Calhoun: The NPS Institutional Archive

Theses and Dissertations Thesis 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

December 1968

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· Thesis P7483 =======================~

T~ dooument h~ been appAoved 6oA public Ae­.te.~e and ~ a.le.; 1.:U dU.t!Ubu..tion .iA unlimited.

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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

Thesis Advi 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 .

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LIBRARY NAVAL POSTGRA DUA TE SCHOOL MONTEPEY, ~DLfF. q39~0

SECTION 1

SECTION 2

SECTION 3

SECTION 4

SECTION 5

SECTION 6

SECTION 7

APPENDIX 1

TABLE OF CONTENTS

INTRODUCTION

THE CHARACTER OF A BELL TONE

RECORDING THE BELL

ANALYSIS

4.1 Dis crete Method

4 . 2 Continuous Method

4 . 3 Compar ison of Methods

REDUCED VISIBILITY WARNING DEVICE

5 . 1 Discuss i on

5.2 Timing Circuitry

5 .3 Des cri ption of the Entire System

SYNTHESIS OF THE BELL TONE

6.1 Syn thes i s by Discrete Computat i on

6.2 Synthesis of t he Bell Tone by Electroni c Circuitry

SUMMARY

7.1 Analys i s

7.2 Synthesis

BELL SPECTRUM BY DISCRETE ANALYSIS

1.1 Bell Spectrum , Mean Time 0 . 0625

1.2 Bell Sp ec t r um, Mean Time 0 . 1875

1.3 Bell Spectrum, Mean Time 0.3125

1.4 Bell Spectrum , Mean Time 0.4375

1.5 Bell Spec trum, Mean Time 0 . 5625

1.6 Bell Spectrum, Mean Time 0 . 6875

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seconds

seconds

seconds

seconds

seconds

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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 67 EQUIPMENT

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LIST OF TABLES

TABLE I Partials of a Bell Tuned to the Note F

TABLE II Partials of the Fog Bell

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FIGURE 1

FIGURE 2

FIGURE 3

FIGURE 4

FIGURE 5

FIGURE 6

LIST OF FIGURES

Unijunction Master Oscillator

Timing Pulse Train

One-Shot From ~1914 and Discrete Components

Power Supply for the Horn and Bell

Reduced Visibility Warning Equipment

-Simplified Block Diagram­

Twin-T Oscillator

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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 circuitry. 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 discre 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 relatively new application of discrete Fourier

analysis on a general purpose .digital . computer . This method .of

analysis i s applicable to any discipline .wherein frequency spectrum

information is desired . Recent and future projects at the U. S. Naval

Postgraduate School in this .area include, but are not limited to,

voice pattern recognition, helium atmosphere voice distortion, the

study of surfac e waves on water, and squirrel heart-rates under

stimuli .

As a second method of spec tral analysis, an analog .narrow band

spectrum analyzer was employed _to check the results of the d i screte

method . The comparison .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 .raasonably simulate it with .an eye

to s implicity and minimum cost. . Practically, this goal was achieved

with suitable timing cir cuits driving R~C oscillators . As a check ··on

the validity of the analysis, this sound was also simulated by

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digital/ana l og methods. The waveform was mathematically described i n

the time domain, computed in di screte s teps and converted to analog

voltages . These vo l tages were then conve r ted to sound energy.

To s how the pr acticality of synthesiz 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 reduced .vis i bility as required by

U. S . Coast[ l] Guard Rul es. To comple te the suite of required fog

s i gnals fo r a sailboat, signals for sailing on various tacks and whi le

* under power were added. This reduced _vis ibi l ity warning device was

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 device

on board small private, Naval, and Coast Guard vessels where the crew

may be few i n number and fully occupied with operating the vessel

would be des ireable .

* Refe r to Appendix 6 for a discussion of the required warning signa ls f or a sailboat in reduced visibility .

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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 '·series 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 musical sense .

* Refer to Lord Rayleigh's., The Theory of Sound; Vol I, p 388 for a more complete treatise on the subject.

** Authors disagree on this 'idealized' series.[ 2),[ 3 ] Another series given is 1.0:1.65:2.10:3.0:3.54:4.97 ....

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Ther e appears to be some disagreement 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 vibrations, or if it arises as t he result of a beat

[ 4] [ 5] f r equency. ' Curtis and Giannini appear t o have employed a

prec ise and controlled method for arrivi ng a t t heir results. They

ar gue that the strike note from a particular bell which was analyzed in

considerable detail arose as the result of har monious blending of three

c lose fr equenc ies .

The various partial s of a bell have independent amplitude ver 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 ndependent of all others. The higher f requencies of the

composite wave form appear earliest in t he spec trum after the bell is

struck , and di e away most rapidly. Some of t he lower frequencies may

not appear in the spectrum until as late as 1 t o 3 seconds afte r the

crash. The f ollowing table was extracted fro m a paper by Curtis and

Giannini [6 ] t o illustrate the frequency conten t of a part i cular bell

they studied . The bell chosen was a church bel l tuned to t he musical

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 musician might describe it. The s i gnificant partials found

to be pres en t in that bell are in t he column headed 'Tone Frequency '.

