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THE SYNTHESIS
OF SPEECH
USING A DIGITAL COMPUTER
by
Robert Peel Futrelle
SUBMITTED IN PARTIAL FULFILLMENT OF THE
RE4UIREMENTS FOR THE DEGREE OF
BACHELOR OF SCIENCE
at the
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
June, 1959
of
Author
. . .-... .......
Signature
-
Certified by..
Denartment of Phv1rsin
MT
.
25,5,
1959
*
*
*
0
·
Thesis Supervisor
Accepted by .
_
_
_
_
_
*
0*
*
0
0
0
0
0
Chairman, Departmental Committee on Theses
ABSTRAC T
A program has been written for the IBM-704 digital
computer to synthesize speech.
The input requires detailed
specification of the speech spectrum as a function of time.
The output is audible samples of 2.4 seconds duration with
a signal-to-noise ratio up to 36 db and a frequency response
up to 7 kc.
Included
is a complete
-charts of the program.
from 6 to 10 seconds.
SAP listing
and
flow-
The synthesis of each sample takes
The IBM-704 "Direct-Data" attachment
and a digital-to-analog converter is required.
TACBLE& OC
GCui
NTENTS
pg
Introduction
1
Acoustics of the Vocal Tract
1
Electrical Analogy
2
Solution of the Circuit Equations
3
The Production
4
of Vowels
and Consonants
Previous Methods of Synthesis
5
DIGITAL COMPUTER METHODS
Introduction
6
Digital to Analog Conversion
7
The Instructions
8
Summation
10
Preparation of Instructions
11
The Piece-Wise-Linear Program
11
Pre-emphasis
13
Program Speed, Testing, and Future Plans
14
Bibliography
16
APPENDICES
f
i
i
i
1
A --
Sub-word Arithmetic
19
B --
The 704 Program in Detail
22
C --
Flow-Charts
27
D --
SAP Program
E --
The Format of the Instructions
50
F --
The Instructions Used for Testing
51
(listing)
30
F
2_ - -^^
~~~~~r,Wu. 4.rULLW.
rUUtlon
;~
A
2. d
10A
The
urpose
of this work is the development
of a
device to synthesize speech will be able to manipulate
the
acoustic
"tbuilding
blocks"
of speech in a very
flexible manner. Today a synthesizer is primarily
useful for studying speech by testing various hypotheses
aboutthe interactions
of various speech sounds and the
nature of our perception of speech. Eventually it is
hoped that speech may be added to our methods of communicating with machines.
Before this can be done we need
to have a fairly detailed knowledge of the acoustics of
speech.
Acoustics of the Vocal Tract
The vocal tract begins at the vocal cords in the
larynx and then divides, one section terminating at the
mouth approximately 17 cm. away and the other section
terminating at the nose a slightly greater distance away
tNsso
as shown in Fig. 1.
yt;
For a large class of speech sounds
we need only consider the oral
OvA~
cavity, as the nasal cavity is
virtually isolated from the
system.
To 3 vt
Thus in essence the
vocal tract can be considered to
V6 ca
It'-
i
-n
9.
be a tube oTr ixed length and variable cross-sectional area.
The area varies from O to 15 cm.2 .
i
L
I _
Electrical Analogy
If we define an acoustical impedance as the ratio
of the applied pressure to the volume velocity (cm.3/sec.),
we find that the vocal tract is analogous to an electrical
transmission line with distributed inductance Lp/S
capacitance CS/c
2p
per unit length.
and
Here p is the
density of air, c is the velocity of sound and S is the
cross-sectional area of the tract at the corresponding
point.
A transmission line may be simulated by lumped
elements, inductors and capacitors, provided the wavelength
is long compared to the section being represented.
For speech the highest frequency of normal interest is
of the order of 6 kc. with a corresponding wavelength of
A=c/f which is 3x102 /6x10 4 = 0.05 m. or 5 cm.
Thus the
vocal tract can be adequately represented by approximately
15 sections.
In this analogue the pressure in the system
corresponds to the voltage and the current to the volume
velocity.
The source (for vowels) is represented by a
high impedance (current) generator.
The output is taken
as the pressure (voltage) at the lips which are loaded
by a dissipative impedance representing the loss of energy
to the surrounding air.
See Fig. 2 below.
I
6
.
-2
-
Solution of the Circuit Equations
The elements in the circuit obey the simple equations:
i_ Ci
,4
-a L
iR.
