US2451465A - Transversal filter - Google Patents

Description

FIPBlOb AU .7.33 EX ox. 19, 194s.

nm nb. 2v. 1941 H. L. BARNEY twisvzns/u. rxmza r cli) ruf n. Y

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JMA/ron H. l. BAQNEY ATTURNEY hmmm..

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'Patented Oct. i9. i948 A i i 2.451,465

assists 1 TRANSVRSL FILTER Harold L. Barney. Madison. N. J.. assigner to Bell lTelephone Laboratories.

Incorporated. New

York. N. Y., a corporation of New York applicaties reinem s1. iai-i. serial No. 131.34:

-rs causa (ci. :so-sisi This invention relates to the modification oi' time-varying functions in accordance with preselected patterns: more particularly. it relates to electrical transducers known in the art as transversal filters. l

The behavior of electrical network can be specified in two ways representing two different physical points of view. Ordinarily. one thinks rst of the well-known steady state point of view which describes the network performance in terms l of the concepts of amplitude and phase response versus frequency. In addition to this more conventional view point there is the time function f concept in which the network is described in terms of its amplitude-time response at the rel5 ceiving end resulting from the application of an impulse of infinitesimal duration at the sendinif end. Network response may thus be considered either in terms of frequency or time functions.

The bridge between these two avenues of approach is the Fourier integral which may be thouht of as a mathematical device for expressing a time function in terms of steady state phenamens. Por the most part prior art practice has been to base the design of communication networks upon the steady state frequency-smpiitude characterg istics; and an elaborate theory has been worked out for auch design procedures. The networks l Vthus obtained contain as elements resistances. in-

ductances and capacitances. the frequency and/orphase seicctive effects of which are used in vari- N combinations to secure desired response characteristics. Y

On the other hand when network design is conaidered from time function point of view. that is. when time rather than frequency is taken as the independent variable. one is led to a broad group of selective circuits whose principle of operation does not depend upon resonant combinations of i0 network elements. Thus. selective circuits emf.: bodying the time function concept have been disclosed ln Patents 2.024.900. December i7. i935: 2.12L599. July 28. 1938;.ll1d 2.128.257. Atiillist 30. i938. to N. Wiener and Y. Lee. and elsewhere in the art. A principal obiect of this invention is to pro- ,vlde certain improvements and simplincations I 'in the art of modifying functions of time in ac i 'j cordance with preselected patterns ol amplitude. 50

frequency. and phase variation. V

A more specific obicct of this invention is to provide simplified technique and apparatus for imodifylng an impressed electrical input in aci cordance with a preselected admittance function which may be varied at will without substantial changes in the applied techniques or apparatus.

A certain class ol devices. known in the art as transversal filters. substitute the time-function approach for the conventional steady-state approach in the simulation of network response. operating through a series of steps which include the following;

il) Transitoriiy recording or storing the lnput signal;

i2) Weighting the stored record in accordance with a predetermined multiplying function; and

(3l Integrating the weighted increments ol record to produce a modified output.

In accordance with a preferred embodiment of .the present invention. a supersonic iight valve.

such as disclosed in Patent 2.287.587 to Ci. W. Willard and elsewhere in the art. is utilized in a transversal filter as an element with functions to store progressive portions of an impressed input signal ln the form of modulated supersonic waves passing longitudinally through the cell. A light beam directed through the cell transversely to the direction of travel of the modulated supersonic waves vis difiracted in accordance with the modulations. Weighting of the stored record in accordance with a predetermined multiplying function is provided by a mask interposed in the path of the modulated light beam emerging from the cell. the interposed mask hav ing a iight transmission characteristic which varies in a plane normal to the direction of travel of the beam. The light emergent therefrom is continuously collected and integrated by means of a photoclectrlc cell. in the output of which is produced the desired modied response.

A modified form of the present invention is 'adapted to utilize multiplying functions having both positive and negative components. In accordance with the modified embodiment. the modulated light output oi the supersonic cell is divided. half passing through a mask reprcsentlng the positive component of a multiplying function. and the other half passing throuah a mask representing the negative component of the muli tiplylng function. The lightirom each of the two masks is collected separately on tivo different photoelectric cells. whose respective outputs are combined in reversed phase to produce the desired modified output response.

'Transversal filters designed in accordance with the present invention have certain advantailes over devices of the prior art.