This illus t r at ion cle a r l y shows that only the s trike note came close

to the des i r ed frequency. Additionally , the s t rike note was straddled

by other frequenc ies causing it to be in actua l ity a tr i plet. Curtis

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TABLE I

Partials of a Bell Tuned to the Note F

FREQUENCY TONE NUMBER PARTIAL OF NOTE NOTE FREQUENCY

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 variant.

5 . The various frequencies present are generally not

harmonically related.

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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 equipment except for a microphone was placed outside the

anechoic chamber. The microphone used was an Altec Lansing Model

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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 bell 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 was an Altec Lansing Model 526B microphone power supply. The

response characteristics for the microphone and its associated power

supply are typically within ±1 db from 10 to 3000 hertz and within

±3 db to 15000 hertz. 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.

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r .---------- ·- -- --1

I I I .---------------------~~-+---------~ i I I I L - · ___ A~!=~h~i~- ~~~~-e£ _

...___r- ll------j i I '--------'1 L __ _

Mic . Pwr Supply

Pre- amp Tape Recorder

Block Diagram of the Recording Process

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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 contri-

buted to its selection . These were,

1 . 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 .

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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 was 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 the 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 .

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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-ries consisting

n of N = 2 samples. To perform a discreteFourier transferm. using FFT,

(N log2 N) computational steps are required. For earlier more direct

methods , N2

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 . [10]

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The discret e Fourier transform is defined by[ l l ]

A r

N- 1 2:

k=O r = 0,1, . .. ,N-1

where Ar is the r t h coefficient of the DFT and ~ denotes the

(1)

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 . Since the FFT is an

implementation of this definition, this relationship also defines

the FFT.

Given a time series with a constant sampling interval 0t) between

each successive s ample, the sampling frequency is given by

f = 1/llt s

(2)

By the Nyquist sampling criterion, the resultant bandwidth recovered

from the signal of interest would be

Band Wid th = B 1/2/:::.t (3)

f /2 ( 4) s

This of course is only true if the signal is band-limi ted to B

before being sampled. Given a frequency higher than B in the original

signal, say f1

(B < f1

< 2B), then a finite Fourier s eries for the

signal after analysis would reveal a spectral line at f1-B.[l

2] 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 sampled must be

filtered before s ampl ing. Even with filtering, some error is introduced

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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

sampled data points . Therefore these lines will be separated by ~f where ,.

M = B 2B N/2 N

(5)

f (6) M

s N

With a time variant signal (the coefficients of the associated Fourier

series vary with time) this simple r elationship yields a paradox of

accuracy . For a fixed sampling rate . (i.e . , f is fixed), N must be s

made large with respect to f to recover a small ~f . But if N~t s

is large compared to the time over which the coefficients vary signifi-

cantly, 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 . The penalty paid, of

course, is that ~ f would now be larger and the spectral lines would

be farther apart . [lJ ] This paradox is yet another form of the well

known uncertainty princi ple . A desireable compromise would be t o have

the coefficients change only a small amount over the period N~ t :, and

yet have a sufficiently small ~ f to discriminate between adjacent fre -

quenc~es 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 and N to obtain such a result . One s

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technique used in this research was to analyze a time series once to

obtain a fine ~f, and then to analyze the same series again to obtain

reasonably accurate 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. The sampling frequency used was 1024 . 0

hertz . When this sampling frequency is . translated by 32 ( to correct

for the tape speed reduction), a true sampling speed of 32,768 hertz

is realized. By the Nyquist sampling criterion, this sampling frequency

produces a bandwidth 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. This upper 3 db point corresponds

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' 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. This corresponds to a

record time length (N II-) of 125 ms. Each window overlapped the preceding

window by 50 per cent . 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. The- time duration

for this record length was 500 ms . The computed spectral line separation

for these parameters is 2 hertz . 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

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reference clock . The hybrid installation consisted of an SDS 930

general purpose digital computer interfaced with a Comcor CI-5000

electronic analo g computer. The analog-to-digital converter had an

fourteen bit word 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 exceeded the memory

size of the SDS machine. Due to the different word sizes of the SDS

and IBM machines , an assembly language -subroutine was written to convert

the sampled data word 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 equential 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 series , and then printed out .a permanent 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 points 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 .

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Significant Frequencies

565 1370 2331 3061 3320 3773

TABLE .II

Partials Of the Fog Bell

Commence (sec)

0 . 125 0.125 0 . 0 0 , 0 0 . 0 0 . 0

(End) sec

1.6 1.5 0.875 2 . 0 1.0 1.4

Maximum Amplitude (relative energy)

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.cies 565~ 1370, and 3061 give

the bell its prolonged sound as it dies away . 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

h [14], [15]

ot ers .

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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 integrat 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. As the drum turns, the filter advances ea ch rotation . of the

drum. 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 successive slices

(time windows) of t he spectrum can be made. By manua 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 accuracy 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

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develop the bounds on the accuracy of the coefficient magnitudes for

the continuous method . It is considered . that this amplitude information

is quite dependable . 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

determine phase information about a complex wave form . [l6 ]

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SECTION 5

REDUCED VISIBI LITY WARNING EQUIPMENT

5.1 Discussion

Quite often aboard a pr i vate sailing yacht, a crew may be

sufficient ly occupied with sailing the craft during reduced visibility

that sounding fog signals could . be . a .. burden . Sounding s uch repet itive

timed signals 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 devi ce

could alleviate t he problems created by the aforementioned examples by

providing reduced visibility warning signals for the craft . Such a device

ideally shoul d be simple to operate while provi ding dependable contin­

uous warning signals for underway and at anchor operations .

