Calhoun: The NPS Institutional Archive
Theses and Dissertations
Thesis and Dissertation Collection
1968-12
Analysis and synthesis of a time limited complex
wave form.
Post, Jerry Lee
Monterey, California. Naval Postgraduate School
http://hdl.handle.net/10945/40076
UNITED STATES
NAVA'L POSTGRADUATE SCHOOL
••
THESIS
ANALYSIS AND SYNTHESIS OF A
TIME LIMITED COMPLEX WAVE FORM
By
Jerry Lee Post
De cember
· Thesis
P7483
1968
=======================~
T~ dooument h~ been appAoved 6oA
.te.~e and ~ a.le.; 1.:U dU.t!Ubu..tion .iA
public Aeunlimited.
•
ANALYSIS AND SYNTHESIS OF A
TIME LIMITED CO:MPLEX WAVE FORM
By
Jerry Lee Rost
Lieutenant, United ~ tates Navy
B.S., Naval Academy, 1961
Submitted in partial fulfillment of the
requirements for the degree of
ELECTRICAL ENGINEER
from the
Naval Postgraduate School
December 1968
Signature of Author
/l/
•......
~'
I
Approved by
The si s Adv i s or
Reader
Chairman, Department of Electrical .Engineering
•
Academic Dean
•
ABSTRACT
The problem of analyzing time limited complex wave forms
having time variant frequency domain characteristics is discussed.
A bell tone is selected as a wave form to analyze and it is then
synthesized to produce an approximation to the original sound.
An electronic device is constructed to simulate all required fog
signals for a sailboat, including a rapidly ringing bell .
2
LIBRARY
NAVAL POSTGRA DUA TE SCHOOL
MONTEPEY, ~DLfF. q39~0
•
TABLE OF CONTENTS
Page
9
SECTION
1
INTRODUCTION
SECTION
2
THE CHARACTER OF A BELL TONE
ll
SECTION
3
RECORDING THE BELL
14
SECTION
4
ANALYSIS
17
4.1
Dis crete Method
17
4. 2
Continuous Method
24
4. 3
Compar ison of Methods
24
SECTION
5
REDUCED VISIBILITY WARNING DEVICE
26
5.1
Discuss i on
26
5.2
Timing Circuitry
26
5 .3
Des cri ption of the Entire System
32
i
SECTION
SECTION
6
7
APPENDIX 1
SYNTHESIS OF THE BELL TONE
36
6.1
Syn thes i s by Discrete Computat i on
36
6.2
Synthesis of t he Bell Tone by
Electron i c Circuitry
37
44
SUMMARY
7.1
Analys i s
44
7.2
Synthesis
44
BELL SPECTRUM BY DISCRETE ANALYSIS
47
1.1
Bell Spectrum , Mean Time 0 . 0625 se conds
48
1.2
Bell Sp ec t r um, Mean Time 0 . 1875 seconds
49
1.3
Bell Spectrum, Mean Time 0.3125
so
1.4
Bell Spectrum , Mean Time 0.4375 seconds
51
1.5
Bell Spec trum, Mean Time 0 . 5625 seconds
52
1.6
Bell Spe ctrum, Mean Time 0 . 6875 seconds
53
3
Page
APPENDIX 2
COEFFICIENT AMPLITUDES VERSUS TIME FOR THE BELL
54
2.1
Frequency 565 Hertz
55
2.2
Frequency 1370 Hertz
56
2.3
Frequency 2331 Hertz
57
2.4
Frequency 3061 Hertz
58
2.5
Frequency 3320 Hertz
59
2.6
Frequency 3770 Hertz
60
APPENDIX 3
SUBROUTINE SAMPL
61
APPENDIX 4
SUBROUTINE FORM
64
APPENDIX 5
FAST FOURIER TRANSFORM ANALYSIS PROGRAM
65
APPENDIX 6
REQUIRED FOG SIGNALS FOR A SAILBOAT
66
APPENDIX 7
SCHEMATICS FOR THE REDUCED VISIBILITY WARNING
EQUIPMENT
67
4
•
.
•
•
LIST OF TABLES
If
Page
TABLE I
Partials of a Bell Tuned to the Note F
13
TABLE II
Partials of the Fog Bell
23
•
5
•
..
•
••
,
•
LIST OF FIGURES
Page
FIGURE 1
Unijunction Master Oscillator
27
FIGURE 2
Timing Pulse Train
27
FIGURE 3
One-Shot From
FIGURE 4
Power Supply for the Horn and Bell
31
FIGURE 5
Reduced Visibility Warning Equipment
33
~ 1914
and Discrete Components
29
-Simplified Block DiagramFIGURE 6
Twin-T Oscillator
7
40
•
•
•
SECTION 1
INTRODUCTION
The primary objective of this thesis has been to harmonically
analyze a complex wave form, and then .to synthesize this tone using
solid state circuit ry.
The sound of a ringing bell was chosen to
be evaluated since it represented the most difficult class of wave
forms t o analyze .
The main form of analysis was repetitive sliding
time windows of dis cre te data which were transformed to the frequency
domain .
A Fas t Fourier Transform algorithm was used to transform the
. discrete data .
The techniques are .not original with the author, but
•
they represent a rela tively new applica tion of discrete Fourier
•
analysis on a general purpose .digital . c omputer .
This method .of
analysis i s applic able to any discipline .wherein frequency spectrum
information is desired .
Re c ent and future projects at the U. S. Naval
Postgraduate School in this . area include, but are not limited to,
voice patt ern recognition, helium atmosphere voice distortion, the
study of surfac e waves on water, and squirrel heart-rates under
stimuli .
As a se cond method of spec tral analy sis, an analog .narrow band
spectrum analyzer was employed _to check the results of the d i screte
method .
The compari son .of results was favorable _and -is discussed .
The goal in the synthesis phase of the research was not to
recreate the exact sound, but to . ra asonably simulate it with .an eye
.
to s impl icity and minimum c ost. . Practically, this goal was achieved
with suitable timing cir c uits driving
R~C
os ci llators .
As a check ·· on
the validity of the analysis, this sound was also simulated by
9
digital/ana l og methods.
The waveform was mathematically described i n
the time domain, computed in di screte s te ps and converted to analog
voltages .
These vo l tages were then conv e r ted to sound energy.
To s how the pr acticality of synth e si z i ng the bell, a device was
designed and constructed which employed t he bell sound as the warning
sound f or a vessel at anchor in reduce d . vi s i bility as required by
U. S . Coa st[ l] Guard Ru l es.
To comple te the suite of required fog
s i gnals fo r a sailboat, signals for sai ling on various tacks a nd wh i le
under power were added. *
This reduced _vis ibi l ity warning device wa s
designed f or automatic signalling.
Though t he particular signals were
•
for a sai l boat, the concept is genera l enough for any small vessel
where automatic fog signals may be des i r eab l e .
Use of such a devic e
•
on board small private, Naval, and Coast Guard vessels where the cr ew
may be few i n numbe r and fully occupied with operating the v essel
would be des ireable .
•
*
Refe r to Appendix 6 for a discussion of th e required warning signa ls
f or a sailb oat in reduced visibility .
10
•
SECTION 2
THE CHARACTER OF A BELL TONE
In the literature describing bell sounds or bell tones, the
primary interest and discussions are related to the musical aspects of
these natural sounds.
Most good quality bells are described by their
primary strike note in terms of the musical ljlcale.
Past harmonic
anlaysis of bells in acoustical research dealt almost exclusively with
fine quality church or carillon bells .
There doesn't appear to be
much active research in this field today.
During the period from 1920
to 1935, considerable research effort was applied
•
•
t~ - the
problem .
The physical explanation of the origin of sound from a bell is
an extension of the notion of vibrational plates.
The mathematical
description of the flexural physics is beyond the intent of this
thesis.
>'<
The exact mathematical solution of .this problem has not been
obtained except for the case of thin walled bells.
A bell after being struck gives off a sound composed of several
separate frequencies (partial tones , or · more commonly .-
partials).
Unlike many musical instruments which give off partials in .a nearly
harmonic ratio of 1:2:3:4 ... , a bell.is no.t so constrained.
An
idealized '·s eries for the bell partials would be 1. 0·: !.:.:51 =
·2.02:2.93:
3.43:4.33 . . . **
.
An actual bell does not conform · t'O . this ..ideal series.
The closer a bell is to this series, the purer is the . note from a
qualitative mu sical sense .
•
*
Refer to Lord Rayleigh's., The Theory of Sound; Vol I, p 388
for a more complete treatise on the subject.
**
2
Authors disagree on this 'idealized' series.[ ),[ 3 ]
series given is 1.0:1.65:2.10:3.0:3.54:4.97 . . . .
11
Another
•
The r e appears to be some d isagreement among the various articles
'I
wr i tten on t he subject as to whether the strike no t e is generated by
direct nodal v ibrations, or if it arises as t he result of a beat
f r e quenc y.