In accordance with one feature of the invention. summation of increments representing the I mathematical concepts, auch as that of the "unit senses product of the signal amplitude and the characteristic time function is continuously performed by an optical system utilizing the progressive signal storage of the supersonic cell. thus eliminating the necessity for multiple pick-up points.

In accordance with another feature of the lnventionI the over-all loss-frequency characteris- 'tlc of the system may be changed by merely varying the position of the impulse response mask thereby permitting controllable cut-off frequencies o: iccand high-pass filters. and proportionai variazione in the band widths and mid-band frequencies of band-pass filters. This feature provides a new means for constructing tracking filters which supplements the techniques .naw known in the art.

A further advantage inherent in systems of the vpresent invention is their physical simplicity and lack of bulk as compared to transversal filter systems of the types disclosed heretofore in the art.

Other oblects. features, and advantages of the present invention will bc apparaat from a study of the detailed description hereinafter and the attached drawings in which:

Pigs. ith-lf2) are a series of diagrams illustrating a discussion of the theory of the invention.

Figs. 2M) and 2(3) are graphical representa- A tions of specific nlter characteristics which may in place of the assemblage shown in Fig. SiB) which includes the photoeiectric collecting device Piz. SiC) shows a cross-sectional view of the system of Fig. BfA) in a plane represented by the line Y-Y of Fig. 3M);

. Ns. StD) and 3(2) show alternative forms of f the impulse response mask SII of Fig. 3M);

Fig. ((A) shows a modified form of a trans- V- verrai filter in accordance with the present invcn` tion which is adapted to utilize impulse response functions having both positive and 4negative components;

Fig. 4(8) is a graphical illustration of an impulse response function having positive and negav tive components:

' Pigs. 4fC) and iiD) are respective illustrations of the positive and negative impulse response masks representing vthe function shown in HLMB).

Reference will bc made hereinafter to the transfer indiclal admittance of a system. This quantity is defined by J. R. Carson in Electric Circuit Theory and the Operational Calculus.

McGraw-Hill, i926, page i4. as the ratio of the output current of the system. expressed as a time function. to the magnitude of the steady electromotive force suddenly inserted at the input of the system at time t=0.

hereinafter as the "impulse response" or merely the "r1-function" of a system.

Further discussion and definition of certain e 4. impulse.' which will be relied on in the detailed description hereinafter will be found in volume I of lransients in Linear Systems. by Gardner and Barnes. .lohn Wiley and Bons. i942, pages 25o-263.

The broad principles upon which the time function point of view are based are illustrated in Figs. liA) to lfE), to which reference is now made. Consider a frequency selective network auch as la illustrated schematically by N in Fig. liA). Let us assume that the complex voltage wave Eit) shown in Fig. lfB) which is any continuous function of voltage versus time is impressed upon the input (i) of the network. At the output i!) there will then appear a current wave which we designate as lit). Now iet it be supposed that the voltage wave Eff) is split up into a series of narrow pulses as shown in Fig. iiC). With this pulsed wave impressed upon the input terminals il) one should expect to obtain at the output terminals i2) very nearly the same current wave lit) obtained before.

Y Now referring to Fig. iiD) assume that there is impressed upon the network a single pulse of the sort into which the voltage wave Eff) has been subdivided. At the network output terminals (I) there now appears a function which as the puise-width approaches zero is proportional to the p-function of tho network as defined above. 1t should be noted that any other pulse of difierent amplitude would result in the same approximate o-functlon except that its amplitude would vary in proportion to the applied puise amplitude 'and that moreover its time of occurrence would depend on the time of pulse application. Thus it follows as shown in Fig. liE) that in the limit the current wave iff) which appears at the output terminals l2) as a result of the application of the voltage wave Eit) at the input terminals il) is the sum of a number of overlapping o-funetions whose relative strengths or amplitudes vary in accordance with the impressed voltage wave Eff). Using a somewhat more precise language one can say that if the network is sublected at the input il) to an initial puise at some arbitrary time which for convenience may be called zero. and if this pulse is followed by others at specified values of time, the total response at the output terminals f2) at any later time will be the sum of the responses which have occurred up to that time.

Thus two important principles applicable to this approach to network theory may bc derived from the above. First. the network response to a unit impulse of infinitesimal duration completely determines the response to any other input wave. Second, the response at any time depends upon the history of the applied input wave previous to the time in question so that the past history must be avaliable at least over a time interval within which the o-function is of appreciable maanitude. Y f' Therefore. the network can be looked upon as a circuit for effecting the summation of a series of time displaced a-functions in which the individuai amplitude of each of the respective a-iunctions is proportional to the corresponding time-displaced instantaneous value of the impressed voivtage wave Eff). This process is schematically indicated in Fig. iiEl.