,
By ordinary circuit analysis we obtain a differential
equation
of the form:
...+
+ be-, b e ar|..,~
We are primarily interested in the homogeneous or
force-free (i'$)solution.
The standard method for solving
the above linear; homogeneous, differential equation with
t
constant coefficients is to make the substitutions=
Doing this we obtain the algebraic equation:
Denoting the roots of this equation by 5% we have the
homogeneous solution:
where
values
the of the
onstants,,
are determined by
where the values of the constants,B Y,, are determined by
the initial conditions.
The actual system has distributed losses due to
viscosity, cavity wall absorption and due to the fact that
the process is not adiabatic as the calculations suppose.
In the case of losses the roots are in general complex
numbersS~, CCi+J.,
and the solution for the force-free
condition can be written in the form:
,
6.3t
.('S%
W
...,ECtilw~fl)~8~1
(,t
+
I-
r
The Production of Vowels and Consonants
The current source can be thought of as
Vowels:
delivering impulses spaced at intervals of 1/fo where fo
is the fundamental pitch or voicing frequency.
The
impulse determines the initial conditions and for the
remainder of the interval the circuit decays by the
force-free solution above.
See Fig. 3 below.
F;.3
In general the acoustic network acts as a filter
source spectrum is present,
Ntt
on whatever
as shown in Fig. 4 below.
sM.e+rk..
ourj serIvr
Consonants:
The production of a fricative
such as (s) proceeds in this manner:
consonant
A constriction,
in
pressing against the front
this case caused by the tongue
of the roof of the mouth, causes a high velocity, turbulent
flow of air.
This is a source of noise which
by the cavities
is filtered
ahead of it. around the teeth and to scme
extent by those back of it, giving a spectrum of the type
shown in Fig. 5 on the next page.
-4.-
.
"
_%
_
K
-
.
C Si
X-
2.k.
Sk.
,t . e
The equivalent circuit for the production of
fricative consonants seems to involve a noise voltage
source at the place
Fig. 6 below.
of the constriction
as shown in
))e'se Vd~4t
I
Fin. C
Previous Methods of Synthesis
For the synthesis of speech a number of methods
have been used.
Probably the two most flexible ones are
those at MIT1 6 * and the Haskins Laboratory.4
uses a dynamic analog vocal tract.
analogy
in which the "cross-section"
The first
It is an electrical
of the tract is
continuously adjustable by purely electrical means
(saturable reactors and reactance tube circuits.)
The
other at the Haskins Laboratory in New York is a device
allowing playback of hand drawn speech patterns.
The
patterns are drawn to any desired complexity and the
sound is reproduced by the playback device.
A numberof other devices have been built
9,10,11,13,14,15
but they all suffer in being difficult to "program" for
complex or rapidly changing speech sounds.
Superscripts refer to the bibliography on pgs.
I
I1 - 18-
r
DIGITAL
COMPUTER METHODS
Introduc
ztion
It is possible with certain high speed digital
computers both to compute the waveforms and to have
the waveforms presented at a loudspeaker in their
normal audible form, i.e., as speech sounds.
The
computer can also manipulate at high speed the instructions
specifying the nature of the waveforms.
The differential equation describing the vocal tract
could be converted to difference form and solved continuously to yield the desired output.
However, this involves
rather high order differences and is thus time-consuming.
It is intriguing because it can be made quite exact and
still
retains the analogue form fairly well.
A faster
approach, and the one utilized, is to compute a.number
of samples of solutions and have the program simply
extract the desired sections of the solutions from its
table and present them at the output.
The stored
solutions would contain damped sine waves of many different
frequencies and filtered noise of various bandwidths and
frequencies.
This produces a quazi-static solution quite
similar to the VVEKB
solution of a wave equation.
This
approach is justified by the fact that the vocal tract
parameters change much more slowly than the characteristic
decay rates of the cavity responses.
r
t
A program has been written by myself to perform
these
operations on the MIT-IBM 704 computer.
The
program has been designed primarily for high speed and
flexible operation.
An outline of the program is shown
in Fig. 7 below.
,
Digital to Analog Conversion
The conversion of the synthesized
samples
in their
digital form to an analog voltage which can be recorded
or reproduced in audible form is simply accomplished by
a converter such as the one shown in reference 26, pg. 530.
Within the machine samples are computed to six binary
places
of accuracy.
This gives a maximum
of 36 db
signal-to-quantization level ratio, a rough measure of
the maximum signal-to-noise ratio.