[ 4] [ 5]
'
Cu rtis and Giannini appear t o have employed a
pr ec ise and c ontrolled method for arrivi ng a t t heir results.
They
ar gue that th e strike note from a parti c ular be ll which was analy zed in
considerable detail arose as the result of har monious blending of thre e
c lose fr equenc ies .
The various partial s of a bell have independent amplitude ve r sus
time response characteristics.
And to make t he wave form still more
complex, the various partials may commence at s eparate times after . the
bell has been struck.
•
The attack and decay r a t e . of any single partial
may be i ndep endent of all others.
The higher f requenci es of the
•
composit e wave form appear earliest in t he sp ec trum after the bell is
struck , and di e away most rapidly.
Some of t he lower frequencies may
not app ear in the spectrum until as late a s 1 t o 3 seconds aft e r th e
crash.
The f ollowing table was extracted fro m a paper by Curtis a nd
6
Giannini [ ] t o illustrate the frequenc y conten t of a part i cular bell
they studied .
The bell chosen was a church bel l tuned to t he music al
note F (345 . 3 hertz).
The column headed 'Frequency of no te' r e f ers to t he theoret i cal
bell as a musi cian might describe it.
Th e s i gnificant partials found
to be pre s en t in that bell are in t he column headed 'Tone Frequenc y '.
This il lus t r at ion cle a r l y shows that only the s trike note came close
to the de s i r ed frequency.
Additionally , the s t rike note was straddled
by other freq uenc ies causing it to be in a ctua l ity a tr i plet.
12
Curtis
•
•
TABLE I
Partials of a Bell Tuned to the Note F
TONE
FREQUENCY
NUMBER
PARTIAL
FREQUENCY
OF NOTE
NOTE
1
Hum note
172.6
Fl
160
187
2
Strike note
345.3
F
330
345
365
2.4
Third (tierce)
410.6
Gfl
385
450
3
Fifth (quint)
517.3
c
512
4
Nominal
690.5
F
675
700
5
Upper Third
870.0
A
6
Upper Fifth
1034.6
cl
•
.
1060
and Giannini went on to describe for this bell a total of some twenty
significant partials and "a great many more partials which were weak
compared to the ones which are recorded."
To briefly summarize the complexities of the bell tone, one must
list the following:
1.
The wave form is time limited.
2.
The frequencies that comprise the wave form may commence
and end at independent times.
3.
The amplitude of each partial is generally time
independent of all others.
•
4.
The amplitude of each partial is time va riant.
5.
The various frequencies present are generally not
harmonically related.
13
SECTION 3
•
RECORDING THE BELL
The goal of recording the bell signature was to preserve a high
quality da t a base from which to work.
To achieve this end, it was
desireable to have a good signal-to-noise ratio, preserve the relative
magnitudes among the various frequencies present, and to obtain some
flexibil i t y i n playback speed for sampling purposes.
To mi nimize spurious background noise on the recording, the bell
was placed in a large anechoic chamber and r ung by an assistant .
All
recording e quipment except for a microphone was placed outside the
anechoic chamber.
•
The microphone used was an Altec Lansing Model
21BR-150 broad-band microphone .
The microphone was supported a distance •
of 1 meter from the bell on a level with the bell's soundbow.
The b ell was suspended from its crown fitting and held rigidly in
place so that no movement occured other than normal vibrational movement
after being struck.
The supporting structure for the bell was attached
to ceiling and floor fixtures provided for this purpose in the chamber.
Additional required equipment for the microphone outside the
chamber wa s an Altec Lansing Model 526B microphone power supply.
The
response ch aracteristics for the microphone and its associated power
supply are typically within ±1 db
±3 db to 15000 hertz.
from 10 to 3000 hertz and within
A Hewlett Packard Model 466A broad band (DC to
20000 hert z ) amplifier with a selected gain of 20 db was used as a
preamplifie r prior to the tape recorder.
14
•
•
r .- - - - - - - - - - ·- -- - -
t
1
I
I
I
.---------------------~~-+--------- ~
i
I
I
I
L - · ___A~!=~h~i~- ~~~~-e£ _
_J
...___r- ll------j'--------'1 L__
I
i
Mic . Pwr
Supply
Pre- amp
Tape Recorder
Block Diagram of the Recording Process
The recording device chosen was an Ampex Model CP-100 instru-
•
mentation tape recorder.
This choice was made due to the excellent
linear frequency response characteristics offered by the recorder
over the anticipated frequency range of 100 to 15000 hertz .
Two
other salient features available on this tape recorder also contributed to its selection .
1.
These were,
A frequency modulated recording and playback capability .
This feature provides for a linear frequency translation
without the necessity for amplitude compensation when
the playback speed is . different than the record speed .
2.
A wide choice of speeds for frequency translation
purposes to add flexibility to the sampling procedure
(this feature wil l be elaborated on in more length
in the section on analysis) .
The signal was FM recorded at a speed of 60 inches per second .
15
•
This speed and recording method provided a tape recorder band-pass
from essentially DC to 20000 hertz for . the recorded signal.
'
The overall
band-pass of the recorded signal was 10 to 15000 hertz, limited by
the microphone.
Prior to recording the signal, the tape recorder was aligned so
that the non-linearity did not exceed 0.75% (minimum achievable . with
the given equipment) over the recording - range • . An Ampex Model TC-10
alignment set wa s used for aligning the . tape recorder.
The tape . heads
on the recorder were cleaned and demagnitized prior to . recording to
insure a good signal-to-noise ratio • . Four different constant . frequency
test signals were placed on the tape recorder for calibration purposes
after analysis.
The frequency of each of these s ignals was known to
•
within 0.1 hertz.
No attempt to measure the total power output of the bell was
made due to the quite complex three dimensional . sound .intensity pattern
expected from th e bell.
This was .not required .for the analysis, since
the primary concern was to preserve the relative intensities among the
various part ials present in the bell signature .
16
SECTION
4
ANALYSIS
4.1.
Discrete Method
Discrete Fourier analysis simply stated is an extension of
the Fourier Transform or Fourier Integral.
It is a class of procedures
for transforming a time series (discrete data samples) to its finite
Fourier series .
Many methods have been proposed and demonstrated over
the years since Runge and Konig first described their procedures . [l],[B]
The history of modern techniques , expecially the Fast Fourier Transform
(FFT), are both interesting and well documented.[g]
The FFT , a special
case of the discrete Fourier transform (DFT) , is an algorithm for
efficiently computing the finite series transform of the- discrete data
set.
Its application is suitably fitted to discrete computation on
digital computers.
It finds wide application in digital spectral
analysis , filter simulation, convolution and ether related fields.
The signific ant feature that makes this clever technique appealing over
earlier techniques is the rapid method used to perform the desired
operations .
Time and money are inter changeable when discussing digital
computation .
For a comparison of computational time required for the
FFT as opposed to earlier DFT methods , consider a time se-r ies consisting
of N
(N
=
log
2
2
n
samples.
To perform a discreteFourier transferm . using FFT,
N) computational steps are required.
For earlier more direct
2
methods , N computational steps would be required to perform the same
transformation •
For a time series consisting· of N = 10Q4., approximately
a 50 to 1 savings in computational time is realized thrm:rgh use of the
FFT . [ 1 0]
17
The discret e Fourier transform is defined by[ l l ]
N- 1
A
2:
r
r
=
(1)
0,1, . .. ,N-1
k=O
where Ar is the r t h coefficient of the DFT and
~
denotes the
kth sample of the time series which consists of N samples and i
= ;=I
The relationship between the DFT and the Fourier transform is shown
in a paper by Cochran, Cooley, Favor and others .
Sinc e the FFT is an
implementation of this definition, this relationship also defines
the FFT.
Given a time series with a constant sampl ing interval 0t) between
each successive s ample, the sampling frequency is given by
f
s
=
(2)
1/llt
By the Nyquist sampling criterion, the resultant bandwidth recovered
from the signal of interest would be
=
Band Wid th
B
(3)
1/2/:::.t
f
s
/2
( 4)
This of course is only true if the signal is band-limi ted to B
before being sampled.
signal, say f
1
(B
<
f
Given a frequency higher than B in the original
1
<
2B), then a finite Fourier s er ies for the
2
signal after analysis would reveal a spectral line at f -B.[l ]
1
This
aliasing can be observed with a stroboscope and a rotating machine, or
more amusingly, by watching the wheels of a stage coach in a movie
appear to rotate i n the incorrect direction.
To recover correctly
the frequencies present below B, the signal to be samp led must be
filtered before s ampl ing.
Even with filtering, some error is introduced
18
•
since it is impossible to completely band-limit a signal.
'
Practically
speaking this error is small and can be ignored if the filter chosen
has a high roll-off and the corner frequency is chosen with care .