Adopting a slightly different point of view one can also look upon the output wave as representing at any time a weighted history or record of the input wave where the g-function has acted as the weighting factor.

The foregoing statements may be summarised by deriving a mathematical expression for the mentes network response to an arbitrary driving force where Yniiu) is the transfer admittance between from the assumption that the net behavior of a input and output terminals of the selected net- 5 linear system at any instant is a function of the work and piu) its phase anale. By writing linear superposition of all the responses which Yisliul-oisiul-l-ibuiu) in which als and bis are j' l have occurred up to that time countina from 5 constants. the second of expressions i3) is ob- 3 some arbitrary starting point. Assume, for extained. An equivalent expression may also be ample. that a network is subjected to an initial obtained from (2) or fll. for by inserting voltare pulse El!) at the time t=fl and that this liti-:1l sin at and extendins the ranse of intepulse is followed by others at specified values of :ration to infinity (which means that transient time. then the total response at any later time l0 distortion has died out) one obtains,

will be the sum of the responses which have oel I i eurred up to that time. due allowance beine made I(i) E sin L oosuig(r)di Email sin mgm," 'for the time at which each pulse was applied. (4)

t Let the time axts then bo divided into short interv/als dr of equal width. the electromotive 5 n Mmmm o! u) .nd (4 101m th force El!) being approximated by a series of rec- :angular pulses applied for the duration of each HM'L 0' Imm time interval Af. The total response at a speciand f (d) ned time t is then approximately the sum at that su( l l instant of al1 the elementary responses started 2n n 'l' d previous to that instant. ff the interval .if is very The vom o be emphulud m new um am. mu- "nu mouches ro s um the 'e' that the expressions i5) establish quantitative '90m *t me t um mst Pulse 'Eogm relations between the frequency selection proper "here am l the response to nu 9m r gmnc ties of the network and the response to unit im- U0 dem hfembefmnd "he" Em l 2r puise excitation. and second. that both the mi the amplitude of the voltage wave Eit) at time .nd ummm., component, d he "man, M "o' cm1-def now "he ml'lm pulse- The Y" mlttance can be calculated from a knowledge of y spense-at the time t is Ein-.irl .irait-nov). In the respon o nu uuml. nus mmommp i. this expression it should be noted that ndr is the m" so be further wanted u follows: mmh i time of pulse application. The reason that the an ply me cond of umana (5) mh he mab argument of the o-function in the latter expresmry un .nd .dd u, he mn. um. 'use Euler', alon is f-ndr and not t is that this pulse does not mmm 'The um u i" come into existence until the time nsf and the expression is only valid for time equal to or L r.. seater than ndr. !eisummi arbitrary point on 33 Yum) mr w (e) g e time sca e to eno e y r. us r=ndn mm wm h una n l The current response lit) at the instant t is the t" dmifuce u E; tfnysfle e g aum at time t of ali elementary responses which un mpulse 590mm Prom princpi! point o, r have occurred between time equal to 0 when the ,um n u thm meleum new frequency 3 al Ful s Und nd "um t s "u mmh "f 40 selective'properties of a network are stated in um mm1 A' Wmnhs fem Hence terxm of steady state frequency response to sinusi s t '-1 oidal drivin: forces or whether they are aiven as t '1(0- Ilm zbillraU-v) (l) the time response to a unit impulse. The fre- 5 f 1 Y so f-o queney response la merely the spectral analysis of E 1, i By definition of an intezralthia may also be 45 the time response to a unit impulse. It also foli. written lowsfromiblthat n n !ii) Ll-I (rlr (i f)df ,(g- L |y(|..)(e (sf-sfondo (7) or.." gi