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 bell tone which was .included in the device . The final

form of the device was constructed .out of solid state devices and placed

on printed circui t boards . This device could . be packaged 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 periodic feature common to the anchored warning .signal .

and all the low vis i bility warning sounds while underway is their period

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FIGURE I

UNIJUNCTION

MASTER OSC.

470

SO,.uF

FIGURE 2 TIMING PULSE TRAIN

M.O. I ' ' "',__....__I --,.,--ONE- 7 8 55 56 (SEC)

5 ~ OT .....-I ---.___ _____ "' I 1L--_

2 ....____---ty..--------11

l'---------"v....-----

~4 __________ ~1l~---~--------

5

27

be twe en sounds . All of these sounds (with the exception of the requi r e d

s i gnal f or underway under power in i n ternational waters) have a maximum

period of one minute. The maximum specified period for under power i n

i nternational waters is two minutes. Prudent seamanship dict ates that

thes e i nte r vals not be fixed over any lon g period of time . This

desired aper iodicity pr events two ves se l s from sounding similar warning

signals syn chronously . Synchr onism -could bring about theundesireable

side effect of a collision and t hus .. the . ruination of one's day .

A master clock is required fo r the warning equi pment and i s

specified by a frequency of from les 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 ability to satisfy these

requirement s . The basic form of a .relaxation oscillator with a periodic

pulse out put was chos en and i s shown .in . Figure 1. A potentiometer is

used to va ry the oscillator frequency manually when desired . With the

component values shown, the periodic range i s variable from approximately

55 s econds to 90 seconds .

The periodic pulse output .of this mas ter oscillator 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 generate al l t he required

logic l eve ls . for sounding the various warning s ignals . The puls e fr om

the ma s ter oscillator turns on the first one-shot . When t he fir s t one

turns off , the second one .turns on, etc . Thi s t ur n on/turn off pr o cedes

thr ough all five one- shots until . t he l ast .one is off . This sequence

is i ni t i al ized by each trigger pulse from- the master os cill a tor • .

The t urn on of the next one-shot i s accomplished by inverting the previous

28

N \.0

FIGURE 3

I TRIGGER

INPUT

ONE-SHOT FROM

3.6 v

8

R3

,t.~L914 AND DISCRETE COMPONENTS R3,CI, AND C2

OUT PUT 6

C2

R2

NOT USED

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 accom­

plished by a manual function selector switch . This switch is in

actuality a variable i nput AND gate.

The active devices chosen for the one-shots were Fairchild ~19 1 4

dual two-input NAND gates. By the use of _one external 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 digi 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 . To minimize this occurence , a . large capacitor, C2,

(typically, 50 ~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. A 1000

~f 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. With

the capacitor, some spurious triggering still results, but the one~shot

chain does not go into continuous oscillation. This spurious triggering

30

w f-'

FIGURE 4

_j

POWER SUPPLY FOR THE HORN

+V(X.

RELAY I

FROM

AND BELL

2N404

I I

r--L I I I I I

-----.J

TO HORN OSC THROUGH SWlC IOK

_J1__J1__J"L_

TO BELL CIRCUITRY

NOTE: I. QI-Q4 ARE 2N736

could also be eliminated by providing a constant-vol tage, variable­

current power source. 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 voltage 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 from the chain of one~shots is also applied to a NAND

gate. This gate develops the logical voltage t hat switches in a

listening section and turns off the power amp'Iifie r when signals are

not being sounded. This technique of listening is s i milar to a simple

intercom system. The output speaker for the powe r amplifie~ 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 passengers and crew of ones own vessel during periods of

reduced visibility. 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 features:

1. The three required reduced visibility signals for a

sailboat underway.

32

- . ~ ' • •

FIGURE 5 REDUCED VISIBILITY WARNING EQUIPMENT

-SIMPLIFIED BLOCK DIAGRAM-

BELL

w

I I w

FOG HORN 6 I~

OUTPUT OUTPUT (. kX<>

I AMPLIFER SPEAKER

I ? HORN

LOUD-HAILER

Ll STEN

2 . A reduced visibility signal for a vesse l underway under

power.

3 . A manually operated war n i ng horn for entering or leaving

blind channels and slips .

4 . An aut omat ic and manual listening device.

5. A loud hailer.

6. A rapidly ringing bell for a vessel at anchor in reduced

visibili t y.

7. Test positions for 2 and 6 so these functions may be

checked out i n port at r educed volume f or preventative

maintenance .

The final power amplifier common to all feature s except 4 is a

standard class B trans i stor power amplifier . This output stage, the

oscillator for a ll underway signals, and the loud hailer circuit ry were

taken directly from a commercial fog horn /loudhailer device .

The underway signals employ a unijunction oscillator of a nominal

frequency of 200 her t z. This is .ei ther actuated by t he selected timing

chain associated 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 oscillator which causes

an output f requency of nomi nally 380 hertz .