The FFT yields a finite spectrum of N/2 distinct lines for N
Therefore these lines will be separated by ,.~f where
B
2B
(5)
M =
N/2
N
f
s
(6)
M
N
sampled data points .
With a time variant signal (the coefficients of the associate d Fourier
series vary with time) this simple r elationship yields a paradox of
accuracy .
•
For a fixed sampling rate . (i.e . , f
made large with respect to f
s
is fixed), N must be
to recover a small
s
~f .
But if
N~t
is large compared to the time over which the coefficients vary significantly, then the coefficients recovered by analysis will be averaged
over the time series duration .
If . N is made small with respect to f ,
s
the average coeffi c ients r ecovered will be closer to the true value at
the beginning and the end of the time . series .
course, is that
~f
The penalty paid, of
would now be larger and the spectral lines would
be farther apart . [lJ ]
This para do x is yet another form of the well
known uncertainty princ i ple .
A desireable compromise would be t o have
the coefficients change only a small amount over the period
yet have a suf ficiently small
quenc ~e s
N~t
:, and
to discriminate between adjacent fre -
~f
present in the spectrum .
Stated . in another way , the goal in
analyzing a non-periodic wave form is to achieve . a quasi-stationary
process over which
~f
and the resultant coefficients can be meaningful .
There are many permutations of f
19
s
and N to obtain such a result . One
technique used in this research was to analyze a time series once to
obtain a fine
~f,
and then to analyze the same ser ie s again to obtain
reasonably accura te coefficients.
For the spectral analysis of the bell tone, the recorded signal
was filtered, amplified, sampled at constant intervals, and then stored
on magnetic tape as the discrete time series.
The recorded .signal .
was played back for sampling at 1 7/8 inches per second which yielded a
frequency translation of 32 to l .over the recorded speed . of 60 inches
per second .
This was done primarily due .. to sampling ra te limitations
caused by the manner in which the sampling .was performed.
By sampling
with the program as written (see Appendix 3), samples were written
on magnetic tape after a set of 128 -were collected .
The upper sampling
rate achievable by this method is limited _by . the . magnetic . tape write
speed , which is around 1800 hertz for the stated record length.
The
sampling program stored 520 sequential records of . l28 samples per record
on a 7 track magnetic tape.
hertz .
The sampling frequency used was 1024 . 0
When this sampling frequency is . translated by 32 ( to correct
for the tape speed re duction), a true sampling speed of 32,768 hertz
is realized.
By the Nyquist sampling criterion, this sampling frequency
produces a bandwid th of 16,384 hertz.
This band width is slightly in
excess of that of the recorded signal.
Prior to sampling, the signal. was amplified to ·a peak value of
about 60 volts to minimize the noise introduced by the sampling -process.
Between amplification stages . the bell tone was passed . through a . continuous
band-pass filter.
Ths band-pass of the filter was flat from 10 hertz to
150 hertz and was down 3 db at 260 hertz.
20
This upper 3 db point corresponds
•
'
to 8320 hertz when translated.
This band-pass filter upper limit may
seem low based upon the band- pass of other phases of the recording and
sampling process.
Later analog analysis showed that the original signal
did not contain significant energy in frequencies higher than 6000
hertz.
The sampling frequency was chosen at
32~768
hertz (actual) since
this is a power of two and corresponds to an integer separation of
frequencies in the spectra for a sample size of N -= 4096 .
By formula 5,
~'~f.:_ = 32768
4096
=
8 hertz
For complete analysis of one segment of the signal ,.. the record
size per window was chosen at 4096 samples.
record time length (N II-) of 125 ms.
window by 50 per cent .
This corresponds to a
Each window overlapped the preceding
The time at _whic.h each windo.w was analyzed was
considered to be the time at the center of the window.
Thus the
coeffi ~
cients from window 1 (time of window from 0.0 to 125 ms after the bell
crash) were considered to exist discretely in time at 62.5 ms after the
crash~
and so forth for the remaining windows ef observation .
A total
of 32 windows were analyzed for this record size.
A second complete analysis of the same time series w-as performed
using a record containing 16384 samples per window.
for this record length was 500 ms .
for these parameters is 2 hertz .
The- time duration
The computed spectral line separation
Similarly to the first pass , a 50 per
cent overlap of each successive window was employed.
Sampling of the signal was performed on a hybrid analog- digital
computer using an external frequency source for the sampling frequency
21
reference clock .
The hybrid installation consisted of an SDS 930
general purpose digi tal computer interfaced with a Comcor CI-5000
electronic analo g computer.
The analog-to-digital converter had an
fourteen bit wor d length to represent discrete levels of 12 millivolts,
based upon the analog variable range of +100 volts t o -100 volts.
The Fourier analysis computations were accompli shed on an IBM
360/67 digital computer (see Appendix 5 for the program used) since
the program requi red for the record sizes employed ex ceeded the memory
size of the SDS machine.
Due to the different word sizes of the SDS
and IBM machines , an assembly language - subroutine wa s written to convert
the sampled da ta wor d format.
This subroutine is given in Appendix 4.
The word format change was made on the IBM computer .
For rapid selection
of random windows fr om the entire .time .. series , the s e quential time
series was stored on a pseudo-random access disk pack .
Each pass of
an analysis took the desired time series sub-set from the disk pack,
analyzed the ser ies , and then printed out .a permane n t record of the
Fourier series coefficients.
For selected portions of the analysis,
graphs were drawn by peripherals .to the IBM computer .
The window size consisting .of 4096 .data po int s was considered
sufficiently short to give reasonable accuracy to the resultant
coefficients.
The analysis using 16384 samples per window was used .to
determine the center frequency -of .the broadened spectral line for each
coefficient.
From these procedures, the frequenci e s stated in the
following table are considered to be the significant ones in the
original bel l tone .
22
TABLE .II
Partials Of the Fog Bell
Significant
Frequencies
Commence
(sec)
( End)
sec
565
1370
2331
3061
3320
3773
0 . 125
0.125
0.0
0,0
0.0
0.0
1.6
1.5
0.875
2. 0
1.0
Maximum Amplitude
(relative energy)
1.4
0 . 24
0 . 15
1. 76
LOS
1.68
0 . 80
The time listed when the partials commence are estimates since this
information is relatively uncertain .
The time when each partial ends
•
is based upon the time when they fall to 0.01 per cent of their maximum .
Many other frequencies were present in the spectrum, but these were
either too short in duration or too insignificant in ener gy to analyze
in detail .
The frequencies 2331 and 3320 .hertz contained the most significant
amount of energy in the series for the bell.
Since these frequencies
commence early and die off fairly shortly after the bell crash, it is
felt that these partials comprise .the distinctive sound of the bell
crash .
It would appear that the frequen.c ies
the bell its prolonged sound as it dies away .
565~
1370, and 3061 give
No attempt has been
made to correlate the analyzed data with a musical scale or give a
qualitative explaination of the bell sound .
This was not done since
the bell chosen was for fog signaling and was .. not tuned to . any
particular musical scale .
The analyzed data conforms generally to the
theory and format of the bells described by Curtis, Giannini and
ot h ers .
[14], [15]
23
.
4.2
Continuous Me thod
To check t he results of the analysis by the discrete method,
a continuous band- pass technique was ·. employed.
A special purpose
audio spectrograph (Kay Missilyzer) was used for this task .
This
spectrograph r e cords the signal to be analyzed on an endless magnetic
tape which is moun ted on a rotating .. drum. . The spect r ograph triggers
a 5 ms integra t or with a tuneable 20 hertz band-pass input on the same
position of the dr um each rotation.
.The magnitude of the output of
this integrator i s burned on a recording paper so t he spectrum may be
preserved.
drum.
As th e drum turns, the filter advances ea ch rotation . of the
For the recording speed selected, the band width of the spectrum
analyzed was 5000 hertz.
•
The position . on the drum where the integrator
is triggered can be selectively p'sitioned so that s uccessive slices
(time windows) of t he spectrum can be made.
By man ua lly transferring
the spectral line amplitudes, a time .plot of ampli t ude versus time
for the various pa r tials can be developed.
4.3
Comparison of Methods
The part i als in the bell tone found by . the di screte method were
also found to be present by the continuous method.
The amplitude .
versus time infor mation correlated .between . the techni ques fairly well .
Since . the accurac y for the coefficients obtained by t he continuous
method should be greater due to the much shorter window size, one
would not expect t he amplitude versus time plots to match exactly.
1
~-
By using 16384 discrete data points, the accuracy of the frequencies
of each partial i s ± 2 hertz.
No theory is known to the author to
24
develop the bounds on the accuracy of the coefficient magnitudes for
the continuous method .
is quite dependable .
It is considered . that this amplitude information
Appendix .2 shows.the amplitude versus . time plot
for each of the six significant partials found through the discrete
and
continuo ~ s
methods.