Frequency response
is limited by the maximum obtainable read-out rate of
14,000 points'per second.
The highest component that
can be transmitted is 7,000 cps.; all higher are reflected
into the 0 to 7,000
cps. region and appear as noise.
-7 -
The Instructions
When summing a number of sine and noise samples,
the instructions must specify the nature of the samples
(frequency, amplitude, phase, bandwidth, etc.), the point
at which
the sample is to begin,
of the sample.
information
the duration
and finally
The four instructions used to specify this
are: "Time", Duration,"
Formant,1
and "Noise.t
A marker is kept within the machine which denotes
Time
the present ooint of time.
This point is a certain
location in the 704 magnetic core memory.
is specified it will bein
at this point.
hen any sample
When the Time
instruction is given (abbreviated by T) the marker is
moved ahead by the amount specified b
the instruction.
Thus a series of T instructions interspersed with other
instructions might give the output shown in Fig. 8 below.
W
T;' e
.
aT,
I iset
F;r.
ie
To
It is sometimesdesired to limiit the duration
Duration
of a sample.
Often a noise burst is desired which is much
shorter than the particular smple
in storage.
By giving
a duration instruction (abbreviated by D) we can accomplish
this limiting.
A~
~
~
The amplitude
~~8
of a noise sample is set and
cannot be changed while it is being summed.
if a burst
of increaising amolitude
Therefore,
a series
is desired,
of short bursts of length limited by D can be specified.
Each of these bursts would have a greater amplitude than
the preceding
one.
The value of the duration
is always
that of the last given; it need not be stated frequently.
The effect of the D instruction is shown in Fig. 9 below.
, e,t 9
Formant
t
The Formant instruction specifies a single
damned sine wave.
This instruction (abbreviated F)
specifies the phase(as plus or minus), the frequency,
and the amplitude.
There are normally about 50 frequencies
available between 100 and 5,000 cps.
adjustable
Noise
in 3 db steps over a range of 36 db.
The Noise instruction (abbreviated N) specifies
the amplitude
in 6 db steps and the frequency
The exact character
decided.
I
The amplitude is
of the noise
of the noise.
samples is yet to be
Summation
It is normally necessary to sum a number of different
damped
sines or noise.
This is done very simply by
letting them overlap or coincide in time, when specifying
them in the instructions.
Thus, if a number of different
F instructions are given without an intervening T instruction
the sum of the various F's will be formed, similarly for
noise.
There are no restrictions on the ordering of the
instructions --
they are completely independent in that sense.
To produce a section of a vowel we might give a sequence
of the form FFFTFFFTFFF...... which would produce a sum
as shown in Fig. 10 below.
_b.
*
F.
Rl
F,
A.
.a
a
-
II 1 Voiw
A,&-M
Jlf-ln--
hI--,
[WJ
Er
T
i
T
FtF
T
FF.
t
0
'0
Preparation o
Instructions
The instructions are punched on IBM cards to be
read into the machine.
Once a large number of cards is
punched they need not be re-punched, they need only be
re-ordered to form new sounds.
If a number of identical
cards are required they can simply be reproduced from
a "master" (cf. the last 15 instructions in AoendixF.)
The program considers the instructions in order,
one-by-one.
It is designed so that the parameters such
as the frequencies and the bandwidths of the samples can
easily be altered.
The noise samples are actually
computed by the synthesis program itself using random
numbers, and the T, D, and F instructions.
The noise
can thus be made to have almost any spectral characteristics
desired.
The program is also designed to be readily
modified to receive new instructions that might be wanted
to store the samples on magnetic tape, display the
samples on an oscillograph
screen or present
them at the
audio output for recording.
The Piece-wise-linear Program
The primary disadvantage of the program outlined
above is that we must write too many instructions for
Often there is
each sample we wish synthesized.
great
deal of redundancy in these many detailed instructions
because
-
the sounds are changing
slowly or in some very
regular way, e.g., the fundamental
1 -
pitch or some of the
formants may be changing approximately linearally with
time during some interval.
For cases such as these we
use a coding scheme to eliminate a great deal of this
redundancy.
Even simple schemes can reduce the number
of instructions necessary for a 2 second sample from
many hundred to easily less than one hundred.
The method
of doing this is to write a second program which accepts
the more concise instructions and translates them into
a series of many more of the T, D, F, and 1i instructions.
This operation is outlined in Fig. 11 below.