The listening device partially described under the timing

circuitry sect i on employs a commercially avai lable 500 milliwatt

direct-output audio amplifier and an 8 ohm water pr oof speaker . The

output speaker for the power amplifier is swi tched to act as a micro­

phone input t o the listen amplifier. A 3-pole double-throw re lay

34

'

actuated switch is used to remove power from the output stage to

prevent damage to the transistors, and to switch .the 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 most prominent part ials found during the analysis. The

partials wer e written as t ime variant sinusoids. The time response of

each partial was approximated by fi tted exponential curves.

A FORIRAN II language program was written fo r an SDS 930 digital

computer for computa tional purposes. The equivalent o f sampled data

was computed in discrete intervals of .000125 seconds. The computational

st e p size in seconds and the fr equency present in the wave f orm were

based up on a 'sampling' f r equency of 8000 hertz.

A total of 8000 samples were computed and stor 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 permit parameters of

attack, decay , and amplitude to b e varied. These provisions were made

so that some experimental modifications to the wave form could be made

in l ight of qualita t ive analysi s .

A machine l a nguage (META-SYMBOL) subroutine callable by FORTRAN II

was written to perform the task of digital-to-analog conversion. This

subroutine was controlled at a rate determined by a c lock on the

associated a nalog 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 through a pass-band fi lter with a

band width from 20 to 4000 hertz to minimize sampling noise. The wave

36

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. Practically

speaking, this exact duplication is seldom desireable . 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, light-

weight, relatively inexpensive, reliable, and require a small amount of

• power. Looking at the desireable aspects of a practical bell simulator,

37

one would expec t it to generate a reasonable bell-like tone from a

small inexpensive device. Hopefully not all the partials present in

the original bell sound would be required for reasonable simulation,

and the required par t ials could be simply generated.

The f irs t technique considered for synthesis of the bell tone

was the use o f a very h i gh Q band-pass circuit (400 ~ Q ~ 1000). Such

'bl . . f'l h . [lS] circuits a r e poss1 e us1ng ac t1ve 1 ter tee n1ques. Such a

filter would employ only ac tive devices , capacitors, and resistors. By

causing such a fi l ter to ring b y in t roducing 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 synthetic bell tone. To achieve these very h i gh Q

c ircuits, a multiple-po l e filter is required 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 second technique investigated was the use of a constant

amplitude sine wave oscillator fed into a gain-controlled amplifier.

By varying the gain of this amplifier, the resul tant wave shape wo uld

simulate one partial. Some wave shaping circuitry would be required to

control the gain of t his amp lifier. There are several inex pensive

integrated circ uits pres ently being marketed that could be employed as

the gain-control led amplifier. These integrated circuits are generally

designed f o r int e rmedia te frequency (IF) amplification and t hey have

automatic gain control (AGC) circuitry built into t h em. Typically, an

80 db contro l range can b e achieved for a few volts 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

[19] was twin-t oscillators driven by a variable supply voltage. 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 high-

current 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 . During the time Td'

CfRd form a discharging time constant. The resultant supply voltage

as seen by the oscillator is given by the following equations.

v(t) vb (1

a R cf c c

v(t) V(T ) c

ad Rd cf

exp(-a t)) c

exp(-adt)

39

0 < t < T = c

T < t < T c

(7)

(8)

(9)

(10)

0:. 0

~ _j _j

u (j)

0

r-I

z -3 r-

(0

~ :s ~ c:

0 0::

0 0::

<{

0::

- C\J 0: u 0::

II II • -u

Ill lJ..

u

"

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 the goa l

of simplicity 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 frequency of the

output . Variations of R2 will cause the oscillator to tune over nearly

an octave . For optimum frequency stability, the oscillator should be

adjusted to the center region of its tuneable range. Convenient design

thumb rules are C = 2

can be selected from

2c1

, and R2

= 0.1 R1

; the

easily used n6mograms.[ 20]

values for c1 and Rl

The r es i s tor R is 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 desir 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 construc ted .

Three of t hese frequencies (2331, 3320, and 3773 hertz) reach 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 reach their peak amplitudes significantly later and

41

probably give the bell tone its hum note. These latter frequencie s

were grouped together and given an attack time of 300 milliseconds.

The values chosen for at tack times for each group corresponds roughly

to t he average attack time for that group found in analysis. Admittedly,

this broad group ing is an oversimplication, b ut certainly desireable

from the view point of minimizing the required circuit ry.

The supply vol tage for these oscillators was generated b y employing

a grounded emitter as t able multivibrator driving transistor switches

(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 was 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

transistor 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 each oscillator,

the resulting bell tone was a fair representation of the original sound.

The rapid per iodic rin ging of the bell suggest ed that some of the lower

frequ encies comprising the longer lasting hum note group could be

eliminated. Hope f ully this could be done with little degradation 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 rung at intervals of 700 ms. The final f or m of the bell tone

42

•

•

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

7 .1 Analysis

SECTION 7

SUMMARY

Both the discrete and continuous analysis techniques suffer certain

limitations. These limitations arise due to the finite frequency

s p ec trum r epresentation of time and b and limited complex wave fo rms.

The result ing inaccuracies are inevitab le and ar ise as a r esult of th e

uncertain relationship of the time signal to its frequency trans fo rm.

