SU1735836A1 - Method of determining vector-matrix transformation results in concurrent acoustooptical processing units - Google Patents

Abstract

The invention relates to optical computing with performing mathematical operations using optical or electro-optical elements, in particular to optical means for determining the results of vector-matrix conversion. The invention relates to optical computing technology with performing mathematical operations using optical or electro-optical elements, in particular to optical means to determine the results of real-time vector-matrix transformations; Various methods are known for determining the results of vector-matrix transformations performed on real-time studies. The purpose of the invention is to increase the speed of determination and increase the dimension of parallel-processed arrays of alternating numbers. The generation of radio signals corresponding to the alternating numbers to be processed is carried out without dividing the numbers of the arrays being processed into positive and negative. This is achieved by forming radio signals corresponding to alternating numbers of processed arrays, there is a one-to-one correspondence between alternating numbers and generated radio signals, which eliminates the need for organizing independent computation channels and linear algebra operations on alternating numbers of processed arrays that include the multiplication operations and additions can be performed regardless of the characters of the numbers being processed. 3 il. array elements of alternating data in parallel optical processors for real-time signal processing. In this case, a feature of operations with alternating data in all types of optical processors is that the detectors of light signals, t, e. Photo detectors are quadratic in nature, i.e. register the square of the modular complex ampg (L with | OE el oo w a

Description

Literature of light, which is a deliberately unipolar (positive) value. Therefore, spatial, temporal and frequency separation of computational channels by signs is used to determine the results of vector-matrix transformations over alternating data.

In the spatial separation of computation channels, spatially separated light modulators are used, some modulators are used to input positive data (positive time samples of signals) into the optical processor, and others - to input negative ones. Therefore, taking into account the multiplicand, multiplier and result of multiplying two alternating signal samples, you need at least four light modulators and four photodetectors with a signal processing circuit (summing up with signs) of signals obtained x photodetection. At the same time, to process arrays of alternating data, the elements of the input arrays (arrays of time samples of signals) are divided into subarrays consisting of only positive or only negative elements, and use four channels for determining the results formed by four regions of light modulators divided by space . In this case, the first channel processes the positive elements of one input array and the negative elements of the other input array, the third one processes the positive elements of both input arrays, the fourth one processes the negative elements of both arrays, and then performs the photodetection of light signals in all channels Summation of the signals obtained by photodetection based on the sign of the result in each channel of the calculations.

In time or frequency division of the channels, determination of the results with elements of arrays having different signs use either light sources modulated in time, and at different points in time they are modulated according to the values of elements of different signs, or they form radio signals with frequency multiplexing (separation) -

358364

(frequency bands) to represent positive and negative elements and enter them into

- acousto-optic light modulators, which, when light is diffracted by acousto-optical modulators in optical processors, leads to the separation of computation channels by space (division 10 by the diffraction angle).

In addition, in optical processors, to perform operations with alternating data represented in numerical form, use the redundant representation of alternating numbers in the additional code, choosing to represent the number of bits several times more than is necessary to represent alternating numbers in the additional

15

20

five

0

five

0

five

0

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code, and modulates the light in accordance with this redundant representation, and after performing optical calculations, registering the signals with photo detectors and analog-to-digital conversion of these signals, determine the result by transferring the digital signal from the redundant representation to the usual representation in the additional code.

A common drawback of the known methods for determining the results of vector-matrix transformations is the limited speed of determining the results of transformations and the small dimension of the arrays being processed in parallel, which is either due to the redundant representation of the alternating numbers, i.e. using a numerical representation with an excess bit size, which is several times greater than necessary, or by organizing in an optical processor divided by space, time, or frequency of computation channels, depending on the signs of the elements of the arrays being processed.

The closest to the present invention is a method for determining the results of vector-matrix transformations in parallel acousto-optic processors, which consists in performing parallel separation of input pulse sequences corresponding to parallel elements of two arrays of alternating numbers, pulse sequences corresponding to positive numbers, and pulse sequences corresponding to

indications and radio signal generation by modulating pulse sequences corresponding to positive numbers, harmonic carriers with identical frequencies f, where frequency ff is chosen to represent positive numbers, and modulating pulse sequences corresponding to negative numbers, harmonic carriers. equal frequencies f2, where the frequency ft is chosen to represent negative numbers, and analog addition (frequency multiplexing) for the signals, sponding positive and negative numbers, for which the frequency f and f, J is selected so

