I LlNE(I)=BLANK/'
■ X N A X = - I . E70
X M I N = . 1«E70
D5
2
.
'
1=1,N
I F ( X C I ) * LT » XMI N ■). -XMIN = X ( I )
I F ( X d ) , G T . XMAXi XMAX = XCl )
2 CONTINUE
I F ( XMAX^XMI N ) 2 5 , 3 , 4
3 XMa X = X M I N + ! .
. XMi N = X M I N - I .
'
4 CR1
NT I NUE
DR 5 I = 1 , 1 0
. Z=I
5 HEAD( I ) = (XMAX-XMIN)*Z/10.+XMIN
WRITEt 1 0 8 , 3 0 0 1 )
WRI TE( 1 0 3 , 5 0 7 ) XM IN,HEAD
' WR I T E ( 1 0 8 , 3 0 0 2 )
WRITEC 1 0 8 , 5 0 4 ) .
DC 6 1 = 1 , N
KPLSTX= ( ( X ( I ) - X M I N ) / ( X M A x ' - X M l N ) > * 9 9 * + 1.
I F ( , NOT, BAR) GO TQ 8
DO 7 K = 2 , KPLSTX
7 LINE(K-I)=STAR
8 L I NE( KPL STX) = STAR
WRITE ( 1 0 8 , 5 0 8 ) I , X( I D , LTNE
I F ( . N f i T . BAR) GO TS IQ
DO 9 K = 2 , KPLSTX
9 LINE(K-I)=BLANK
10 LI NE( KPLSTX) =GLANK
6 CONTINUE
Vc? I TE ( 1 0 8 , 5 0 4 )
RETURN
WR I T E ( 1 0 8 , 5 0 6 )
RETURN
' . "
502 FORMAT ( I H l )
504 FORMAT ( I X , I 4 ( I H- ) , I H , ; 2 0 ( 5H- ' - - " ) / I H - )
507 FORMAT ( I X , 5 X, 1 1 ( F 9 » 3 , i H X ) )
5 Cs FORMAT ( I X , 13, F l 1 , 4 , I H I , 9 9 A1 , A l , I H I )
506 f o r m a t ( i x , 1 2 HPl o t e r E r r o r . )
300.1 FORMAT ( 5 1 X, 12HSCAUNG OR X
)
3002 FORMAT ( I X , 14 ( 1 H - ) , 1 H I , 1 0 ( 9 X , I H I ) / 1 2 X , 1 HX , 2 X , I H L 1 0 ( 9 X , I H I ) )
END
'
4
1
2
3
5
I
s u b r o u t i n e TAPER ( D I S C 1 , D i s c , 'N P T S , D T , " I X , B R U I T )
DIMENSION I X ( I ) , D I S C ( I ) , D I S C l ( I )
LOGICAL BRUIT
WP I T E ( 1 , 4 )
WRI TE( I , I . ) ( D I S C I ( I ) , 1 = 1 , 2 0 ) . .
WRITEf1 , 2 ) B R U I T , (DISC( I ) , 1=1,6)
WRI T E ( 1 , 3 ) NPTS
WR I T E ( 1 , 5 ) DT ■
WRI TE( 1 , 3 ) ( I X ( I ) , 1 = 1 , NPTS)
FORMAT(80H
)
FORMAT( 2 0A4)
FORMAT( L 6 , 6 A 4 )
'
FORMAT( 1 4 1 5 )
FORMAT ( F l O e 6)'
RETURN
END .
-87-
•
Dn on
C
.
5
88
-
.
-
10
THI S SUBROUTINE NORMALIZES THE SIGNAL ( I X ) SB THAT THE NAX VOLTAGE
IN THE SAMPLE = IOOO V.
I T OUTPUTS THE MEAN, FI RST MOMENT ( MOMENT
SECBNn MOMENT OR VARIANCE ( V A R I A N ) , ANq THE STANDARD DEVI ATI ON (
(STDEV).