Using a lower sampling frequency for the discrete analysis
method, the bandwidth of the time series could have been reduced .
If
this were done, it would have been possible to use a shorter .window
length and still maintained a small
~f .
The .result of the analysis
would have been amplitude information .with higher confidence .
One distinct advantage of .. the . discrete method over the c ontinuous
one for some applications is an ability to present phase infor mation
about each frequency present in the . spectrum.
This addit i ona l piece
of information was not required for this research since the ear cannot
6
determine phase information about a complex wave form . [l ]
J
25
SECTION 5
.
REDUCED VISIBI LITY WARNING EQUIPMENT
5.1
Discussion
Quite often aboard a pr i vate sailing yacht, a crew may be
suffic ient ly occupied with sailing the craft during re duced visibility
that sounding fog signals could . be . a .. burden .
Sounding s uch repe t itive
timed si gnals is a boring but quite important . task .
Additionally, the
specified 'at anchor ' warning signal may be required at a time when .no
crew members are on board the cr aft.
A semi-automatic s ignalling dev i ce
could alleviate t he problems created by the afo rementioned examples by
providing reduce d vi sibility warning signals for the c raft .
Such a device
ideally shoul d be simple to operate while provi ding dependable continuous warning signals for underway and at anchor operati ons .
The next two sub-sections describe t he design for a device
which can generate t hese signals.
A later section describes the
synthesis of the b ell tone which was .included in the device .
The final
form of the device was constructed .out of so lid state device s and pla c ed
on printed circui t boards .
Thi s device could . be packa ged as a small
portable unit or permanently mounted aboard a yacht.
5.2
Ti ming Circui try
The low vis i bi lity warning . equipment . has bas i c periodic
features.
These are dictated .by the methods of generating the various
sounds and the requi rements for .these sounds.
The major peri odic feature common to the anchored warning .signal .
and all the low vis i bility warning sounds while underway is their period
26
FIGURE I
470
UNIJUNCTION
MASTER OSC.
SO,.uF
FIGURE 2
M.O.
ONE5
~ OT
2
TIMING PULSE
TRAIN
I
'
' "',__....__I--,.,--
7
8
.....-I---.____ _ _ _ _"'
55
I
56 (SEC)
1L--_
....____---ty..--------11
l'---------"v....----~4__________~1l~---~-------5
27
b e twe en so un ds .
All of these so unds (with the exception of the requ i r e d
s i gnal f or underway un der power in i n ternational waters) have a maximum
period of one minute.
The maximum specified period for under power i n
i nternatio nal waters is two minutes.
Prudent
seamanship dic t ates that
thes e i nt e r vals not be fixed over any lon g period of time .
This
desired ape r iodicity p r events two ves se l s from sounding similar warnin g
signa ls syn chronously .
Synchr onism -could bring about theundesireable
side e ffect of a collision and t hus . the . ruina tion of on e's day .
A master clock is required fo r the wa rning equi pment and i s
spe cifie d by a frequency of from le s s than one cycle per minute to
less t han one per two minut es .
Unijunction oscillators are immediately
sugge s t e d by their extreme simplicity and ab ility to satisfy these
requ irement s .
The basic form of a .relaxation os cillator with a periodic
puls e out put was cho s en and i s shown .in . Figure 1.
A potentiometer is
used to va ry the oscillato r frequency manually when desired .
With the
component values shown, the peri odic range i s variable from approximately
55 s econds to 90 seconds .
The periodic pulse output .of this mas ter oscillato r was fe d to .
the t rigger input of the first of a series of f i ve mono-s t able (one- shot )
mult ivibr a tors .
These one- shots serially gene rate al l t he required
logic l eve ls . for sounding the various warning s ignals .
the ma s ter oscillator turns on the first one-shot .
turns off , the second one .turns on, etc .
The pul s e fr om
When t he fir s t one
Thi s t ur n on /t urn off pr o cede s
th r ough all five one- shots until . t h e l ast . one is off .
This sequen ce
is i n i t i al ized by each trigger pulse fro m- the maste r os cill a tor • .
The t urn on of the next one-shot i s accomplished by inverting the previous
28
3.6
FIGURE 3
v
8
R3
N
\.0
OUT PUT
6
R2
I
TRIGGER
INPUT
NOT
USED
C2
ONE-SHOT FROM
,t.~L914 AND DISCRETE
COMPONENTS R3,CI, AND C2
3
pulse and then differentiating .it.
Direct differentiation of the
'conjugate' wave-form of the previous one-shot is impractical since the
trigger pulse propagates through on .this wave-form.
Additionally, ..
some isolation i s required for the devices chosen s i nce drive capability
is limited.
The 'on' t i me pulse of each one-shot is shown in Figure 2 .
Selection of the proper pulse . train . for the various sounds is accomplished by a manual function selector switch .
This switch is in
actuality a varia ble i nput AND gate.
The active devices chosen for the one-shots were Fairchild
dual two-input NAND gates.
~19 1 4
By the use of _one e x ternal resistor (R3),
and capacitor (Cl), these gates become one-shots . [ll]
Figure 3 shows
the internal circuitry of these .gates and the application of the external
components.
These devices are designed .. for
high~speed
dig i tal logic
. applications and as such turn . on .with . small signal levels.
Spurious
noise and small supply voltage variations can cause unwanted triggering
of the one-shots .
(typically, 50
To minimize this occurence , a . large capacitor, C2,
~ for
greater) was placed .as shown i n Figure 3 . .
These micrologic devices employ a supply voltage in the range
of 3.0 to 4.2 vol t s .
The nominal recommended voltage is 3.6 volts.
A zener diode was employed to give this desired supply level.
~f
A 1000
capacitor was r equired in parallel with the zener to give additional
stability to . the s upply-voltage .
Without this capacitor, spurious .
triggering result s and the chain of one-shots fiprm an oscillator.
the capacitor, some spurious triggering still results, but the
chain does not go into continuous oscillation.
30
With
one~shot
This spurious triggering
FIGURE 4
POWER SUPPLY FOR THE HORN
AND BELL
2N404
TO HORN OSC
THROUGH SWlC
IOK
w
f-'
+V(X.
RELAY I
I
I
r--L
-----.J
I
I
I
I
FROM
_j
I
_J1__J1__J"L_
TO BELL CIRCUITRY
NOTE:
I. QI-Q4 ARE 2N736
could also be eliminated by providing a c onstant-vo l tage, variablecurrent power sour c e.
This .further complexity and cost is not required
in this applicat i on since the correct output from the timing chain
is achieved .
After the fun ction switch selects the proper chain of pulses,
these pul ses are applied to a relay actuated switch which connec ts .the
supply v oltage to ei ther the .horn .oscillators or to the bell circuitry.
The supply vol tage for the bell oscillators also goes through a
transistor switch which fo r ms the voltage . wave form shown in Figure 4.
The pul ses fr om the chain of
gate.
one~shots
is al so applied to a NAND
This gate develo ps the logical voltage t hat switches in a
listening section and turns off the power amp'Iifie r when signals are
not being sounde d.
intercom system.
This technique of listening is s i milar to a simple
The output speaker for th e powe r
ampli fie~
ac ts
as the microphone input to an amplifier-speaker combination during this
listening period .
This remote listening device provides a degree of
safety for the pass engers and crew of ones own vessel during periods of
reduced visib ility.
This listen feature can also be selected continu-
ously by the master function selector switch.
5.3
Description Of The Entire System
Figure 5 s hows in block diagram form the relat i onships of the
various sub-parts of the entire .reduced visibility warning equipment.
Functionally, the sys tem provides . the· following fea tures:
1.
The three required reduced visibility signals for a
sailboat underway.
32
-
.
~
FIGURE 5
•
'
REDUCED VISIBILITY WARNING
EQUIPMENT
-SIMPLIFIED BLOCK DIAGRAM-
BELL
w
w
I
I
FOG HORN
HORN
I
I
6
I~
(.
?
OUTPUT
AMPLIFER
LOUD-HAILER
Ll STE N
kX<>
OUTPUT
SPEAKER
•
2.
A reduced visibility signal for a vesse l underway under
power.
3.
A manually operated war n i ng horn for ente ring or leaving
blind channe ls and slips .
4.
An aut omat ic and manual listening device.
5.
A loud hailer.
6.
A rap idly ringing bell for a vessel at ancho r in reduced
visibili t y.
7.
Test positions for 2 and 6 so these functions may be
checked out i n port at r educ ed volume f or preventative
maintenance .
The fi nal power amplifier common to all feature s exce pt 4 is a
standard class B trans i st or power amplifier .
This output stage, the
oscillator for a ll underway signals, and the loud hailer c ir cuit ry were
taken directly from a commercial fog horn /loudhailer device .
The unde rway signals employ a unijunction oscillator of a nominal
frequency of 200 her t z.