@I j 7* -I o where Yuitul denotes the amplitude and sie) I()"l"("")9(')d' a the phase of the steady state transfer admittance. .-1 I Equation (1l in principe allows gli) to be cal 5.1 m mum um express the stem mmm culated from a knowiedze of the frequency specu n "binary drm for m um d "he n' trum of the steady state transfer admittance. i. e. -.aporisetioaunit impulse of infinitesimal duration. 55 "am he lmpmude eque, chncmuc of Thus it follows that a knowledge of the response he network Marcom. e h." "om (s) gi: to a u nituinpulse, thug is, ar 1 applied glisse i Aw c in e mtapproac esuntareaan n" nniteslmal duration is sufficient to specify com 'm' d pletely the system performance. This implies en and 2 (a) i in particular that t e steady state per ormance L' l ,C1/of a particular network may aiso'be determined 'm I "M n du i if from aknowledze of am for that network. Bup- Hence n mno ha ma me response am m pose for example, that the network is a filter ummm pulse is completely determined when either passino a certain band of frequencies. This is l5 the n orme mummy component o! the und! then merely a reflection of the fact that uit) be- In t ransfer impedance is specified over the haves in a very definite manner. To illustrate mme frequency um L Y a "Us ln l aeneral way. arsme that a simioldl siressinz the physical interpretation of the man '"mr in "2 W "e Bremen t e facts presented rather than the mathematical steady-state amplitude and u the annular fre- 1o .mmm "me eps e um by mum of 1 Wem" h" bec ppucd me ein "t "0 which a siven input function may bo modified in f d th n "mmm" m" dcd nut" The und accordance with certain admittance character t V ne current n me be me istics to produca a desired output response with- 1mg: i you i sin rst-,mw out resort to the conventional concepts of selouis) sin et+-Ibn coeuf i3) u lectivo networks. They are:

` statues f f. Recording or storage of the input wave.

as building blocks in frequency selective devicesoperating on a time function basis. It should be i noted that in arriving at these steps no reference has been made to vibrating systems such as coil I and condenser combinations nor has any use been made of the concepts of amplitude and phase versus frequency response. These concepts have 'now been replaced by the single concept of the g-function. In other words the physical phe- I i nomena conventionally described by the amplitude and phase versus frequency functions are -now described by the single function gif).

As concrete examples of o-functions consider two eases of functions in which the positive and negative values are symmetrical with respect to a certain value of time, say time Te. where Toll. Consider first a low pass filter having a uniform transfer impedance equal to K from frequency aero to a cut-off frequency angular se. Outside this range it ls assumed that no transmission occurs. Ls a consequence of the stipulation of aven time response the phase shift cial is linear and is given bythe following equation:

ller) UTM-n.2! (9) Por the low pass filter under consideration there I. have.

latory lobe is inversely proportional to the bund width le. It is also seen that the received sigvnal reaches its maximum at the time t=Te and that the maximum response is proportional to the area eK under the amplitude characteristic.

As a second example we consider an idealized band-pass filter of even time response and with Y a flat amplitude characteristic between the cutoff frequencies we. and es, i-, Outside this frequency range it is assumed that no transmission can take place. From Equation 'i substi- I tuting the conditions imposed by Equation 9, and

A integrating over the angular frequency range from en. to vez, there is obtained a function which will be designated mit), which represents the particular case of the generalized c-function citi as applied to an idealized band-pass filter having the above characteristics.

Il gnam! (wl -es To) du which may be reduced to 1 to-T e ...u-1u vim Bere w represents the band width ep-un. and n i a t" the arithmetic mean of the two cut-off frequenr cies n, and s, andvmay thus be considered to 7s element fil! in compressional vibration.

s I s coincido with the mid-band frequency. Equation il which is roughly piotted on Fig. SIB) represents an amplitude modulated carrier wave with a carrier frequency equal to that of mldband. The maximum response occurs at t=Ts and is proportional to wK which is the area under the amplitudercsponse characteristic and the length of the main oscillatory lobe is which is inversely proportional to the band width.

The examples selected show that several important properties of the steady state characteristics can be obtained directly from an inspection of the plots of the a'functions. It must be emphasized. however. that too much significance cannot be attached to the calculated a-functlons since they are based upon assumptions which cannot be realized. On the other hand. the general qualitative and quantitive properties of the g-functions for the filters in question are believed to have been preserved. although one is not Justifled in attaching very much significance to any of the finer details.

The computation of the a-function, as discussed herelnbefore. has necessarily been in broad general terms with several specific applications by way of illustration. From the previous discussion. the procedure will be apparent to those skilled in the art for uniquely computing c-functions to comply with specific sets of conditions imposed in other particular cases.