I T REQUIRES THE NPTS AND THE KMAX PLUS THE DATA ARRAY
SUBROUTINE D A T A I D ( MEAN, KMAX,MOMENT,VARI A N , STDEV)
■COMMON I X ( 9 0 1 0 ) , N P T S , D T , LERR
. '
TOTAL=O
DB. 5' I = I , NPTS
NORMALIZE THE SIGNAL
I X ( I ) = I F I X d X d ) * 1 0 0 0 / F L 0 A T (KMAX) >
TBTAL = T O T A L ^ I X d )
CONTINUE
MEAN=TFlXdQTALZFLeAT(NPTS))MBMENT=O
VARlAN=O
DO 10 J=- I , NPTS
MOMENT = MOMENTdX( U) - MEAN
VARI AN=VARI A N + ( I X ( J ) ^ M E A N ) * * 2 / F L G A T ( N P T S - I )
CONTINUE
STDEV = ABS(VAR I A N ) * * 0 . 5
RETURN
END
■
' ..
Rt a p e • ( d i s c i ^ d i s o d t , b r u i t , * )
DIMENSION RM( S I 0 0 ) / R n ( 4 2 0 0 ) , D I S C ( 6 ) , DI S C I ( 2 0 )
COMMON M/ N/ RM/ RN
' l o g i c a l BRUI T
READ ( 1 > 1 , E N D = 9 9 ) !BLANK
READ ( 1 , 2 ) ( D I S C I ( I ) , 1 = 1 , PO)
READ ( 1 , 3 ) B R U I T , ( D I S C ( I ) , 1 = 1 , 6 )
. READ ( 1 , 4 ) M .
READ ( 1 , 5 ) DT
subroutine
READ (I,ft) (RM(I),I=I,M )
1 FORMAT( I X , A 4
2 FORMAT(20A4
.3 FORMAT( LA, 6A4
4 F O R MA T ( 1 5
)
)
)
)
5 FORMAT( F10- 6 ■ 5
6 FORMAT( 1 4 F 5 « Q )
GO T9 7
99 RETURN I
7 RETURN
END
.
.
-90-
SUBROUTINE' T ' T E S T ( Y l , Y 2 , L G , I l , I 2 , l F i ; i F 2 , T , A i ; A 2 )
DIMENSION Y l ( l O O , 2 ) , Y 2 ( l 0 0 ' 2 ) , T ( I O ) , A K 10 >, A2{ 10 )., X l ( 1 0 0 ) ,
I XE(100 ) .
.
' LOGICAL LO
N l= IF l-Il+ !
NE=IFErIE+!
' . 1
FNl=Nl
FNE=NE
DS
5 1=1,10
5 T(I)=O
L =I
T X l =O
TXE =O
DO 6 K = I l , I F l
6 X l ( K) = Y K K , L)
I F ( . N S T - L O ) GO TO 17
DO 8 K = I E , I F E
8 XE(K)= Y l(K,L)
1
GO TO 100
17 DO 7 K = I E , I F E '
'7 XP(K)=Y 2(K ,L)'
100 DO 10 I = I K I F l
•
.
•
10 T X l = T X K X l ( I )
'■
K.
A U D = T X 1/ FLO AT ( N I )
DO 20 I = I S K F E
'•
''
EO T XS= T X2 + X2 ( I )
'
AE( L ) =T XEXFL OAT ( NE)
'
SXl =O
DO 30 I = I K I F l
'i
30 S X l = S X K ( X K I ) - A l ( L ) ) * * 2
••
SXE=O
' DO 40 I = I E , I F E
40 S X 2 = S X E + ( X 2 ( I ) - A 2 ( L ) ) * * 2
S%AR=((SXl+SXE)/(Nl+N2-2))**,5
T ( L ) = A B S ( A K L ) - A S ( L ) ) / ( SBAR*S0RT ( I • / F N K l • / F N g ) )
50 CONTINUE.
RETURN
END
.
. 100
120
HO
C40
50
60
65
80
' 200
220
250
104
300
SUBROUTINE PEAK( Mf PDS) '
D I MENS I 9N P D S ( 1 ) , N P ( 1 2 ) , L ( 1 2 )
NPTS=BQ
. .
'03 100 J = I f 12
MP( J ) = O
PMAX=O
03 H O I J = HNPTS- - '
. .
I F ( P D S a J H P M A X ) ' H O , I l O f 120
PMAX=ABS(PoS(IJ))
CONTINUE
LSS =O
DO 200 I = Sf NPTS
CHECK SLOPE .