I
At this point it is useful to discuss a convenient
representation of the speech we want to synthesize.
A common way to represent the dynamic acoustical
properties o
speech is by "visible speech" patterns2 1 .
These are produced by certain devices used for the analysis
of speech.
The patterns
are constructed
so that the
vertical axis represents frequency, the horizontal time,
and the density of the shading represents intensity.
Vowels then appear as horizontal bars called formants
and fricatives appear as grey regions of no very definite
structure in the high frequency region.
in Fig. 12 at the top of the next page.
This is shown
I
7i
_- Ird-'
fELtiVCe
~~~~~A
I
l__
i
I
I-
t
V} IS@Le
-' PESC
-
II
1||ithhu
,S11U0W
AllluJI
program we first
To code for the piece-wise-linear
segments.
the movements of the formants by straight-line
of the formant
At each break-point we state the properties
somewhat as an F instruction
does.
approximate
We do the same for the
This is shown
noise and for the fundamental frequency.
in Fig. 13 below.
'rV'
1
_
-.
.
.
..
riec.r a. ks -ki% av
Ccks,
itOf f Ite
oa,,
,lie Spi
F,
c' _,.o
010-
I
rT;
-
F,
I
_
13
e
These patterns are then coded and presented to the
piece-wise-linear program which interprets them and
composes the proper detailed instructions.
The present writer has not worked on the above program
in detail but another student is studying the problem.
Pre-emohasis
By programming unnaturally large amlitudes
for the
higher frequencies we can, in an approximate way,
pre-emohasize them.
i
Filtering the output will bring
43
them back to their"natural'level but now with less noise
in the higher frequencies. This is done, of course, at
the expense of adding noise and reducing the dynamic range
in the lower frequency
region.
It has been found that the
higher frequencies are quite important in the production
and recognition of speech even though their normal amplitudes
are lower than the low frequency region.
of the noise and filtering
is shown in Fig. 14 below.
a'
'
is
The action
*e.
,I*.. :...
Level
f .0
row
a
ace
e W_
· I·
,---
As SRlt$l;eA6
.M
l
Aktvr F;lt et
t
'Le
bl
*-tvred Lvel
Program Speed, Testing, and Future Plans
The maximum length for a single continuous sample
that can be read out of the machine is 2.4 seconds at 14 kc.
In synthesizing a sample involving the first three
formants the program can run as fast as twice real time,
i.e.,
it would take the machine
1.2 seconds
a sample which would last 2.4 seconds.
to synthesize
The slowest rate
a which synthesis proceeds is half of real time.
The
major delay in time is preparing the sample for the output
device which takes half of real time.
Thus it would
normally take between 6 and 10 seconds to compute the
semtle and ready it for read-out.
-14--
7
The program has been tested and debugged to a large
extent.
A cursory examination of the scope display of the
synthesis using the instructions in Appendix F indicated
that the program was functioning properly though no films
have been received as yet.
Further testing using scope
display is in order.
The next steps in the development of this program
might be the inclusion of tape routines for storing the
bank samples, the piece-wise-linear program, and finally
the setting up and use of the digital-to-analog equipment.
One of the runs of the program
should be devoted
to
computing the noise samples.
A reasonable arrangement for the actual operation of
the program would be to have all of the programs and bank
samples on tape.
Then the piece-wise-linear instructions
would be read in from the on-line card reader.
Synthesis
would then proceed, the samples finally being recorded on
an audio tape recorder for listening tests.
ACKNiOWLEDGMENT
The author would like to thank Professor Kenneth
N. Stevens for his helpful advice relating to all problems
of speech acoustics.
Thanks are due also to Professor
Dean N. Arden and Mr. Ercolino Ferretti of the RE
for
stimulating discussions on various computational techniques.
5 -
BIBLIOGRAPHY
(The Journal of the Acoustical Society of America is
denoted by JASA.)
1.
Don Lewis, "Vocal Resonance," JASA, _
2.
Ralph K. Potter and Gordon E. Peterson, "The Representation
of Vowels and their
3.
Movements,"
,
(1936), -?q.
JASA, 20, (1948), 528-535.
R. M. Fano, "The Information Theory Point of View in
Speech Communication," JASA, 22, (1950), 691-696.
4.
Franklin S. Cooper, "Spectrum Analysis," JAS,
22,
(1950), 761-762.
5.
W. H. Huggins, "System-Function
JASA, 22,
6.