By s e lection of proper sampling frequency and time series duration ,

a quas i-sta tionary p rocess can be approached for the purpose of obtaining

both frequency and amplitude information. Permutations of sampling

f requ ency and time duration of the series allow optimization of frequency

information, or amplitude info rmation, but not both.

7 . 2 Synthesis

Complex wave forms can be approximated qui te simply using solid

state devices if the 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 desired, 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 demon­

stra 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

the engineering techniques a nd expertise for suc h a device.

44

•

•

•

BIBLIOGRAPHY

1. United States Coast Guard, Rules of the Road, International-Inland , CG 169, U. S. Government Printing Office, 1965, p 26.

2. J. J. Josephs, The Physics of Musical Sound, D. Van Nostrand Co., Inc., Princeton, N. J., p ~33.

3. A. T. Jones, The Strike Note of Bells, J. Acoust. Soc. 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. 1933, 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 Electroacoustics, 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 Publications, Inc . , New York, 1954, (t ranslated from the German edition of 187 7), p 126.

45

17. D. E. Lancaster, Using New Low-Cost Integrated Circuits, Electronic World, March 196 6, p 52, 80.

18. W. R. Kundert, The 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: Design and Applica tions, Electronics World, Aug. 1968, p 200.

20. F. B. Maynard, Twin-T Oscillators, Design and Application, Electronic Wor ld, May 1963, p 41.

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 cies .

For these spectra, a sample size of 4096 data point s was used for the

transformation which yielded a 6 f of 8 hertz .

47

2.5

BELL SPECTRUM I I I I I I I I

2.0. . .. . . . MEAN TIME

>- 0.0625 SEC. b (_') 0:: :B w

I I I z 1.5

[fi w

I~ ~

~ 101 I I II I I I I I I I co

~·

I I I II I II I I=::: _j I I I ~I w 0::

0.5

A

0.8 1.6 2.4 3.2 4.0 4.8 5.6

FREQUENCY (KHZ}

" ~ •

APPENDIX 1.2 •

~ :=) 0:: r-- w u u ~ w - (./)

w 1--

Q_ 2 l[)

(j) <! f'-.

w OJ

_j :E d _j w m

•

• L{) . q q N

A8d3N3 3/\ll~l3d

49

l[)

d

........:;

~ <

<

' ~ "1

-5 ~

)

) .........._

)

""""""

~

q <;j"

N 1'0

<;j"; N

(X)

0

... Q oo d

N I :X: -

>-u z w :=)

0 w 0:: LL

\.Jl 0

2.5

2.0

>-<..:> 0: w 1.5 z w w > 1.0 1-<( _j w a: 0.5

o.o 0.0

. ..

Jc A 1 0.8 1.6

_..I. ...I\. ..;\.

2.4 3.2

FREQUENCY

•

BELL SPECTRUM

JL

4 .0

(KHZ)

MEAN TIME

0.3125 SEC.

.Jw )1._ 1 4.8

j_

5.6

I

I

f

:D.

:8 ~ C5 ~ -:::-..... GJ

Vt t-'

f

2.5

2.0

>-(.9 0: w 15 z· w w > 1.0

~ _J w a: 0.5

. 0.0

0.0

A A

0.8 1.6

'

J Ji\.. _.\.

2.4 3.2

FREQUENCY

BELL SPECTRUM

\

4.0

(KHZ)

MEAN TIME

0.4375 SEC.

~ .A. .A 4.8

J.

5.6

.. ..

~

] ~ c:s X ~

APPENDIX 1.5 . . --

~ ::J 0: w . l- ~ ~ u - c.J)

w t-lO

0... z N <.f) <( ~

w lO

_j ~ 0 _j w m

I{') . N

~ l/1 q d A.9CI3N3 3/\llV'l3Ci

52

-~

..

-: ~

.)

' ..

---=..,

.........;

-

0 . ~

N r<>

~ N

co d

0 od d

-N I ~ ->-u z .. w ::J a w 0:: LL

\.Jl w

r "'

2.5

2.0

>-<...9 0: W I 5 z· w w > 1.0 1-<( _) w 0::: 0.5

o.o 0.0

A A 0.8 1.6

•

BELL SPECTRUM MEAN TIME

0.6875 SEC.

1 J\o. J . ~~ A

2 A 3.2 4.0 4.8 5.6

FREQUENCY (KH Z)

...

b

:8 ~ G 5< '7---

0J

APPENDIX 2

COEFFICIENT AMPLI TUDES VERSUS TIME FOR THE BELL

By discre te and continuous analysis, the magnitudes of the

coeffic ient s for each significant partial was found as discussed in

Section 4. Append ice 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 uld not be precisely the same.

Fo r those coefficients with a slow rate of change (e.g ., 565,

1370, a nd 3061 her tz ), the results of t he two methods used compare

fairly well. For t he partials with a faster time ra te of change

(particularly 2331 and 3320 hertz), the correlation of the results

was poorer. The genera l s hape of these plots were similar however.

54

•

r

'

APPENDIX 2.1

55

(

(

0 :.;

r 5 u l'l

~ .:. ~ ,N ::' t!l

~ ~ ~ f- - "­

"-0 ~ :)

0 -~

56

0 u:>.