• '
I F ( P D S ( I ) - P D S ( I - I ) ) 40* 5 0 f 60
LS=-I
GO TO 65
LS=LSS
GO TO 65
LS=I
I F ( L S - L S S + Z ) SOOf SOf 200
PK=PDS( I - I ) * 1 0 » /PMAX
KP=PK+!
NP (KP) =NP (KP) 4-1
'
LSS =LS ■'
Mp(105=NP(10)+NP(ll)
U = IO
L(Il)=O
L(IJ)=NP( I J )+ L (I J + l )
IJ= IJ-I
I F ( I J ) 2 5 0 f 2 5 0 f 220
CONTINUE
DO 300 K = I f l l Kl=IO*(K-I)
WR I T E H O S f 104) L ( K ) f K l FORMAT ( I X f 16, I
PEAKS ABOVEH I 6 f t
CONTINUE
RETURN
END
PERCENT')
APPENDIX C
VOLTAGE LI MI TER
Back t o
voltage
of
back z e i n e r
2.6 v o l t s
v o l t a g e woul d
schemat i c
is
of
shown i n
not
insure
h a v i n g a br eakdown
that
Sc h e ma t i c
digital
equi pment .
voltage
limiter
wh i c h was b u i l t
2.6 V VZ
OUTPUT
of
excessive
to
15.
INPUT
15.
anal og
c ha nne l
7.5 K
Figure
1N702,
wer e used t o
reach t he
the f i v e
Fig.
diodes,
the Vol t ag e
Limiter
A
APPENDIX D
POSSIBLE MECHANISM FOR THE BRUIT
This
investigation
the s t e n o t i c
for
the
bruit'differs
13 p a t i e n t s
s p e c t r u m was f o u n d
trated
in
higher
spect r um.
From t h e s e
is
the
from t h a t
studi ed..
to
frequencies
t he
innocent
The e n e r g y i n t h e
stenotic,
distributed
t h a n t h e en e r g y
in
bruit
and c o n c e n ­
the
innocent
s p e c t r u m had an a v e r a g e o f 7 . 5 5 m a j o r
innocent
results,
t he e n e r g y s p e c t r u m o f
of
be more b r o a d l y
The s t e n o t i c
peaks w h i l e
has shown t h a t
spect r um averaged o n l y
speculation
5 . 2 3 peaks.
on t h e mechani sm o f
bruits
possible.
Looking
that
the v o r t e x
a "perfect"
flowing
fluid
discrete
tent
at
multitude
frequency.
of
represented
by t h e
Sh o u l d t h e
pr o d u c e s
is
orifice
in a
a tone of
of
inconsis­
a n o i s e composed o f a
note.
a "slightly
Let
di amet ers
r o u g h " r od
i s ma c hi ne d t o one d i a m e t e r ,
be
on a f i n e l y
half
the ■
the o t h e r h a l f
r od
s t r e a m t wo t on es wou l d be o b s e r v e d , g i v i n g
two
in
the
. From t h i s
roughness
rough"
peaks
diameter.
can be seen
shape be r ough o r
number o f d i f f e r e n t
Be g i n w i t h
bei ng a d i f f e r e n t
discrete
velocity
circular
f r e q u e n c i e s , not a c l e a r
o f wh i c h
in a flowing
phenomena i t
rod or
t h e sound p r o d u c e d
ma c h i n e d r o d .
length
cylindrical
of constant
diameter
shedding
en e r g y d e n s i t y
"slightly
s p e c t r u m.