In accordance with an embodiment of the invention shown in Figs. 3M). 3(8), and SiC) of the drawings. portions of the impressed signal are progressively stored in the form of modulated supersonic waves passing longitudinally through a supersonic light cell. The impressed function so Is continuously multiplied by a predetermined This function is shown as Fig. 2M). It may be .'demomtrated that the width of the main oscilweighting function through the agency of a light beam passing transversely through the supersonic cell and an impulse response masi: positioned adiacent thereto. The increments of emerging light. which are proportioned to the weighted product, are focused on the input of a photoelcctric cell where they are progres'lively integrated to produce a desired filtered output current.

The system shown in Fig. 31A) comprises in combination s supersonic light cell lili of a type such as disclosed, for example. in Patent 2.287.587 to G. W. Willard. June 23, 1942. For present purposes. the cell lili is constructed substantially as shown in Pigs. l and 2 of the above-cited patent, but with the separate outer electrode elements 2l and 28 as shown in those figures replaced by a single outer electrode I0! as shown in Fig. 31A) of the present drawings. The electrode lil! is attached to the outer face of the piezoelectric crystal element lill which comprises a section of X-cut quartz diswsed. at oneend of the cell lili. The electrode 3M is attached to the inner face of the crystal element lill.

The input system connected across the elecn. mwa" The eomprcssional vibrations generated by the piezoelectric element 303 set up waves in the liquid medium 300. such as water, which fills the cell 30|. the resulting condensation: and rarefactions progressing longitudinally therethrough io the far end of the cell. where they are absorbed by several layers of wire mesh 30| and other devices designed to prevent reflection. such as more fully t described in the patent to Willard supra.

Positioned along a line approximately perpendicular to the center point of ono of the sides of the cell 30i and at a short space therefrom. is a light source 3ii which is focussed on the vertical siit 3i! by means of the lens 3H. The emergent face of the slit 3i3 is positioned at the line of focus of the cylindrical lens 3M. whereby a uniform light beam is produced having the shape of a paraiielopiped which has a depth perpendicular to the plane of Fic. Sill) which is substahtiaily coextensive with the depth of the -ceii 30|. and enough breadth in a horizontal direction to include a large portion of the cell 30i in its path. The beam is directed to pass through the cell 30| transversely to the direction of travel ofthe eompresrional waves from the driving eiement 303.

The beam emerging from the opposite side of the cell 30| falls on s. second cylindrical lens lil. so positionedthat the central undiflracted portion of the beam ls focussed on the vertical bar 324 which is formed in the central portion of the baille lil, which is disposed in a plane perpendicular to the path of the beam. Adiacent to the bar 324. on each side. are disposed vertical slits 323 and nl perpendicular to the plane of hg. 3M), which are coextensive. and so positioned that only diilracted portions of the beam pass therethrough. For the purposes of illustration. the light output of the slits 320 and 320 is ...".shown as passing through the lens 3i! which serves to focus the diilracted light images on the screen 320.

In the absence of the impulse response mask Ill. which will be fully discussed hereinafter.

the system operates as follows. Assume. for example. that a carrier frequency of l megacycies modulated by a frequency of 100 kilocyciea is impressed across the electrodes 30! and lili. Bands 0f high amplitude modulated waves alternating l cell from the source 3H are diifractcd as though passing through a diffraction grating having a line spacing in accordance with the periodic rarefactions and compressions of the carrier wave. However. whereas an ordinary diffraction grating allocates a fixed amount of light to each order of diflracted beam including the zero or undifh'actedorder. the supersonic wave grating lives an amount of iight in the different order beams which varies with the changes in amplitude of the waves. Thus. when the waves are zero' amplitude, all of the light fails in the principal or undiilracted beam: whereas. as the amplitude of the waves is increased. the amount of iight in the principal or undiflracted beam in de- A creased, and that in the higher orders proportionately increased. Thus. as the rays are diffractcd at any given spot in the cell. a smaller proportion of the iight therefrom is focussed in i the undiffraeted beam on the bar 320. and proj portionateiymore iight is focussed in the diffracted beams directed on the slits 323 and 320. the iight passing therethrough being therefor a function of the amplitude modulation of the supersonic waves passing through the cell i.

The images cast on the screen 120 thus take the form of alternate iight and dark bands traveling across its surface at a hiifh rai-e of speed in the direction of travel of the supersonic waves through the cell 00|. The carrier wave. in effect. provides a bias un the modulating signal. such that with no signal modulation. the amount of iight transmitted is a median value. The maxima and minima in the envelope of the signal modulated carrier wave then correspond to less and more iight. respectively, than the amount transmitted when there is no signal modulation.