(1950),
Analysis of Speech Sounds,"
765-767.
Ralph K. Potter and J. C. Steinberg, "Toward the
Specification of Speech," JASA, 22, (1950), 807-820.
7.
J. C. R. Licklider and Irwin Pollack, "Effect of
Differentiation, Integration, and Infinite Peak
Clipping upon the Intelligibility of Speech," JASA,
20, (1948), 42-51.
8.
Franklin S. Cooper, Pierre C. Delattre, Alvin M. Liberman,
John M. Borst, and Louis J. Gerstam, "Some Experiments
on Synthetic
9.
Seech
Sounds,"
JASA, 24, (1952), 597-606.
Cyril M. Harris, "A Speech Synthesizer," JASA, 25,
(1953), 970-975.
10.
R. L. Miller, "Auditory Tests with Synthetic Vowels,"
JASA, 25, (1953), 114-121.
11.
Kenneth N. Stevens, S. Karowski and C. Gunnar M. Fant,
"Electric Analog of the Vocal Tract," JASA, 25, (1953)
734-742.
12.
Kenneth N. Stevens and Arthur S. House, "Development
of a Quantitative Descrintion of Vowel Articulation,"
dA1A, 27, (1955),
13.
14.
Harry F. Olson and Herbert Belar, "Electronic Music
Synthesizer,"
JASA, 27, (1955), 595-612.
E. S. Weibel,
"Vowel Synthesis by Means of Resonant
Circuits,"
15.
484-493.
JASA, 27, (1955), 858-865.
James L. Flannagan, "Note on the Design of 'Terminal-Analog' Speech Synthesizers," JASA, 29, (1957), 306-310.
16.
George Rosen, "Dynamic Analog Speech Synthesizer,"
JASA, 30, (1958), 201-209.
17.
E. E. David, Jr., "Artificial Auditory Recognition in
Telephony,"
The IBi Journal of Research and Development,
2, (1958), 294-309.
iisconsin, 1952)
18.
R-Ml.S. Heffner, General
19.
Colin Cherry, On Human Communication, (New York, 1957)
20.
C. E. Shannon and W. Weaver, The Mathematical Theory
Phonetics, (Madison,
of Communication, (Urbana, Illinois, 1949)
21.
R. K. Potter, G. A. Kopp, and H. C. Green,
Visible Speech, (New York, 1947)
22.
P. M. Morse, Vibration and Sound, (New York, 1948)
23.
E. A. Guillemin, Communication Networks, vol. II,
(New York, 1935)
24.
M. F. Gardner and J. L. Barnes, Transients in Linear
Systems, (New York, 1942)
25.
C. G. M. Fant, Acoustic Theory of Seech
Production,
(The Hague, 1959)
26.
Notes on Analog to Digital Conversion Techniques,
ed. A. K. Susskind, (Cambridge, Mass., 1967)
27.
Coding for the MIT-IBM 704 Computer, ed. F. Helwig,
(Cambridge, Mass., 1958)
28.
704 Electronic Data-Processing Machine - - Manual of
Opertion,
IBM Corporation, (New York, 1954 to date)
m11 -
Appendix A
Sub-word Arithmetic
When little accuracy is desired it is useful to divide
a 36 binary digit 704 word into a number of smaller words
called sub-words.
Each sub-word carries a sign with it
and one position must be left open for a carry so that one
sub-word will not interfere with another.
The sign and
carry bit are indicated by S and C respectively.
The
negative is handled by using the two's complement. These
numbers are convenient because addition, subtraction and
multiplication
can be performed
a 704 word without ever
on all of the subwords
unpacking" them.
in
In this program
five sub-words are stored in a 704 word as follows:
1 2 3 4-8 9 10 11-15 16 17 18-22 23 24 25-29 30 31 32-36
x C
S
C .....S
.....
5
4
.
C
S
C
S
a
,I
A single n-place signed sub-word is of the following
formn:
C
D
S
a.
X
X......C
We have assumed the binary point to be to the right of the
first place but the argument below can simply be generalized
to this case (normally the sub-word is surrounded by others.)
The n +
st place designate the sign, S. A zero in
indicates a positive number, a one indicates a negative number.
-II
-i
-
lace is a carry bit for absorbing any changes of
The nt2nd
sign --
it is erased after each computation.
If a number
of these sub-words in a 704 word are added to another similar
704 word, each of the n-place numbers will be added algebraically
to the corresponding number
(sub-word),in the other 704 word.