Listening
to
-94a "very
r o u g h " r od composed o f a l a r g e
diameters,
a large
to
number o f
a large
analogy could
cal
it
peaks
could
be c o n c l u d e d t h a t
in
its
obstruction
innocent
with
wh i c h
distributed
It
during
or
peaks
is
period
such f a c t o r s
in
at
in
If
so,
h a v i n g more
p r o d u c e d by an
producing
pulsatile
be r e c o g n i z e d
f l o w the
i s more l i k e l y
band r a t h e r
16.
using
t o be
t ha n a pur e
of flow
its
this
the
size of
t h e f r e q u e n c y o f a f ew
the energy d e n s i t y
spectrum al ong w i t h
t hr ough the o r i f i c e
peak r a t e
by u s i n g
a "typical"
relating
Fig.
bruit,
than t h a t
f r o m a r od
orifice
Possibly
such as t h e o r i f i c e
shown i n
(non-cylin d r i-
t o make an e s t i m a t e o f
the v e l o c i t y
varying.
constructed
that
a frequency
innocent
The f l o w
this
is
this
and i m p e r f e c t o r i f i c e s .
is
rise
same t y p e o f c o n c l u s i o n may be dr awn.
the g r e a t e r
bruit.
imperfect
spectrum,
shedding
throughout
a value f o r
include
Possibly
t h e p r o b l e ms wh i c h must
analogy
may be p o s s i b l e
a stenotic
still
One o f
vortex
but the
spect r um.
i s more i r r e g u l a r
type of
frequency of
the
the s t e n o t i c
energy d e n s i t y
bruits.
this
tone,
in
r ods
perfect
t o n e s wou l d be hear d g i v i n g
be e x t e n d e d t o
and r o ugh s u r f a c e d )
peaks
of
number o f
number o f
during
this
period,
t h e av e r a g e f l o w
family
of curves
during
rate
could
a v e r a g e t o t h e degr ee o f
but
(LI )
be
obstruction,
d i a m e t e r . ( d Q) . • Such a p r o p o s e d f a m i l y
The members o f
as b l o o d
pressure,
t h e f a m i l y wou l d d i f f e r
pulse
is
by
r a t e , an d/ o r di ameter
- 95of artery
( Cig ) .
A trial
be empl oyed u s i n g t h e
correct
frequency
and e r r o r met hod woul d t h e n have t o
points
along
t he c o r r e c t
curve
i n t he
relationship:
N -
Ug/ 3 ( d a - d o ) . . . i n n o c e n t
bruit
(large
orifice)
N -
0 . 6 Ug/ d o . . .
bruit
( smal l
orifice ),
wher e N i s
the f r equency
hopefully,
arises
through
an o r i f i c e
stenotic
of
the
peak i n t h e
when an a v e r a g e
or approxi mat e
pulsating
spectrum whi ch,
velocity
U passes
Cl
d i a m e t e r dQ, i n an a r t e r y
of diameter d .
Figure
16.
Av er age V e l o c i t y
over Ob s t r u c t i o n
vs
its
Size.
LITERATURE CONSULTED
LITERATURE CONSULTED
Bi ngham, C h r i s t o p h e r ,
ejt aj_.
"Moder n T e c h n i q u e s o f
Power Spec t r um E s t i m a t i o n " , IEEE T r a n s a c t i o n s on Audi o
and E l e c t r o a c o u s t i c s , A u - 1 5, No. 2 ( June 1 967 ) , pp. 56- 66
Bl a c k ma n , R. B . and T u k e y , J . W.
The Measur ement o f Power '
S p e c t r a , New Y o r k :
Dover P u b l i c a t i o n s , I n c . , 1 9 58.
B r a u n , H a r o l d A . , et^ aj_.
" A u s c u l t a t i o n o f t h e Neck; *
I n c i d e n c e o f C e r v i c a l B r u i t s i n 4,296 Consecut i ve
Patients",
Rocky Mo u n t a i n Me d i c a l J o u r n a l , V o l . 63,
5, (May 1 9 6 6 ) , p p . 5 1 - 5 3 .
No.
B r u n s , D. L .
"A Gen er a l T h e o r y o f t he Cause o f Murmur s i n
t h e C a r d i o v a s c u l a r S y s t e m" , Ame r i c a n J o u r n a l o f M e d i c i n e ,
V o l . 27, No. 3 ( 1 9 5 9 ) , pp.
Co c h r a n , W. T . , e_t al_.
" B u r s t Measur ement s i n t h e Fr equenc y
D o ma i n " , P r o c e e d i n g s o f t h e I E E E , V o l . 54, ( June 1 9 6 6 ) ,
p p . 830-841.
C o c h r a n , W. T . , et_ al_.