Thus, the radio signal spectra corresponding to frequency-compressed radio signals, into which pulse sequences for positive and negative numbers were converted, were non-overlapping, parallel input of frequency-compacted radio signals into a parallel acousto-optic processor, in which the determination of the results of vector-matrix transformations was performed parallel optical formation of discrete convolutions followed by optical summation of signals, corresponding to results of obtaining discrete convolutions, direct parallel photodetection of the output optical analog signals of an acousto-optic processor, analogue parallel subtraction from the group of signals formed by direct photodetection and corresponding positive results of the vector-matrix transformations, groups of signals also formed by direct photodetection and the corresponding negative sign on the results of vector-matrix transformations, with the formation of differential signals , subsequent analog-to-digital conversion of difference signals to digital form and digital weighting and summing of these signals to put the results of calculations in digital form. In this case, separate photodetection of the results of vector-matrix transformations taking into account the characters of the processed numbers is possible because when entering radio signals with frequency multiplexing into acoustooptics

o

0

five

Due to the diffraction of light by acousto-optical cells, the optical cells of the optical processor undergo spatial separation (separation by diffraction angle) of optical signals corresponding to the numbers of different signs,

The disadvantage of the known method is the low speed of determining the results of vector-matrix transformations and the small dimension of parallel-processed arrays of alternating numbers, since the redundant representation of alternating numbers is used, t. the division of numbers into positive and negative is organized and four independent channels for determining the results are used, followed by summing up the results, taking into account the signs. At the same time, frequency multiplexing of channels is used to organize four independent channels for determining the results, i.e. generation of frequency-compressed radio signals, where part of the frequency band is equal to (W / 2), provided that W is the pass band for each input of the acousto-optic processor, is assigned to represent positive numbers, and the other part is also equal to (W / 2) , to represent negative numbers, followed by inputting radio signals to the acousto-optic processor. Moreover, if each individual input of an acousto-optic processor is considered, its throughput will be determined by the amount of information transmitted through it per unit of time. However, it is known that, according to the Shannon theorem, the transmission capacity of a channel with a frequency band W in which there is arbitrary noise, limited by inequality

wbgtji-cswiogJ- s.,

where P is the average power of transmitted signals;

N is the average noise power;

 entropy noise power

0

five

0

five

those. geometric mean noise power at various frequencies in the band

 exp j: logN (f) df,

N

W

where N (E) is the noise power at frequency f.

Therefore, when using frequency channel multiplexing to represent positive and negative numbers, the throughput of each of the inputs of the acousto-optic processor is halved compared to the case of processing only positive numbers, because each time the acousto-optic processor enters either the positive or the negative a number, and for each of them a band is assigned (W / 2). Moreover, since the dimension of each of the two parallel processed acousto-optic it doubles the array of alternating numbers (to form arrays of either only positive or negative numbers) and uses frequency multiplexing to represent arrays of double dimension, the speed of determining vector-matrix transformation results, the number of arrays processed per unit time , is reduced by four times compared to processing arrays of only positive numbers. In addition, with a fixed value of W, t „e„ bandwidth on the inputs of an acousto-optic processor, the dimension of parallel-processed arrays is possible reduced by half as compared with the processing of arrays of only positive numbers.

The aim of the invention is to increase the speed of determining the increase in the dimension of parallel-processed arrays of alternating numbers.

This goal is achieved by the fact that in the method of determining the results of vector-matrix transformations in parallel acousto-optic processors, based on the formation of two-level input pulse sequences corresponding to the digital representation of alternating sign elements of parallel processed arrays, radio signals, input to an acousto-optical processor implementing parallel optical formation of discrete convolutions of pulse sequences with subsequent summation eskih signals corresponding to the results obtain discrete convolutions parallel output photodetection optical signa

five

five

Fishing, analog-to-digital conversion of photo-detected signals and subsequent digital weighting and summation of the converted signals form three-level pulse sequences from the input two-level pulse sequences, in the process of obtaining which each two-level input sequence is delayed by a pulse in the two-level pulse sequences, subtract from the delayed signal the input two-level pulse sequence and stop the formation of a three-level pulse sequence after the arrival of the last pulse in the input two-level pulse sequence and in the process of forming radio signals input to the acousto-optical processor, the three-level pulse sequences are balanced by modulating the harmonic carrier signals with the same frequencies and initial phases, and the parallel photodetection of the output optical signals is carried out by their heterodyne photodetection at twice the frequency of harmonic carriers, synchronously detect the received signals with radio signals at twice the frequency of the harmonic carrier signals, and then subject the detection result to analog-digital conversion, carry out

0 above the result of the conversion is digital weighting and summation with alternating signals presented in the additional code.