The negative of a number is obtained by subtracting
(complementing it.)
it from 2
(and then adding 1)
First we restrict all numbersof interest so that
a,
o
lal-lb1
oA
.
< z
We will show that the negative of a number always
has a one in S.
a number-
Trivially
2
has a zero in S
so that complementing it always produces a one in S.
It is interesting to note that the number 2
properties
2A
(- m') *
>O
has the
.
Laws of Addition
by the normaladditionprocess.
(a+¥)
(+e)+(th)
o 0.
have 4d or 2
4):l
"w'e
For (+I)4+
so that 2 -2'>(N&i)->12 giving a zero in S, a positive
number as we had assumed.
a zero.
If LE} *)t)a,
IfA b4 then $>&A.b-2' or ,a(-!))2
2
-
giving a one in S.
For ,,)+(- ,
giving a minus
)
we have Z
.()+(4-]
- 2
sign in S.
All of the sums considered here are 42
meaning
that no C ever overflows into and interferes with the
sub-word
on the left.
- 20-
Subtraction
of the sub-words
"in bulk"
is similar to
addition but the C bits of the minuend must be loaded with
l's to prevent borrowing
from the sub-word
on the left.
MultiDlication
We can multiply a number by a factor of 2 , if it is
positive, by shifting it m places to the right and inserting
zeros on the left.
If we consider the digits shifted past
position 1 to be lost we have, originally,
c-
k,@t2k
2
kook
...
After shifting m places we have decreased each exponent
by m, giving,
C's o
c
_
towithin2
If c is the negative of a number c-:
.
,
we insert
l's on the left after shifting.
Originally
0 I X...X
and we add to this
O
Thenumberaddedis
sothatc'
c
2'(I s.
is shifted to 0O...Gx..
...I 6...b
(2.a
) +X
.
)-(
22
2
which is the negative of the number
-
-2
2 z
a
as desired.
If a digital-to-analog converter is used which only
handles absolute values we add 2
to each of the sub-words.
This is a 704 word with l's in the S bits and O's elsewhere.
We can also accomplish the same operation by simply changing
the sign which can be seen to be equivalent.
Appendix B
The 704 Program in Detail
The 704 program as tested in May 1959 is made of
tbo basic sections.
First is the synthesis program itself,
and second the auxiliary routines --
one to initially
compute the damped sines and another to display synthesized
waveforms on the cathode ray tube unit attached to the
computer.
Synthesis Program
The present point of time may occur at a sub-word
within a 704 word so that addition, when it occurs, will
involve shifting the store
samples to the right or left
so that their beginning will correspond with the present
point of time.
On the other hand the present point of
time may be at the beginning of a 704 word which means no
shifting is required.
Since the second operation is much
simpler than the first, an otimum
program could be written
that would make the simple routine run much faster.
multiplication may or may not be required
quite- a difference of seed
Also,
nd there is
when multiplication is omitted..
To take advantage of these possibilities to gain speed,
routines have been designed to handle each case separately.
The phase (plus or minus) is also handled separately at times.
There are three working areas in the machine: the bank or
sample block containing the damped sines and noise, a short
work space called the multiply block, and finally the assembly
block in which the entire synthesized sample is formed.
The various possible sequences of operations are
shown in Fig. 15 below.
The instructions are tested by the program one at
a time and completely executed before the next instruction
is studied.
Whenever the synthesis (sometimes called
is entered
"assembly")
program
initialized
so that it begins
block.
all of the markers
are
at the origin of the assembly
After an instruction has been executed a return
is made to obtain the next instruction, or an error count
is stepped by one if an illegal instruction was given
(amplitude
terminate.
is found
or frequency
out of range),
or the assembly
may
Termination occurs if an all zero instruction
(this is a T zero instruction,)
or if the present
Doint of time becomes located near the end of the assembly
block.
-2.3-
The T instruction causes the setting of three markers:
the present point of time measured in sub-words from the
beginning of the assembly block, the number of 704 registers
from the beginning of the assembly block, and the position
of the present point of time in sub-words as measured from
the beginning of the 704 word which contains it.
The D instruction sets the duration as measured in
sub-words. If the duration is found to be greater than the
length of the longest sample (a noise sample), then it is
reduced to this value.
The F instruction first computes the phase of the
sample as plus or minus and sets a marker denoting this.