~f./) ~·o

z .oo ~. U :

UJ , ~ t.f) _: .

~

_m· 0

0

~ 0

APPENDIX 2.3

•

4---· I I

I

•

! i I I

I I I i-' i ___ _!_

-·

(

(

(

0 ,... ~·

t • u

I 5

(

u Ul z Ul -I!' UJ ,.... ~ ~

~ ~ 0 I .

9 ~ :J

X X :.:

o:::c - I·

(

APPENDIX 2.4

58

Vl 1.0

' "

;· 'i I

~+.:L -L-

-1

~s

~~~~ a:

.. i• -~---

I

~

~·· I

I I .. -----~ ,. ·-. :-;----

-1 I . ~~~

I

i L._' - - -----,-· i

AMPLITUDE vs

' . ill~ E -- : I

; 1 I : ;F...tE~.~ut:;~ J(SY ~ ~~~~Q:~. Pf~ . I ' H ~-r-L~--- I • ' .

I .. - I . I I ' - r-r-· ~ , 1 , · I

. · i . . . _, -. -I - -I· I -- . -'- . •-- -·-·- -. :I r : . ' . .

-+-- - . ---:--'--,--.. ,--. - . _· ... rc= : . ' ---~-· I I i ,· *I -._ -· I. --+ .

• : - I ·;~ : . - : : •· : . t~ltou~-~J-=~-~ ~ . ' I "'r [, I .

, I . I I J..· . . ' . ' r· ;: I - -+--- - '-·;. . .. i ·. ' I I 'I. I ~ -·r-~, :r:; 1 •• , • l. ": __ l -~~- 1· :;- -t- -·~--'J ~ n-. I - I - I I J !· ' .. l : I ~ I. I ....

' I ; I ' I • L--·---+-- --1 .. I I .•.• -- ---r-·-T----. -- ·I I ' ! I I

. =r--- A ::TT:-·~---r:-1 I I . -T~, ~~- :-J -+-t-·t~, . ~:. - ~--·1 : ~ I · .- · --- -~~ .. r: : : ·t ·1- __ ~:--: -- 1.:r·t ' .. ·• : +'-_L_I -~ · ·1 ~--'+--Ll· ---~~ · .... _, --.,t~

i, ·!· 1 ' ' ' I t· I ·;•J" ,[r[ I .... . I I I.' '-~ t · . ~-- I -·-1 1 . -r- 4- ;- r:-.-, · .. ·, l.: I ;a1

~--t- -~~ ~~ -+:. --~~t~rtr:.:Gl~ ~ i+··:.~ .. -. -1---r :+- 1~ ! _· i I ·4·' ~:-.. I i ,. I ___ )_ __ --1·- f- ., .

I I ~-- ·---.,~ -, . . I ' II · ·r: - .· r .. , ;· f" 'j i ·l . --·I ·+.· .H ·:.:L .: •

1

_I· _k 1 --t--,.~ ~,· .. T':.. -=~--:-- -~- I ' f 1 . : ' l • I 'L f ~; + ,.,: I . ':. ! . I · . .. L: . ..:.f.-..:-.+.- -- -·-r::r J •• - -,.,..... ' · r -*·1~-=.' I - 1 I . . (" .l I I·=

., ; . . ' _:.t___ -[+I ------- ...,- I.-,----, · I ' I p ;_; : . l I ' '. I . .. ': , •. +

I j ' • I -· • . ;.....-1.

I• ', l .. . +-=4 ~. J._:__d . t-- _....._ . ---- I ; . . :. t· ':i

L ~- ---.}---· - -1· •' I i -

I .;,_ ~ ~

-~ ' ---~-

-r-

.j

i ___ 0 I

I 0 .04 .08 .12 .16 .20 .24 .28 .32 .36 40 .44 .48 .52 .56 .60 .64 .6.8 Tl ME (SECONDS)

?; "tl 1:%:1 s H :X

N

Vl

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(

(

0 u

l: ~ u ~

z "' u

(

: -~ 4:: =*-~~ ' t----'":'-. -: -t :.d..: .:::::.t-

••• -.- ~ ..J ::-J. .

-:-:: ... . . - .-!

. .• • • • .l - · .lt-1 ;

. : : . !:": : : ::rll=tf::. ; ; :}'....! ~ ~ :r-++

.w '17-,_ - ••.. I~- I I • C: . L • ' 1+-t-c·f

. ~~ ~ : ·- : :i.;: -::. :=. :..: : .. ~ ' ::1 i J: _, ~- w ..... . .. • · - • ·- I •

.... -· :L! ...

·J·· I I

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r 1-.:.. - +- ~ - -! . -1 · ·: +-~ 1 I I

! -~ I I _l_, __ . 60

(X)

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C\J l{)

<X> ~.

~ 'ln ~· 0

z 0~ ~. U w (,S) $ ~

C\Jw r<) :[ ;

. - · <Xl. C\J

.st.. C\J

Q _ C\J

ru

......

co -~ Q

•

..

APPENDIX 3

SUBROUTINE SAMPL

SS4MPL •

PZE

• • * • • • • * * • • • • • • • • • • • •

SUBROUTINE SAMPL(NOBLKS,LENGTH)

THIS PROGRAM SAMPLES ONE ANALOG SIGNAL ON TRUNKLINE 05CO 4T A RATE DETERMINED BY A CLOCK PULSF. APPEARING ON TRUNKLINE 0210. ANALOG TO DIGITAL CONVERSION IS PERFORMED AND THE RESULTING DATA IS STORED IN DOUBLE BUFFERS OF LENGTH 1 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 JS 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 •

9SETUP2 2

BLKNO DATAT A

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

5 X2

AGAIN

i~~y ~~f k~~ LOA LLSA STA MRG STA

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

*

LOA MP,G STA LOA ADD STA STA LOA ADD STA LOA MRG STA STA SKS BRU EIR EOM HLT BRU BRU