"What i s t h e Fa s t F o u r i e r T r a n s f o r m ? "
IEEE T r a n s a c t i o n s on Audi o and E l e c t r o a c o u s t i c s , A u - I 5,
No. 2 ( Juns I 967 ) , pp. 4 5 - 5 5 .
C o o l e y , James W. , e_t aj_.
" A p p l i c a t i o n o f t he Fast F o u r i e r
T r a n s f o r m t o C o mp u t a t i o n o f F o u r i e r I n t e g r a l s , F o u r i e r
S e r i e s , and C o n v o l u t i o n I n t e g r a l s " , IEEE T r a n s a c t i o n s on
Au d i o and E l e c t r o a c o u s t i c s , A u - T S , No. 2, ( June 1 9 6 7 ) ,
pp. 7 9 - 8 3 .
C o o p e r , Geor ge and McGi 11em, C l a r e .
Met hods o f Syst em and
S i g n a l A n a l y s i s , New York.: H o l t , R i n e h a r t and Wi n s t o n ,
1 967.
D u r i n , R. E . , e j t a l _ .
" H e a r t Sound S c r e e n i n g i n C h i l d r e n by
A n a l o g - D i g i t a l C i r c u i t r y " , P u b l i c Health R e p o r t s , V o l .
80 , No. 9, ( S e p t e mb e r 1 9 6 5 ) , pp. 7 6 1 - 7 7 0 .
Gr e en, D. G.
" P h y s i o l o g i c a l A u s c u l t a t i o n C o r r e l a t i o n s : Heart
Sounds and P r e s s u r e P u l s e s " , I n s t i t u t e o f Radi o E n g i n e e r s
T r a n s a c t i o n on Me d i c a l E l e c t r o n i c s , V o l . PGME- 9 ,
( December 1 957) , pp. 4 - 5 . •'
-98Hel ms, Howard D.
" F a s t F o u r i e r T r a n s f o r m Met hod o f Comput i ng
D i f f e r e n c e E q u a t i o n s and S i m u l a t i n g F i l t e r s " , IEEE
T r a n s a c t i o n s on A u d i o and E l e c t r o a c o u s t i c s , A u - I 5, No.
2 ( June 1 9 6 7 ) , pp. 8 5 - 9 0 .
J a c o b s , J . E . , et _aj _.
" F e a s i b i l i t y o f Aut omat ed A n a l y s i s o f
Phonocar di o g r a m " , ( u n p u b l i s h e d r e p o r t ) . Bi omedi cal
Engi neer i ng Center Te c hno l ogi c a l I n s t i t u t e , Nort hwestern
U n i v e r s i t y , Evanston, I l l i n o i s (1968).
L a n d o wn e , M i l t o n .
"A Met hod Usi ng I n d u c e d Waves t o Sfrudy
P r e s s u r e P r o p a g a t i o n i n Human A r t e r i e s " , C i r c u l a t i o n
R e s e a r c h , Vol . V, ( November 1 9 5 7 ) , pp. 5 9 4 - 6 0 1 .
Lees,
S i d n e y and D o u g h e r t y , Ray C.
" Numeri cal F o u r i e r
Tr ans f o r m C a l c u l a t i o n s f o r Pul se T e s t i n g P r o c e d u r e s " ,
Ame r i c a n S o c i e t y o f Me c h a n i c a l E n g i n e e r s Paper No. 66,
A u t - A , (May 24, 1 9 6 6 ) .
L e p e s c h k i n, E. and L a r e a u , D.
" Q u a n t i t a t i v e A u s c u l t a t i o n of
H e a r t Sounds w i t h I n t e r n a l C a l i b r a t i o n " , I n s t i t u t e o f
Radi o E n g i n e e r s T r a n s a c t i o n s on Me d i c a l E l e c t r o n i c s ,
Vol . PGME- 9 , [ December 1 9 5 7 ) , p. 16.
Mal i n g , Geor ge C . , ejt aj_.
"Digital
Oct ave and F u l l Oc t a v e S p e c t r a
IEEE T r a n s a c t i o n s on Au d i o and
A u - I 5, No. 2, ( June 1 9 6 7 ) , pp.
Mc Don al d, Donal d A.
Bl ood
A r n o l d , L t d . ( 1 960) .