Assume now. that the supersonic light cell 30| is to be used to simulate a given network responso or admittance characteristic.as taught by the present invention. To adapt the system described hereinbefore for this purpose. an impulse response mask 3i! is interposed in the path of the diflracted beam emerging from the cell 30i. The masi: 3i! takes the form of a rectangular plate having a light as transmission characteristic which varies in acthe difiracted iight beam in the direction of travel of the supersonic waves through the cell 30|.

The impulse response mask III may alternatively assume different forms. two of which are shown in Figs. 3fDi and Sti-3). A variable area -i0 mask. such as shown in Fig. StD). can be simply made by merely plotting a large-scale graph of the weighting function. blaclring 'in the area above the curve so that the transmitting portion of the mask represents the weighting function.

and reducing the picture to the desired size by a photographic process. A variable density mask of the type shownin Fig. ME) can be made by focussing a vertical-ribbon-shaped light beam which is intensity varied inaccordanco with a desired weighting function to shine on a light sensitive film whichia moved transversely across the path of the beam at a uniform rate. and then making a positive reproduction-of-thc-negatlve film so that the light ultimately passed by the variable density mask will be proportioned to the desired function. rather than its inverse.

Preferably. the weighting function utilized in the preparation of the mask 3i! is the chosen g-function which is calculated as discussed here- Mi inbcfore in accordance with a desired output function and which represents the time rate-ofchange of the indiciai transfer admittance to be simulated. Assume the calculated curvo in this case to be a function of time. mit). which will bo translated into a function of space mit). As will be apparent from the dLseussion hereinafter. it may be desirable to introduce an additional exponentinl factor. et". in combination with the calculated curve for the impulso response mask.

il in order to compensato for attenuation sustained prix) is the p-function discussed s bovgv is the by the modulated supersonic waves as they move down the cell 30|. Therefore. the impulsa respense mass will be prepared in accordance with a function which taires the form miele". where .rea/f1 A i eally as follows.

"am fieras. Y I A v distance from'aome referencepoint measured in the direction of travel oi the supersonic wave along the cell lili. and a is an attenuation conatant.

Assume then. that the impulse response mask .il is placed in the system in the path of the light Y screen 320 will trace out a pattern of intensity variations with time which is a replica of the space variations in the light transmission characteristic of the impulse response mask I il. Now if a complex signal is sent down the cell. it may e-'ft ao that the product as given in Equation i2 is truly representative of the response integral.

an additional factor. et" must be introduced into the calculations for constructing response mask 5 Iii. so that the actual mask function plotted is be considered as divided into an infinite number of very short pulses in succession. each one of which will trace out the impulse response function. The total output of light from the slits 32S and Il. will accordingly be the summation of all of the increments of signal multiplied by the vimpulse response function.

This operation may be expressed mathemati Assume that a signal Eli) is impressed across the input terminala. and that the signal Eifl travels down the cell Sill without attenuation. and is completely absorbed in the characteristic impedance 808 at the far end of the cell. ao that no reflections are produced. At any distance r. which ts measured in a honizontal direction from the edge of the beam nearest the input. the instantaneous amplitude of a wave 'passing down the cell is Eif-r/ul where u is the speed of wave propagation. Assume that the leale of the impulse response mask has been ad- )usted by a constant factor i/u to make it correapond to the velocity of travel of the compres-V aional waves down the cell. Then the g-function value measured at any point z in a horizontal direction along the mask Si! equals mfr/ui.

` Thus. the light passing throuch an infinitesimal vertical segment-of the cell Iili having a 'width .1.: .dr and through a corresponding portion of the 'I mask til. is proportioned to the quantity Replacing .t/u by r. the delay. and letting t=0 when r=0. it is apparent that the total iight. L.

falling on the screen I2C from the cell lili and interposed mask til is' proportioned to the fol- Alowing quantity.

Hence. the action Equation i2 above. specifies the operation of the system under ideal conditions which are not actually attained in practice. In order to more closely approximate actual operating conditions. it must be assumed that the supersonic waves traveling down the cell till undergo a constant decrease in amplitude because of attenuation. so

that the actual amplitude of the waves at any point: in thc horizontal direction of travel along the cell "i is represented by the quantity mifiet". as pointed out hereinbefore.