START 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 CfMM =AU FFl =-1 ORI Gl ocw =COMM svcw cw 030 010 ANALCG IN COMPUTE TEST S-1

0330 04 CLOCK LINE

S-1 S-2

TOGG L TOG GT LOA DO C0"4 M C3400 0 cw RIDL E,X2 ORI GO COMM . svcw CW

THIS IS THE IDLE LOOP

THIS PROCEDURE TES TS TO DETERMINE WHICH BUFFER TO LOAD

TOGG L SDAT AT,X2 0,1 0 S-2 *Cl4000 CWl 0,1, 4 INCR

ST ORE DATA ON MAGT APE

* THIS DI VIDE S THE SUBROUTINE INTn BUFF ~RS

* LOA DO

R TE S T3

RTEST4 FILLO

I NCR

*C RIDLE

MPO EOM POT BRX LOA STA LOA STA MPO LOX TRT CAT BRU E0"4 POT WTB SKR BRU

BRC BRC LOA STA EOM

COMM 034000 cw RIDL E,X2 OPIGl COMM svcw cw TOGG L SDAT AT,X 2 o,1 0 S-2 *Gl400C CWI') 0,1,4 COUN T RIDLE S+2 *START BPMPL G 051 0330 00

STORE DATA ON MAG TAPE BLOCK COUNT IS REDU CED . IF NEGATIVE, All DATA HAS REF~ TRANSFERRED.

62

•

..

..

• BRC $+1 SWT 1 SENSf SWITCH 6 TEST RRU S-3 PROGRAM CONTINUES IF NOT SET HLT TO CLEAR HALT, IDLE/RUN BRU AGAIN TRT 8'1 CAT BRU $-2 LOA SVOlO STA 010 LOA SVOll STA 011 LOA SV040 STA 040 LOA S\1051 STA 051 E!R BRR SAMPL

* ~t; END OF SUBROUTINE * CON FORM 9 15 CONT FORM 10' 14 SPACE CONT 150 ,0 ocw DATA 0100)00 svcw PZE cw PZE r 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

•

63

(

c

APPENDIX 4 .

SUBROUTINE FORM

SU~POUTINE 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~

LOf"JP

DATA Nil~

~TART STM BALR USING USING SR L t L LR SR OL SRL SROL ~R l SRDL SRL SRDL ~T L.A 8CT LM MVI RCR DSECT DS END

('l 14,12,,2(1~) 6,0 .,, OdTd,7 7 7 d,:F'l28 1

12,C(!) ?.,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

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

THY S l S THE 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

c c

DIMENSION ~ (16384)fC(l6384),M(3),1NV(4Cq6),S(41 96) DIMENSIO~ 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)

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= 11 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 11 29X,•FREC 1 ,2qX, 1 FREQ 1 /(4(1X,

lo6 1 ;a~~~li;;~x:rR~wF6At!~,,~~i6:t~t,, 107 FORMAT(/3X, 1 TIME REOUIRED TO RFAD INPUT DATA IS•,Fl~ ~ l

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)

END

65

APPENDIX 6

REQUIRED FOG SIGNALS FOR A SAILBOAT

Definitions for the sailing terms used:

Relative wind in this sector

Relative wind in this sector is a port tack 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 Signal Maximum interval sailing vessel between signals

(minutes)

,·~

Starboard Tack 1 blast of 1 foghorn

Port Tack 2 suC'.cessive blasts 1 of fo ghorn

Wind abaft the beam 3 successive blasts 1 of foghorn

*-ic While motoring 1 prolonged blast 1 (Inland)

of foghorn 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 the r educ ed

visibility warning equipment and schematics f or l:he various s ub - parts

which the author designed .

67

0\ CXl

horn tim ina

bell tlmina

' ...

be II clanaer

I I

horn pwr SUPJIY

L-----

bell pwr supply

.____., harn osc

bell cl rcuitry

hailer

ln[IUt speaker

output StillS

listen amp

Reduced Visibility Warning Equipment

Expanded Block Diagram

•

listen teaic

au listen

switch output s[lnker

/

3 (/) ..... 0 I (/) I

w z 0

~ 0 a: LL

5)

2

I I I

oOG> g I

00

FROM RELAY. I

0~ I

0

FUNCTION SELECTOR SWITCH

WAFERS A-8-C

> TO RELAY I

DRIVER

HORN POWER

0 SW IC

~------------------------4~~-----TO HORN

osc

69

FROM MICROPHONE

FUNCTION SELECTION SWITCH

WAFERS 0-E-F

FROM HORN OSC

0 SWID fl TO PA ~-----~ DRIVER ))>---

FROM BELL ~ ~ I >~--------~:~~~~~M~

FROM LISTEN LOGIC

POWER INPUT

TO RELAY 2

-----~»~--D_R_I_VER