This is .ei th e r actuated by t he selected timing
chain associat e d with a specific signal (1 or 2) or manually ac t ivated
by a push-but ton switch for feature 3 .
When activated manually, a
different load resistor is p l aced in the os cillator whi ch causes
an output f requency of nomi nally 380 hertz .
The list ening device partially d es c ribed under the timing
circuitry sect i on employs a commercially avai lable 50 0 milliwatt
direct-output audio amplifier and an 8 ohm water pr oo f sp eaker .
The
output speaker for th e power amplifier is swi tched to act as a microphone input t o the li sten amplifier.
34
A 3-pole doubl e-throw re lay
actuated switch is used to remove power from the output stage to
prevent damage to the transistors, and to switch .t he speaker to the
listen amplifier input.
The manual .selection of 'listen' is achieved
by placing a constant drive voltage on .. the base of the relay driver .
The automatic ' listen' feature is accomplished by placing the output
of a NAND gate as described under . the.. timing circuitry section on th.e .
base of the same transistor.
When installed on a vessel, the 'listen'
output and the calling and emergency channel of a
ship-to~shore
receiver
could be mixed and placed on a SP'eaker -in the cockpit near the helmsman ,
This entire system provides .for .a typical sailboat all the
advantages of semi-automatic warning ..and signalling devices.
The
object of the equipment is to provide greater safety and flexibility.
for yacht sailing, motoring, or anchoring in a reduced visibility
environment.
'
35
SECTION 6
SYNTHESIS OF THE BELL TONE
6.1
Synthesis By Discrete Computation
The bell sound was described mathematically as the superposition
of the six mo st prominent part ials found during the analysis.
partials wer e written as t ime variant sinusoids.
The
The time response of
each partial was approximated by fi tted exponential curves.
A FORI RAN II language program was written fo r an SDS 930 digital
computer for computa tional purposes.
The equival ent o f sampled data
was computed in discrete intervals of .0 00125 sec onds.
The computational
st e p size in seconds and the fr equenc y present in th e wave f orm we re
based up on a 'samplin g' f r equency of 8000 hertz.
A total of 8000 samples were computed and sto r ed i n a data t ab le
for a r ecord length of 1 s econd at the stated clock freq uency of 8000
hertz.
Provisions were made in t he program to pe rmit parameters of
attack, decay , and amplitude to b e varied.
These provisions were made
so that some exp erimen tal modifications to the wave form could be made
in l ight of q ualita t ive analysi s .
A machine l a nguage (META-SYMBOL) subroutine callable by FORTRAN II
was written to perform the task of digit al-to-anal og conversion.
This
subroutine was controlled at a rate determined by a c lock on the
associated a n alog computer.
If t he clock were something different from
the program o rient ed 8000 hertz, the equivalent of frequency/time
translation would be performed on the data.
The resultant analog
vol t age from this program was passed th rough a pass-band fi lter with a
band width from 20 to 4000 hertz to minimize sampling noise.
36
The wave
form was then amplified and reproduced through a speaker.
The basic
program had provisions for continuously repeating the same one. second
data record.
The resultant effect was a bel l being struck at one
second intervals and ringing until being struck
again~
The results of this experiment were quite encouraging.
The
bell-like sound that resulted was considered to be a reasonable likeness
to the original sound.
.
Therefore, the decision was made to proceed on
the assumption that simple exponential approximations to the time
response of each partial would be satisfactory for an engineering
approximation.
It was felt that some experimentation with the rise and
decay times and the maximum magnitude of each partial would be necessary
to optimize the sound.
It was felt that this synthesis technique was a useful tool in the
overall project as a verification of the engineering assumptions for the
synthesis and analysis techniques used.
If an investigation of more
complicated sounds such as those involving voice inflection and accents
were being conducted, then this step would have been invaluable.
6.2
Synthesis of the Bell Tone by Electronic Circuitry
Any analyzed sound can be exactly duplicated by man if sufficient
complexity of circuitry and design time are expended.
speaking, this exact duplication is seldom desireable .
Practically
Basic engineering
concepts dictate that some of the objectives to be pursued when designing
a portable sound production device are that it should be small, lightweight, relatively inexpensive, reliable, and require a small amount of
•
power.
Looking at the desireable aspects of a practical bell simulator,
37
one would e xpec t it to generate a reasonable bell-like tone from a
small inexpensive device.
Hopefully not all the partials present in
the original bell so und would be requir ed for re asonable simulation,
and the re q uired par t ia ls co uld be simply generated.
The f irs t techniq ue considered for synthesis of the bell tone
was the use o f a very h i gh
Q band-pass circuit (400
~
Q ~ 1000).
.
.
f'l
circ uits a r e poss1'bl e us1ng
ac t1ve
1 ter tee h n1. ques. [lS]
Such
Such a
filter would emplo y only ac tive devices , capacit ors, and resistors.
By
causing su c h a fi l ter to ring b y in t rod ucing the required driving
func tion , it would be possible to have a rising and decaying sine wave .
By superposition of severa l of these waves, it would be possible to
build up the synth etic bell tone.
To achieve these very h i gh
Q
c ircuits, a mu ltipl e-po l e filter is requir ed whi ch would dictate
sev eral active devices per filter.
As a further disadvantage, the
rise and decay rates of the sine waves generated in this manner would
not be independent of each other.
The seco nd technique investigated was the use of a constant
amplitude sine wave oscillator fed into a gain-c ontrolled amplifier.
By varying the gain of this amplifier, the resul tant wave shape wo uld
simulate one partial.
Some wave shaping circuit ry would be required to
con tr ol the gain of t his amp lifier.
There are several inex pensive
integrated cir c uits pr es ently being marketed that could be employed as
th e gain- control led amplifier.
These integrated circuits are generally
designed f o r in t e rme dia te frequency (IF) amplific ation and t hey hav e
automatic ga in control (AGC) ci rcuitry built into t h em.
Typically, an
80 db contr o l range can b e achieved for a few vo lts of AGC voltage.
38
The manufacturers of these devices list the useful frequency range of
these devices from DC to several megahertz.
This method of tone
generation was put aside when a still simpler method was discovered
and investigated further.
The method finally chosen to generate the individual partials
was twin-t oscillators driven by a variable supply voltage.
[19]
The
significant feature of the twin-t oscillator for this application is
that it can be made sufficiently frequency stable during variations
of supply voltage .
Most oscillators vary in output frequency and
amplitude as the supply voltage varies.
For the twin-t oscillator,
the frequency variations can be kept to less than 1 1/2 per cent at
the design frequency for large (O to 10 volts) excursions of supply
voltage .
The resultant output magnitude varies almost linearly with
the supply voltage.
The oscillator is made frequency stable by selecting a highcurrent gain transistor (hfe from 150 to 200) as the active device
and including a large resistance in the base feedback path.
If the
supply voltage has a wave form as shown in Figure 6, then Reef form
a load charging time constant during the time Tc .
CfRd form a discharging time constant.
During the time Td'
The resultant supply voltage
as seen by the oscillator is given by the following equations.
v(t)
a
c
v(t)
'
ad
vb (1
exp(-a t))
c
0 <
t
<
=
T
R cf
c
c
(7)
(8)
V(T ) exp(- adt)
c
T
c
< t
< T
(9)
(10)
Rd cf
39
0
0::
0:.
0
~
_j
_j
0:
u
u-
C\J
0::
(j)
r-I
II
II
0
0
0::
-
u
z3
•
r-
Ill
<{
0::
lJ..
u
(0
~
:s
~
c:
"
40
It is implicitly assumed that the partial amplitudes versus time
can be so simply approximated.
As it turns out, this assumption is
correct, the approximations of the partial amplitudes versus time b eing
non critical.
The true test is not the mathematical justification, but
rather the ear of the observer.
Compromise must be made for th e goa l
of simpl ic ity and low cost .
The choices of Rc, Rd and Cf affect both the ampli tude (Rc and
Rd comprise the load) and to a lesser degree the frequen cy o f the
output .
Variations of R will cause the oscillator to tune over nearly
2
an octave .
For optimum frequency stability, the oscillator should be
adjusted to the center region of its tuneable range.
Convenient design
0.1 R ; the values for c and Rl
1
1
2
can be selected from easily used n6mograms.[ 0] The r es i s tor R is
thumb rules are C
2
=
2c
1
, and R
2
=
0
used as a feed to a mixing bus with other oscillators .
R was also
0
used to limit the gain of each oscillator to the desi r ed value and
provide a degree of isolation from other oscillators.
The mixing bus
was t he input to an emitter follower amplifier which provided a h igh
input impedence for the oscillators.
For the first attempt at synthesis, six oscillators corresponding
to the six most prominent partials ( those at 565, 1370, 2331, 3060,
3320, and 3773 hertz) found in the original bell tone were constru c ted .
Three of t h ese frequencies (2331, 3320, and 3773 hertz) reac h their
peak amplitudes earliest and probably give the bell its d i stinc t ive
sound shortly a fter being struck.