Determination of Thirdof Acoustical Noise", ■
Electroacoustics, Vol.
98-104.
F l ow i n A r t e r i e s .
London:
Edward
R a p p a p o r t , M. B.
( D i s c u s s i o n o f S e s s i o n I - A)
" Symposi um:
P r e s e n t S t a t u s o f H e a r t Sound P r o d u c t i o n and R e c o r d i n g " ,
I n s t i t u t e o f R a d i o E n g i n e e r s T r a n s a c t i ons on M e d i c a l .
E l e c t r o n i c s , Vol . PGME-9, [ December 1 957 ) .
R e n n i e , L a u r i e , ejt a%.
" A r t e r i a l B r u its in Cerebrovascular
D i s e a s e " , N e u r o l o g y ( M i n n e a p o l i s ) , V o l . 14, ( Au g u s t
1 9 6 4 ) , pp. 7 5 1 - 7 5 6 .
R o d b a r d , Si mon.
" V a s c u l a r M o d i f i c a t i o n s I n d u c e d by F l o w " ,
Ame r i c a n H e a r t J o u r n a l , V o l . 51, No. 6 ( June 1 9 5 6 ) ,
• pp. 9 2 6 - 9 4 2 .
99R o d b a r d , S i mo n .
" P h y s i c a l For c es
An n a l s o f I n t e r n a l M e d i c i n e ,
. I 959) , pp. I 339- 1 351 .
and t he V a s c u l a r L i n i n g " ,
Vol . 50, No. '6, ( June
R o d b a r d , Si mon and J o h n s o n , A l o n z a C.
" D e p o s i t i o n o f Fl o wbor n M a t e r i a l s on Vessel W a l l s " , C i r c u l a t i o n Re s e a r c h ,
V o l . X I , ( O c t o b e r 1 9 6 2 ) , pp. 6 6 4 - 6 6 8 .
S c a r r , R. W. A.
" Z e r o C r o s s i n g s as a Means o f O b t a i n i n g
S p e c t r a l I n f o r m a t i o n i n Speech A n a l y s i s " , IEEE
T r a n s a c t i o n s on A u d i o and E l e c t r o a c o u s t i c s , Vol . A u - 1 6,
No. 2, ( June I 968) , pp. 2 4 7 - 2 5 5 .
Si mps o n, E r n s t , and Nakagawa, K.
" E f f e c t o f Age on Pul se
Wave V e l o c i t y and ' A o r t i c E j e c t i o n Ti me ' i n H e a l t h y Men
and i n Men w i t h C o r o n a r y A r t e r y D i s e a s e " , C i r c u l a t i o n
R e s e a r c h , V o l . X X I I , ( J u l y I 9 6 0 ) ' , pp. 1 2 6 - 1 2 9 .
S m i t h , D. H . , ejt al_.
" P o s s i b l e Appr oac h es t o M u l t i p l e Channel Tape R e c o r d i n g f o r B i o m e d i c a l P u r p o s e s " ,
I n s t i t u t e o f Radi o E n g i n e e r s T r a n s a c t i o n s on Me d i c a l
■ E l e c t r o n i c s , Vol . ME- 6, No. 3” ( Se p t e mb e r 1 9 5 9 ) ,
p p . 171-174.
T a b a c k , L . , e_t aj_.
" D i g i t a l Recordi ng o f E l e c t r o c a r d i o ­
g r a p h i c Dat a f o r A n a l y s i s by a D i g i t a l C o mp u t e r " ,
I n s t i t u t e o f Radi o E n g i n e e r s T r a n s a c t i o n s on Me di c al
El e c t r o n i cs , Vol . ME- 6, No. 3~, ( Sept ember . 1 959) ,
pp. 1 6 7 - 1 7 1 .
Volk,
William.
A p p l ied S t a t i s t i c s f o r E n g i n e e r s ,
New Y o r k ,
T o r o n t o and L o n d o n :
M c G r a w - H i l l Book Company, I n c .
1 958.
3 1762 1001 I092 9
N378
B677 Bowers, Joel Morris
cop.2
A study of arterial
blood noises
MAMK
AND
AOC
W 31%
'BCll
Cof a