SWIE

Vee r------~>~--

SW IF

70

..

..

•

FROM RADIO

FROM LISTEN AMP

0

71

COCKPIT SPEAKER SWITCH

SW2A

SW28

TO COCKPIT SPEAKER

-....1 N

FROM MASTER OSC

'--v---/

+3.6

3.6M

IOK TO

ONE-SHOT 3 ETC.

ONE- SHOT I (2 SEC. DELAY)

IN276

-=- '--v---J ONE-SHOT 2

(I SEC. DELAY) IN276

OUTPUT

.. ...,

OUTPUT

TIMING CHAIN SCHEMATIC ONLY ONE-SHOTS I AND 2 SHOWN

' " ;. .

-...j

w

'V ..J

....1...+ 30"1

• ..,

BELL CIRCUITRY

2N2924

100 K lOOK

.OOIJA - .001,.

~~

....1...+~ 20"1 2N2924

lOOK lOOK 100 K

.OOIJJ - .OOIJJ

~;;

OUTPUT TO SWID

~ q )

.. •

200K

LISTEN CIRCUITRY

t/) .,.__ 0 I I ----,"'ee lf) w2 ---11-e

z 0 ,.t~L914 ~ 0 a: LL.

3 ------1 ....

-8

5--HIII 4--~=--

pl914

TO SWIE t----~~>--

LOGICAL EQUIVELENT

I -----i 2 -----i 3----t 4 ---1

5 ---t____.;

L ISTEN= 1+2+.3+4+5

74

LISTEN

..

r

INITIAL DISTRIBUTION LIST

1 . Defense Documentation Center Cameron Station Alex andria 9 Virginia 22314

2. Library Naval Postgraduate School Monterey ~ California 93940

3. Professor D. B. Hoisington (Thesis Advisor) Naval Postgraduate Schoo l Monte r ey 9 California 93940

4. LT Jerry L " Post 8541 S . E . ?1st Street Mercer Island Seattle , Washington 98040

5. Commander , Naval Ordnance System Command Department of Navy Wash i n gton , D. C. 20360

6 . Mr . R. L . Limes Code 52EC Na val Postgraduate School Monterey 9 Cali f ornia 93940

7 . Associate Pr ofessor G. E . Rahe Naval Postgraduate School Monterey , California 93 940

8. Associate Professor G. D. Ewing Naval Postgradua e School Monterey, Californi a 93 940

75

No. Copies

20

2

2

3

1

2

1

1

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 title , body o f abs tra ct ~nd in dexin g an no tation mu s t be entered when the ove rall report i s c la ss ifi ed)

1 O R I G INATING ACTIVITY (Co rp o rate a uthor) 2a. REPORT SECURIT Y CLA SS IF ICATION

Naval Postgraduate School UNCLASSIFIED Monterey, Califo rnia 93940 2b. GRO U P

• 3 REPORT TITLE

Analysis and Synthesis of a Time Limited Complex Wave Form

4 . DESC RIPTIVE NOTES (Type of report and. inclusive dates)

Electrical Enqineer's Thesis s . AUTHOR(S) (Firs t name , middl e initial , last n a me)

Pos t, Jerry Lee, Lieutenant, USN

6 . REPORT DAT E 7a. TOTAL NO. OF '~GES rb. "fs OF REF S December 1968

ea. CONTRACT OR GRANT NO . Qa, ORIGINATO R 'S REPORT NUMBER(S)

h . "PR OJEC T NO .

c. 9b . OTHER REPORT NO(S) (Any other numbers that may be assif!Zn c J th rs repor t)

d.

I 0. D ISTRIB UTION ST ATEMENT

Distribution of this docu,nent is unlimited.

• 11 . SUPPLEMENTARY NOTES 12 . SPONSORING MILITARY ACTIV I TY

Nava l Postgraduate School Monterey, California 93940

13 . ABSTRACT

The problem of analyzing time limited complex wave forms having time variant

fr equency domain characterist i cs 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 f og signals for a sailboat, including a rapidly ringing bell.

-·

DD /NOOR:6S 14 73 (PAGE 1) UNCLASSIFIED Security Classification

A- 31408 S / N 0101-607 - 681 I

77

UNCLASSIFIED Sec ur i ty Cla s si t c att o n

I 4 LIN K A LINK B L I NK c KEY WORD S

ROLE WT R O LE W T ROLE W T

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 lass ifi ca t ion ·1 -l

78

. '

29 JA 7\

'thesis pJ483 c.2

Thesis P7483 c.2

1o::sso Post Analysis and syn-

thesis of a time l\mtt­ed compleX wave form.

109550 Post

Anal ysis and thes· syn-

1 s of a t' ed comp 1

une 1 i mit-ex wave form.

thesP7483

Analysis and synthesis of a time limited

IHIIIIDIIIIiiiiiBIIIH 3 27S8 ooo 99296 o DUDLEY KNOX LIBRARY

~. .