An attack time for all of these
os c illators was chosen at 100 milliseconds (ms) .
The remaining th r ee
frequencies re ach their peak amplitudes significantly later and
41
prob ably give the bell tone its hum note.
These latter frequencie s
were g rouped together and given an attack time of 300 milliseconds.
The values chosen for at ta ck times for each group corresponds roughly
to t he average attack time for that group found in analy sis.
Admittedly,
this broad group ing is an oversimplication, b ut certa inly desireable
from the view point of minimizing the required circuit ry.
The supply vol tage for these oscillators was gene rated b y employing
a grounded emitt er as t able multivibrator driving transistor switche s
(see Figure 4).
The on time of these switches corresponds to the attack
time of the partials.
The periodic nature of the astable multivibrator
yields the effec t of a bell being repeatedly rung.
The wave f orm of the
astable multivibrator wa s a rectangular wave having an on time o f 100 ms
and a period of 700 ms.
For the longer attack-time g roup of partials,
a monostable multivibrator was used to extend the on time of the
associated s witch to 300 ms.
A relay actuated switch in series with the
transist or swit ches was used to control the on time of the ringing bell
to 5 seconds out of every minute.
By properly adj usting the maximum amplitude of eac h oscillator,
the resulting bell tone was a fair representation of th e original sound.
The rapid per iodic ri n ging of the bell suggest ed that some of the lower
frequ en cies comprising the longer lasting hum note group could be
eliminated.
Hope f ully this could be done with little deg rad ation of the
simulated bell tone.
By experimentation, it was f ound that only the
partials a t 2331 and 3320 hertz were required to repres ent a bell being
repeatedly run g at intervals of 700 ms.
42
The final f o r m of the bell tone
•
simulator therefore contained only two variable amplitude oscillators .
In light of the stated objectives, it is felt that the simulated bell
tone adequately fulfills the requirements for a warning device of an
anchored vessel .
•
43
SECTION 7
SUMMARY
7 .1
•
Analysis
Both the discrete and continuous analysis techniques suffer certain
limitations.
These limitatio ns arise due to the finite frequency
s p ec tr um r e present ation of time and b and limited complex wave fo rms.
The result ing inaccuracies are inev itab le and ar ise as a r esult of th e
uncertain relatio nsh ip of the time signal to its frequency trans fo rm.
By s e lection of proper sampling frequenc y and time series duration ,
a quas i-st a tionary p rocess can be approached for the purpose of obtaining
both frequency and amplitude information.
Permutations of sampling
f req u ency and time duration of the seri es allow optimization of frequency
•
information, or amplitude in fo rmation, but not both.
7. 2
Synthesis
Complex wave forms can be ap proximated qui te simply using solid
state devices if th e exact wave form is not to be duplicated and
compromises can be accepted.
This synthesis can also be done in the f orm
of a mathematical model if de si red, s o the model can be examined mo r e
closely before expensiv e and time consuming 'bread-boarding' is at t empted .
It is felt that the low vis ibility warning equipment has demonstr a t ed the feasibility and practicality of such a device .
The object
was not to develop a r evo lutionary apparatus, bu t rather to demonstrate
th e engineering techniques a nd expertise for su c h a device.
44
BIBLIOGRAPHY
1.
United States Coast Guard, Rules of the Road, Internationa l-Inland ,
CG 169, U. S. Government Printing Office, 1965, p 26.
2.
J. J. Josephs, The Physics of Musical Sound, D. Van No strand Co.,
Inc., Princeton, N. J., p ~33.
3.
A. T. Jones, The Strike Note of Bells, J. Acoust. So c. Am ., April
1930, Vol I, P 373~
4.
A. T. Jones and G. W. Alderman, Further Studies of the Strike Note
of Bells, J. Acoust . Soc . Am., Oct. 1931, Vol III, No. 2, p 297.
5.
A. N. Curtis and G. M. Giannini, Some Notes on the Character of
Bell Tones, J . Acoust . Soc . Am., Oct. 19 33, Vol V, No. 2, p 165 .
6.
Ibid.
7.
G. A. Carse and G. Shearer, A Course in Fourier's Analysis and
Periodogram Analysis, G. Bell and Sons, Ltd . , London, 1915,
pp 16-23.
8.
J. W. Cooley, P. A. W. Lewis, and P. D. Welch, Historical Notes
on the Fast Fourier Transform, IEEE Trans . on Audio and Electroacoustics, June 1g61 , Vol AU- 15, No. 2, p 77.
9.
Ibid., pp 76-77.
•
10.
W. T. Cochran, J. W. Cooley, D. L . Favin, et al, What is the Fast
Fourier Transform?, IEEE Trans. on Audio and Ele ctroacoustics,
June 1967, Vol AU-15, No. 2, p 48.
11.
Ibid . , p 46.
12.
R. B. Blackman and J. W. Tuckey, The Measurement of Power Spectra,
Dover Publications, Inc., New York , 1958, p 32 .
13.
R. W. Hamming, Numerical Me thods for Scientists and Engineers,
McGraw Hill Book Co., New York, 1962, pp 311-312.
14 .
A. N. Curtis and G. M. Giannini, Some Notes on the Charac ter of
Bell Tones, J. Acoust . Soc. Am., Oct. 1933, Vol V, No. 2, pp 164-165.
15.
A. T. Jones and G. W. Alderman, Further Studies of the Strike Note
of Bells, J. Acoust. Soc. Am., Oct. 1931, Vol III, No. 2, p 304 .
16.
H. L. F. Hemholtz, On the Sensations of Tone, Dover Publi cations,
Inc . , New York, 1954, (t ranslated from the German edition of 187 7),
p 1 26.
45
17.
D. E. Lancaster, Using New Low-Cost Integrated Circuits, Electronic
World, Ma rch 196 6, p 52, 80.
18.
W. R. Kundert, Th e R. C. Amplifier-Type Active Filter: A Design
Me thod for Optimum Stability, IEEE Trans. on Audio, July-Aug. 1964,
Vol AU-12, No . 4, p 70.
19.
F. B. Maynard, Twin T's:
World, Aug. 196 8, p 200.
20.
F. B. Mayna rd, Twin-T Oscillators, Design and Application,
Electronic Wor ld, May 1963, p 41.
Design and Applica tions, Electronics
46
•
APPENDIX 1
•
BELL SPECTRUM BY DISCRETE ANALYSIS
Appendices 1 . 1 through 1.6 show contiguous time windows which
have been transformed to the frequency domain for the first 750 ms of
the bell tone.
Of interest i s the rapid fall of the spectral line
amplitudes above 4000 hertz, and the slow rise of the lower frequen c ies .
For these spectra, a sampl e size of 4096 data point s wa s used for the
transformation which yielded a 6 f of 8 hertz .
47
2.5
I
I
2.0.
I
.
I I
I
..
I
I
.. .
BELL SPECTRUM
MEAN TIME
>-
0.0625 SEC.
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•
APPENDIX 1.2
•
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~~
4.0
(KH Z)
A
4.8
5.6
APPENDIX 2
COEFFICIENT AMPLI TUDES VERSUS TIME FOR THE BELL
By discr e te and continuous analysis, the magn itudes of the
coeffic ient s for each significant partial was found as discussed in
Section 4.
Append ic e s 2.1 through 2 .6 show a compar ison of these
coefficients as a function o f time.
As discussed in Section 4 .3, t he
plots wo ul d not be precisely the same.
Fo r those coefficients with a slow rate of change (e.g ., 565,
137 0, a nd 3061 her tz ), the results of t he two metho ds used compare
fairly well.
For t he partials with a faster time ra te of change
(particularly 2331 and 3320 hertz), the correla tion of the results
was poorer.
The g ener a l s hape of these plots were simil ar however.
•
54
APPENDIX 2.1
r
'
55
(
(
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56
APPENDIX 2.3
•
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APPENDIX 2.4
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58
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I _l_,__.
APPENDIX
•
3
SUBROUTINE SAMPL
SS4MPL PZE
••
SUBROUTINE SAMPL(NOBLKS,LENGTH)
•
••* THIS PROGRAM SAMPLES ONE ANALOG SIGNAL ON TRUNKLINE
• 4T A RATE DETERMINED BY A CLOCK PULSF. APPEARING ON
•*
•*•
••
••
••
•••
05CO
TRUNKLINE 0210. ANALOG TO DIGITAL CONVERSION IS PERFORMED
AND THE 1 RESULTING
DATA IS STORED IN DOUBLE BUFFERS OF
LENGTH DATAT 1 e
THE NUMBER OF BUFFERS STORED IS
SPECIFIED BY ''BLKNO'• THE DIGITAL DATA IS STORF.D ON MAG
TAPE UNIT ONE IN BINARY FORM AS AN ANALOG CODED VOLTAGF •
THIS DATA CANNOT BE INTERPRETED BY A FORTRAN READ
STATEMF.NT. USE A MACHINE LANGUAGE SUBROUTINE FOR THIS
PURPOSE CE.Gef RDTP)
THIS SUBROUTINE
FORTRAN IV
CALLABLE~ TH S P•oGlAM CO"MENCES SAMPL ~G WHEN COMCO~ IS
IN COMPUTEt AND WILL NOT EKIT UNTIL SENSE S~ITCH 6 IS ON •
TO LOOP 8A~K THROUGH THE PROGRAM FOR ANOTHER SET OF
SAMPLES, INSURE SENSE SWITCH 6 IS OFF, THEN GO TO IDLE
AND THEN TO RUN •
•
BLKNO
DATAT
A
X2
AGAIN
.