In the foregoing description for the purposes of illustration. lt has been assumed that the light output of the system of Fig. MA) traces out patterns on the'screen Ill. fn accordance with the present invention. the photoelectric collecting system shown in Fig. SKB) is substituted to the right o f the line X-X for the screen 820 and associated elements shown in Fig..3iAl. The diffracted light beams passing through the slits IN' and ill' falls on the light sensitive surface of the conventional photoelectrlc cell lli. producing an electrical output current therefrom which is proportional to the response integral described above. The output current from the cell Iii. which is continuously modified in accordance with a preselected admittance characteristic as described. passes through the amplifying circuit l!! and is impressed on the output terminals 323.

As pointed out in the introductory portion of the specification, a particular novel feature of systems. in accordance with the present. invention is that their over-ail frequency characteristics may be altered in each case by simply rotating the impulse response mask about an axis in such a way as to change the proportion of light from the supersonic cell which is intercepted by the mask. Assume. for example. that the impulse response mask Il! isrotated about an axis 321 perpendicular to the plane of the paper, and aligned with the bounding edge of the mask Il! nearest the input end of the cell 30|. 1f the mask til is rotated from the position AB to the position AC, only half of the llghtbcam emerging from the cell lili is intercepted by the mask. Therefore. the impulse response iunctionoccu pies only half as long a time period as were the entire beam intercepted by the mask. thereby doubling the frequency scale of the over-all loss characteristic of the system. For example. if the 4system were set up to simulate the operation of for simulating the operation of a band-pass filter. I the band-width could be made tochange in the aame ratio as the mid-band frequency by a similar operation.

- .The above is seen to be the equivalent of the responae integral derived in the early part of the specification as Equation 2'.

of a network is simulated without conventional network elements.

Another problem which arises in a system of the type described is the necessity for taking into account impulse response functions having both positive and negative components. A system modified to perform this function is shown in Fig. (iA) of the drawings.

Fig. (iA) shows a side elevation view of a system in accordance with the present invention which is in general similar in structure and operation to the system shown in the plan view of Figs. 3U.) and 3(8), like elements being correspondingly numbered in the two systems. However. the

system of Fig. Ai differs from the system of A Figs. SiAl and IiiBl in that the light output from the cell lli is separated horizontally by the opaque barrier it into two equal components. each of which passes through a separate system including a respectively different response mask.

' lens system. and receiving photocell. the separate photoceil output currents being combined in re verse phase.

i Assume 4that the impulse response function senses and takes the form Uhr) mule) -Ni (u) 14 aald space interval in accordance with a predetermined weighting function.

2. The method which comprises generating compressionai waves in a medium. said waves be- In ccordlnce the presenny descbcd in! modulld In ICCUl'dnCe 'uh In lmpl'CSSed systems. the positive and negative components of the curve Gir) are recorded separately on two different masks. Mir), the positive component. on mask lila. as shown in Fig. 4(6). and Nif). the negative component. on masi: lith. as shown In Fit. (iD).

The portion of the diffracted beam emerging from the upper portion of the supersonic cell i above the barrier lll passes through the mask function. directing a beam of electromagnetic radiant energy to pass through said medium transversely to the direction of propagation of said compressions! waves therethrough. whereby components of said beam are dillerently dilfracted. varying the intensity of the respective components of said beam in accordance with a predetermined weighting function. and collecting and summing said components thereby to prolilo, and is thereby multiplied by the function l5 du" l Uwdmd will function.

Mir). The weighted increments oi light from I vthe mask Ilia are then focussed by the cylindrical lens Illa on the slits in the banle lila. which are similar in form. the slits 32! and l!! described 3. The method of modifying a given input function which comprises storing portions of said function as supersonic waves in a supersonic light cell. producing variations in the light output of reference zu nl. 3(^)' ging therethrough ld ce 1n .iccurdnce l predtermlncd onto the light sensitive surface of the photoelectric cell lila. and thence into the output through the amplifier 2a. Light passing through the mask lith is weighted in accordance with the weighting function. and summing increments of said light output to produce a modified output function.

4. The method of modifying a elven input nenuve response functie Nu) .nd rives by e 25 function ln accordance with a predetermined adsimilar series of steps at the output of the ampliuer uib. The photoeiectric cells la and nib and their respective amplifying circuits are connected in what is known as "push-pull relation.

mittance characteristic which comprises storing portions of said function as supersonic waves ln a supersonic iight cell, producing space variations in the intensity of said light output of said cell ,o that their respective output currents e eem. 30 in accordance with a function of said admittance blned 180 degrees out of phase. l The total output current may be expressed as follows.