Since the multiplication routine can only handle shifts
of multiples
of 6 db in amplitude
(powers of 2), and 3 db
steps are desired, each sine is stored at two amplitudes
separated by three db.
Thus both the amplitude and the
frequency enter into the calculation of the location in
storage.
Both the number of places to shift, for
multiplication, and the sample location are then computed.
Finally, advantage is taken of the fact that the sine waves
damp out in shorter times for lower amplitudes.
daming
If this
time is shorter than the duration time already
specified, the routines handle the sample for the minimum
time necessary and do not compute useless strings of zero's.
The F routine then transfers control to the proper assembly
routine for the actual synthesis.
The N instruction is quite similar to the F except
that the phase is always plus and because of storage
requirements
the amplitude
In this program
is in 6 db steps.
the end of assembly
the (TV) routine for scope display.
is followed
by
In a production
version the end of the assembly would cause the sample
to be stored or to be read out.
Then a new set of
instructions would be obtained and the next sample synthesized.
Auxiliary Routines
To compute
the damped
sine waves, one cycle of a
55 cps. tone and one exponential of somewhat longer duration
are computed.
The nth harmonic is then formed by indexing
through the block of the sine wave, picking every nth point.
The computations for the indexing are done modulo the
block length (which is conveniently 256-28), so that the
point picked is always constrained to lie within the one
cycle block.
This is a very fast way to produce multiples
of a waveform in time.
These harmonics are multiplied
by the decaying exponential, scaled to two different values
and the resulting samples stored.
All harmonics of 55 cps.
up to a pre-set limit are computed and then every even
harmonic up to a second limit.
The limits in the present
version of the program are 550 and 5500 cps, respectively.
This routine is finished at a point called "End Computation."
At this point a routine can be inserted to store the samples
on tape so that they need not be computed for each run.
The scope routine first titles the run and then
takes blocks of 100 words (500 sample points) and displays
them a number of times, numbering each block sequentially
from 1.
The right edge, left edge and the x-axis are also
displayed.
The role of this routine is quite flexible, as
it is only needed when there is some question of whether
or not synthesis is proceeding correctly
useful in debugging.
I
--
it is quite
C
Appendix
FLOW
General
Synthesis
JIHARTS
Program
.
. .
.
.
.
.
Auxiliary Routines. .p........
. page
28
page 29
On the flow-charts the symbols in parentheses refer
to points of entry and data words in the SAP program.
The actual locations of the most important of these in
the SAP program are indexed on page 30.
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Aooendix D
SAP - PROGRAM
Index of the more important entry points.
'
-
o n s
General Synthesis Program
Instruction Number
Syb ol
A
80
D
148
E
103
EA
106+1
F
155
FmUL
210
N
385
NFUL
202
MA
297
MAL
324
MDA
244
MDAL
263
MMA
279
MMAL
289
346
MP
352
MP L
368
PDA
213
PDAL
232
30
Program Index (continued)
Symbol
Instruction Number
PM?
349
PSKO
207
S
107
SNMPY
381
T
133
TD
193
Auxiliary Routines
A
80
DSP IC
427
EC
79
HARML
27
HOUT1
54
NEXTT
458
SETV
413
SMWL
434
SMT~WLR
430A
6S1TART
1
75
THNH
TV
405
TVE
468
380A
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Apoendix E
The Format of the Instructions
Octal
numbers are based
on the numbers
0 through 7
as our decimal system is based on 0 through 9.
Octal
numbers are especially useful in computer work as there
is a one-to-one correspondence between an octal digit
and a group of three binary digits.
The instructions
will be composed of six octal digits so that two will
occupy each 704 word.
The positions are numbered from
the left.
T
will have a 0 in position
the value
1. Positions
2-6 contain
of the shift in units of one sub-word,
from 0 to 77,7778
(O to 32,76710.) A 0 will terminate
assembly.
;D
will have a 1 in position 1. Positions 2-6 contain
the duration in units of one sub-word.
F
will have a 2 in position 1. Position 2 is even for
a starting phase of 0
phase of 180 ° (minus.)
(plus) and odd for a starting
Positions 3 and 4 contain
the number of the sam-oleand thus determines the frequency.
Positions
N
5 and 6 contain the amplitude.
will have a 3 in position
1. Positions
2 and 3
soecify the nature of the noise desired.
The samples
would be numbered and their characteristics listed
--
for the programmer's convenience.
the amplitude.
Position 4 specifies
Positions 5 and 6 are disregarded.
50
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