JS
BRM
PZE
PZE.
PZE
EQU
EQU
LOA
XMA
STA
LOA
XMA
STA
LOA
X~A
STA
LOA
STA
TRT
CAT
BRU
EOM
POT
EFT
LOA
ADO
STA
LOA
STA
i~~y
~~f
k~~
LOA
LLSA
STA
MRG
STA
9SETUP2
2
5
2
BRMPLG
010
SVOlO
BRMPLG
011
SVOll
BRMPLG
040
SV040
051
SV051
0,1
MAGTAPE READY TEST
0
S-2
*014000
SPACE
0,1,4
ERASE MAGTAPE
*BLKNO
z-1
COUNT
*OAT AT
OAT
PLACE
~~~~~+
r8&8~
BRMSAM
~i~
OAT
•BUFFO
CWO
*
START
LOA
MP,G
STA
LOA
ADD
STA
STA
LOA
ADD
STA
LOA
MRG
STA
STA
SKS
BRU
EIR
EOM
HLT
BRU
BRU
PZE
LOA
SKG
BRU
LOADl MPO
EOM
POT
R TESTl BRX
LOA
STA
LOA
STA
STZ
RTEST2 LOX
FILLl TRT
CAT
BRU
EOM
POT
WTB
BRU
*
DAT
=BlJ FFl
CWl
=AU FF O
=-1
ORI GO
CfM M
=AU FFl
=-1
ORI Gl
ocw
=COMM
svc w
cw
•
030 010
ANALCG IN COMPUTE TEST
0330 04
CLOCK LINE
THIS IS THE IDLE LOOP
S-1
S-1
S-2
TOGG L
TOG GT
LOA DO
C0"4 M
THIS PROCEDURE TES TS
TO DETERMINE WHICH
BUFFER TO LOAD
C3400 0
cw
RIDL E,X2
ORI GO
COMM .
svcw
CW
TOGG L
SDAT AT,X2
0,1
.
0
S-2
*Cl4000
CWl
0,1, 4
ST ORE DATA ON MAGT APE
INCR
**
THIS DI VIDE S THE SUBROUTINE INTn BUFF ~RS
*LOA DO MPO
COMM
EOM
034000
POT
cw
RTE S T3 BRX
RIDL E,X2
LOA
OPIGl
STA
COMM
LOA
svcw
STA
cw
MPO
TOGG L
RTEST4 LOX
SDAT AT,X 2
FILLO TRT
o,1
CAT
0
BRU
S-2
E0"4
*Gl400C
CWI')
POT
WTB
0,1,4
STORE DATA ON MAG TAPE
I NCR
SKR
COUN T
BLOCK COUNT IS REDU CED .
BRU
RIDLE
IF NEGATIVE, All DATA HAS
TRANSFERRED.
*C
BRC
S+2
RIDLE BRC
*START
LOA
BPMPL G
STA
051
EOM
0330 00
62
REF~
..
•
$+1
BRC
SWT
SENSf SWITCH 6 TEST
1
RRU
S-3
PROGRAM CONTINUES IF NOT SET
HLT
TO CLEAR HALT, IDLE/RUN
BRU
AGAIN
TRT
CAT
$-2
BRU
LOA
SVOlO
STA
010
LOA
SVOll
STA
011
SV040
LOA
040
STA
LOA
S\1051
STA
051
E!R
BRR
SAMPL
* END OF SUBROUTINE
*CON
FORM
9 15
CONT
FORM
10' 14
SPACE CONT
150 ,0
ocw
DATA
0100)00
svcw
PZE
cw
PZE
COMM
PZE
PZE
SDATAT RES
1
ORIGO RES
1
ORIGl RES
1
OAT
RES
1
CWO
RES
1
CWl
RES
1
TOGGT RES
1
TOGGL RES
1
COUNT RES
1
SVOlO RES
1
SV011 RES
1
SV040 RES
1
SV051 RES
1
PLACE DATA
077700000
BRMSAM BRM
START
BRMPLG BRM
INPLUG
INPLUG PZE
NOP
NOP
NOP
BRC
*INPLUG
BUFFO RES
1C24
BUFF1 RES
1C24
END
8'1
~t;
r
•
•
63
APPENDIX 4 .
SUBROUTINE
(
c
SU~POUTINE
FORM
FOR~(INOATAt
C THJ l) ~UAROUTINE WILL CONVERT 24 RIT RIN4RV WnRDS STnRED IN
C
INDATA OF AN ARRAY LENTH SPECTFIEO BY THE INDEX VALUF.
C
Tn 32 BIT PINAR Y WORDS AND PLACE THESE SA~E WOROS
C
BACK TNTO INDdTA.
c
(
F!lQ~
~TART
('l
STM
.,,
SR
L
t
L
7
14,12,,2(1~)
BALR 6,0
USING
USING OdTd,7
LOf"JP
LR
SR OL
SRL
SROL
~R
l
SRDL
SRL
DATA
Nil~
SRDL
~T
L.A
8CT
LM
MVI
RCR
DSECT
DS
END
TH I c: S IJAR OUT J NE C f) NV~ RTS
24 RIT RINARV WnROS Tn
3 2 R IT W'1 R DS
7
d,:F'l28 1
12,C(!)
THY S l S THE
?.,NUM(12t
3,7
2,1:>
2,2
2,6
2,2
2,A
2,?.
2,6
3 1 NUM(l2)
ll,4(J2)
11 lOOP
2ti2t?.R(13)
l~(l3),X'FF
1
15,14
11=
64
tNDEX Vl\l!IE
•
APPENDIX 5
FAST FOURIER TRANSFORM ANALYSIS PROGRAM
c
..
c
C THI S PROGRA~ WAS USED FOR FAST FOURIER ANALYSIS OF THE
C DISCRETE TIME SERIES OF A RECORDED ~ELL TONE
c
c
DIMENSION
~
c
c
~ (16384)fC(l6384),M(3),1NV(4Cq6),S(4 1 96)
X(500),Y 500),IIf4096)
COMPLEX*S Af4Qq6 l1lt
DEFINE FILE lf52C,512,L,K)
CLOCK2=IT IME(0)* 0 •01
READf5,1 S4) NRUN,N
"11=N+1
FJNOfl'Nl)
1<=12
OT= !./( lC 24 . *32.)
AT=DT
NPT=2**1<
RW=l .. /f2.*DT)
OELTAF=l . /fDT*NPTt
F=-DELTAF
XN=N
.
T=OT*l28 . *XN
WRJTE(6,ll0) T
NPT12 =NPT/2+1
~(l)=K
M(2)=(
M(3)=0
CLOCKl =ITIME(O)*O. Ol
READfl' Nl) B
CLOCK1 =1TIME(0)*0 • 01-CLOCK1
WRITE(6,106) (B(J)il=l,512)
WR!TE(6{107) CLOCK
DO 3 I= ,NPT
Afi,l,U zB(t)
CONTINUE
CALL HAR~(A,M,INV,S,-l,IFERR)
DIMENSIO~
C SUBROUTINE H~RM IS A LIBRARY SUBROIJTINE WHICH PERFO~MS
C DISCRETE FOUPIE~ TRANSFORMATIONS BY THE FAST FOURI ER
C TRAN SFnRM ALGORITHM.
c
g~tr=~A~~ ~~Tr,t,ltt
F=F+DELT~F
II ( 1)=1-1
Bfi)=F
T=T+DT
2 CONTINUE
WRITE(6,101) BWfDELTAF,NPT,Nl,OT,T,NRUN
WRTTE(6jl05) (T (I){C(tt 1 B(J), t=1,NPT12t
CLOCK2= TIME(O)*O.O -CLOcK2
WRITE(6, 108) CLOCK2
101 FORMAT(/3XF 1 BAND WIDTH= 1 1 F8.2/3X, 1 DELTAF= 1 ,1PE1 0. 3/3X
lt~~~~~~to~o ~~~~T§iix!~~i~P~~~g~~~~~v~trf)~~;~~~~ b~~
-.