" cargan-harman-xL'EafiNmdf l' afan-'nsfm-Nmiaf 1 (lll characteristic and summing increments of said light output to produce a modified output func tion.

'5. The method which comprises storing portions of an impressed function as supersonic waves in a supersonic light cell. producing variations in the light output of said cell in accordance with a predetermined weighting function. and directing components of said light output Substituting Equation i3 above. the expression o to fall on the light sensitive surface of a photobecomes '1m-x fo eti-name.

" which is seen to be the response integral. as de- 5 rived hereinbefore in Equation 2'.

It will be apparent, that for best performance of the system of Fig. Al the same attenuation correction should be applied to Gif) of Equation lo as was discussed with reference to Equation A 12 above.

The supersonic light cell. which is utilized as an element of the combinations disclosed in both Figs. 3M) and 3(8) and Fig. 4, may take many other forms than the particular one shown. For

" example. the lateral slits 32| and lil which are disclosed in Fig. BfA) as separated by the bar 12B. may be replaced by a single vertical slit. in which case the ouput of the photoceli lll is merel! w reversed in phase.

Many modifications of the apparatus comprising the illustrative embodiments disclosed herein which are within the scope of the present inveniight output is space varied in accordance with i a function of said admittance characteristic. and directing components of said iight output to fall on the light sensitive surface of a photoeiectric cell. whereby the desired modified function is produced in the electrical output of said photot 5 electric cell.

7. The method in accordance with claim d in which said predetermined admittance characteristic is varied by variations in the position of said mask with respect to the light output of said cell.

l. A system which comprises in combination means for propagating elastic waves across a given space interval. a source of electromagnetic on will be apparent to those skilled in the an, u energy. means for directing said electromagnetic .What is claimed is:

l. The method which comprises translating applied waves into elastic waves progressive across a predetermined space interval. directing electro.

energy through said space interval in a direc tion transverse to the direction of Propagation of said elastic waves. means for receiving and integrating components of said electromagnetic energy that pass through said elastic waves. and

sion of said elastic waves. receiving and integrat- '1 that pass through said progressive elastic waves, and weighting various of said energy components that pass through respectively diifercnt parts of magnetic energy through said space interval in a direction transverse to the direction of pregresmeans for weighting various of aald energy componente that passthrough respectively different parts of said space interval in accordance with a predetermined weighting function.

9. A system adapted to modify an applied ining components of said electromagnetic energy 7 put function in accordance with a predetermined I8 i, admittance characteristic which comprises fn combination means for propagating waves across a given space interval. a source of abesm of radiant energy. means for modifying components of said beam in accordance with certain variations in said waves. means for receiving and integrating various components of said beam that pass through said space interval. and means for weighting respective ones of said components that pass through diiicrent parts of said space inter- 'al which comprises a mask interposed in the path of said beam of radiant energy. said mask having a transmission characteristic for the enam components of said beam which varies in I Iplce in accordance with a function oi said predetermined admittance characteristic.

l0. A system in accordance with claim i which includes means for changing the position of said mask with respect to said beam. whereby to vary said predetermined admittance characteristic.

l1, A system in accordance with claim 0 in which said certain variations in said waves comprise variations in the amplitude of said waves.

12. A system comprising in combination means for generating elastic waves in a given medium. means for modulating said elastic waves in accordsnce with a given impressed function. a source of a beam of electromagnetic radiation. means for directing said beam to pass through said. medium transversely to the direction of ,ssmos means interposed in the path of said beam for varying the intensity oi said beam in accordance with a predetermined weighting function. and means for collecting and summing components oi said beam.

i3. In combination with a system comprising a supersonic light valve. said valve including a vessel containing a medium adapted for the propagation of elastic waves therethrough. a piezoelectric means disposed at one end of said vessel for generating elastic waves in said medium. means comprising an input circuit connected to said piezoelectric means for impressing modulations on said elastic waves in accordance with an applied input function. and a source of a beam of iight disposed relative to said vessel whereby said beam is directed to pass through said medium transversely to the direction of travel of said elastic waves through said medium. means comprising at least one mask positioned in the path of said beam and having a light transmission characteristic which is space varied in accordance with a predetermined weighting function,

. and means comprising a photoelectric responsive device positioned to receive and integrate weighted components of said beam.

HAROLD L. BARNEY.

No references cited.

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