•
11 1
SECONDS 1 /3X,'RUN NUMBER•,t4)
104 f0RMAT(2110)
·
105 FORMAT(1Hl 1 3X, 1 MAGNITUOE OF FOURIER COEFFtCI~NTS
l'/ /23X, •FREQ'i29XL'FREQ 1 1 29X,•FREC 1 ,2qX, 1 FREQ 1 /(4(1X,
lo6 1 ;a~ ~~li;;~ x:rR~wF6At!~,,~~i6:t~t,,
1
107 FORMAT(/3X, TIME REOUIRED TO RFAD INPUT DATA IS•,Fl~ ~
1)
108 FORMAT(/3X,•TOTAL COMPUTJNG TIME REQUIRED J~'rF10.1)
11 n FOR MATf/3X, 1 TIME AT BEGINNING OF RECORD IS ',lPF.1 0. 4)
EN D
65
l
APPENDIX 6
REQUIRED FOG SIGNALS FOR A SAILBOAT
Definitions for the sailing terms used:
Relative wind
in this sector
is a port tack
Relative wind
in this sector
is a starboard tack
Relative wind in this sector
is called wind abaft the beam.
Sound signals fo r sailboats in reduced visibility while
underway in Inland and International waters:
Operation of
sailing vessel
Signal
Maximum interval
between signals
(minu tes)
,·~
Starboard Tack
1 blast
of
1
Port Tack
2 suC'.cessive blasts
of fo ghorn
1
Wind abaft the beam
3 successive blasts
1
foghorn
of foghorn
While motoring
1 prolonged blast
of foghorn
*-ic
1 (Inland)
2 (International)
A sailboat shall sound at intervals not to exceed 1 minute
a rapidly ringing bell £or about five seconds.
•'
*
**
Blast is de fined as a duration of not over 2 seconds.
Prolonged blast is defined as a duration from 4 to 6 seconds.
66
•
APPENDIX 7
SCHEMATICS FOR THE REDUCED VISIBILITY WARNING
EQUIPMENT
This appendix contains an expanded block diagram for th e r educ ed
visibility warning equipment and schematics f or l:he various s ub - pa rts
which the author designed .
•
.
67
/
horn pwr .____., harn osc
SUPJIY
listen
teaic
hailer
horn
tim ina
output
StillS
I
I
L-----
be II
clanaer
bell pwr
supply
bell
cl rcuitry
listen
amp
ln[IUt
speaker
Reduced Visibility Warning Equipment
Expanded Block Diagram
'
...
listen
switch
output
s[lnker
bell
tlmina
0\
CXl
au
•
FUNCTION
SELECTOR SWITCH
WAFERS A-8-C
3
>TO
(/)
.....
0
I
RELAY I
DRIVER
(/)
I
w
z
0
~
I
0
I
I
a:
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LL
5)
g
I
00
2
HORN POWER
FROM RELAY. I
0~
I
0
0
SW IC
~------------------------4~~-----
TO HORN
osc
69
FUNCTION
SELEC TION SWITCH
FROM MICROPHONE
WAFERS 0-E-F
FROM HORN OSC
0
fl
SWID
TO PA
~-----~))>-DRIVER
-
~
~
I
>~--------~:~~~~~M~
FROM BELL
TO RELAY 2
-----~»~--D_R_I_VER
FROM LISTEN
LO GIC
SWIE
POWER IN PUT
Vee
r------~>~--
SW IF
70
.
..
COCKPIT SPEAKER
SWITCH
FROM RADIO
SW2A
FROM LISTEN
AMP
TO COCKPIT
SPEAKER
0
SW28
•
71
+3.6
FROM
MASTER OSC
IOK
TO
ONE-SHOT 3
ETC.
3.6M
'--v---/
-....1
N
ONE- SHOT I
(2 SEC. DELAY)
-=IN276
'--v---J
ONE-SHOT 2
(I SEC. DELAY)
OUTPUT
IN276
OUTPUT
TIMING CHAIN SCHEMATIC
ONLY ONE-SHOTS I AND 2 SHOWN
..
...,
'
"
;.
.
'V
•
..J
.
..,
BELL CIRCUITRY
2N2924
30"1
....1...+
2N2924
20"1
....1...+~
-...j
w
100 K
.OOIJA
lOOK
-
lOOK
.001,.
~~
lOOK
100 K
.OOIJJ -
.OOIJJ
~;;
~
q
OUTPUT
TO SWID
)
200K
•
..
LISTEN CIRCUITRY
t/)
.,.__
0
I
lf)
I
w2
z
- - - - ,"'ee
---11-e
,.t~L914
0
~
0
a:
LL.
TO SWIE
t----~~>--
8
3 - - - - - - 1....
5--HIII
4--~=--
pl914
LOGICAL EQUIVELENT
I
2
-----i
-----i
3----t
4
---1
5
---t____.;
LISTEN
L ISTEN= 1+2+.3+4+5
r
74
INITIAL DISTRIBUTION LIST
No. Copies
1.
Defense Documentation Center
Cameron Station
Alex andri a 9 Virginia 22314
2.
Libra ry
Naval Po stg raduate School
Monte r ey ~ California
93940
2
3.
Professor D. B. Hoisington (Thesis Advisor)
Naval Postgraduate Schoo l
Monte r e y 9 California 93940
2
4.
LT Je rry L " Po st
8541 S . E . ? 1st Street
Mercer Island
Seattle , Washington 98040
3
5.
Commander , Naval Ordnance System Command
Department of Navy
Wash i n gton , D. C. 20360
1
6.
Mr . R. L . Limes
Code 52EC
Na val Po stgraduat e School
Monterey 9 Cali f ornia 93940
2
7.
Ass ociate Pr ofessor G. E . Rahe
Naval Postgraduate School
Monterey , California 93 940
1
8.
Associate Professor G. D. Ewing
Na val Postgradua e School
Monterey, Californi a 93 940
1
75
20
UNCLASSIFIED
-
Se c urit y Clas s ification
DOCUMENT CONTROL OAT A - R & D
( Sec urity c l as s ifi ca ti on o f titl e , body o f abs tra ct
1
O R I G INATING
ACTIVITY
~ nd in dexin g an n o tation mu s t be entered when the ove rall report i s c l a ss ifi ed)
(Co rp o rate a uthor)
2a. REPORT SECURIT Y CLA SS IF ICATION
UNCLASSIFIED
Naval Postgraduate School
Monterey, Califo rni a 93940
•
2b .
GRO U P
REPORT TITLE
3
Analy sis and Synthesis of a Time Limited Complex Wa ve Form
4 . DESC RIPTIVE NOTES (Type of rep ort and. inclusive dates)
Ele ctric al Enqineer's Thesis
s . AUTHOR(S) (Firs t name , middl e i nitial , last n a me)
Po s t, Jerry Lee, Lieutenant, USN
6 . REPORT DAT E
7a. TOTAL NO. OF
December 1968
ea.
CONTRACT OR GRANT NO .
'~GES
rb.
"fs
OF REF S
Qa, ORIGINATO R 'S REPORT NUMBER(S)
h . "PR OJEC T NO .
c.
9b . OTHER REPORT NO(S) (Any other numbers that
th rs repo r t)
may be assif!Zn c J
d.
I 0. D ISTRIB UTION ST ATEMENT
Distribution of this docu,nent is unlimited.
•
11 . SUPPLE MENTARY NOTES
12 . SPONSORING MILITARY ACTIV I TY
Nava l Postgraduate School
Monterey, California 93940
13 . ABSTRACT
The problem of analy zing time limited complex wave forms having time variant
fr equency domain charact erist i cs is discussed.
A bell. to ne is selected as a
wave form to analyze and it is then synthesized to produce an approximation
to the original sound.
An electronic device is constructed to simulate all
req uired f og signals for a sailboat, including a rap idly ringing bell.
-·
DD
/NOOR:6S
14 73
(PAGE 1)
UNCLASSIFIED
S / N 0101-607 - 681 I
Security Classification
77
A- 31408
UNCLASSIFIED
Sec ur i ty Cla s si t c att o n
LIN K
I 4
KEY
A
LINK
B
L I NK
WORD S
ROLE
WT
R O LE
WT
c
WT
ROLE
Wave Form Analysis
'
Wave Form Synthesis
I
'
I
Bell
Fog Signals
Discrete Fourier Analysis
UNCLASSIFIED
', I •,
·J
1 r; 1 • ~
'> -: ·
~
"'
1
Se curit y C l ass ifi ca t ion
78
·1 -l
29 JA
7\
1o::sso
'thesis
pJ483
c.2
.
Post Analysis and synthesis of a time l\mtted compleX wave form.
'
Thesis
P7483
c. 2
Post
109550
Anal ysis and
thes·1 s of a t' syned comp
une 1 i mit1ex wave form.
th esP7483
Analysis and synthesis of a time limited
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3 27S8
DUDLEY KNOX
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LIBRARY
.
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