The proposed method differs from

5 is known that the formation of radio signals corresponding to the alternating numbers being processed is carried out without dividing the numbers of the arrays being processed into positive

0 and negative and organizations of four independent channels for determining the results taking into account the signs of the processed numbers by means of frequency multiplexing of channels when forming

5 radio signals followed by addition of the results on four independent channels, taking into account the signs. In the proposed method, an unambiguous correspondence is achieved between enacops

five

belt numbers and generated radio signals, thus eliminating the need to organize independent channels, and determining the results of vector-matrix transformations, including elementary multiplication and addition, can be performed regardless of the signs of the numbers being processed. This is explained as follows. A particular feature of acousto-optical processors based on the algorithm of multiplying numbers by means of discrete convolution is that the bulk of the operation in determining the results of vector-matrix transformations, namely the multiplication and addition operations, are performed by a linear analog optical system, after which photo-registration of optical signals at the output of the linear optical system of the acousto-optic processor is performed and electronically performs simple nonlinear operations of analog-digital conversion of signals obtained by photodetection, and their digital weighing and summing, therefore, to carry out the operations of multiplying and adding alternating ch ate in a linear optical system, an analog representation of the alternating-necessity such numbers, which would not require performing non-linear operations to determine the sign of the product and the amount of numbers. At the same time, before entering the numbers into the acousto-optic processor and after photographing the output optical signals of the acousto-optic processor, such non-linear operations are possible. Typically, an additional representation (additional code) is used to represent alternating numbers, and the multiplication and addition operations in the additional code are essentially non-linear. Therefore, to enter alternating numbers represented in the additional code, it is necessary to transfer alternating numbers from the additional representation to the representation of a number with alternating digits into the acousto-optic processor. At the same time, it is necessary to ensure the unambiguity of the transfer of numbers from one representation to another that is achieved due to the unambiguous translation of alternating numbers,

presented in the additional code by two-level pulse sequences, in numbers with alternating digits, which corresponds to a three-level pulse sequence with levels -1.0, + 1.

Mathematically, this is described as follows. By definition, the binary complementary code (representation) of a k-bit x is the number in the silt

 Zon

X3op Eoo

 x,

2k-x

received by pralesley x 0; if x 0.

Similarly for x, normalized to 1, that is, dl -1 6. xb 1

. x

if x O if x Omozhno 2k + x,

AEop

 - x

Generally, the expression for x Eop is written as the sum of Xgop k which is valid under the following restrictions: x gon has a limited number of divisions, namely k bits, and x is in the range - (. K-l) € Xb2 k -1. In terms of arithmetic terminology in residual classes, additional code can be

imagine. how

f

i + x expressions

deduction by ie

C3on, k

 m

odzk

where x is an alternating variable, i.e. the expression in square brackets can be 24,

if, and 2, if. Let us consider how alternating numbers in the additional representation (additional code) can be converted into a number with alternating numbers x «, where x; Ј {-1,0, lj, i.e. represent the number x in the canonical form of the polynomial x

1s-1

k - 2 x-v2 i 0

Using the rules for performing operations in residual classes, one can transform an expression for x e0n to the form

xaonrke C2 +

C2 + xLod "k 1

eleven

"

JmoJjk Mmoe kJCJir) cv, k L J ModzkJmoJzk

J "odzk

+ X

+ x

rood r k JmocJ, k

bnjk 2 X3on2Kjmo32K XK

where xj is the representation of a number in the canonical form of a polynomial with alternating digits x

1 TO

those.

(

: Ex3on7k 2 X3ontk

k-1

2 theirs 2)

mod2k k-i

- s

(0

X 3onlk 1

2;) J ki§4-03on, k JmoeUk

-H. l) x

 3onfk

-2,

Where

 x (i-09ana

ir2 k x

and Xl-Son2k 0 with and in accordance with

4 will be hao „r1

- x;

wt f r

- one

expression to obtain x fc from the additional xgon representation, it is necessary to have a two-level pulse sequence, which with logic levels 0 and 1, is delayed by one clock interval corresponding to the pulse following period in the two-level pulse sequence (one bit of the numbers being processed) delayed two-level pulse sequence, i.e. from the value (.,% gon, input (non-delayed) pulse sequence value x; gor, and the operation is performed by stopping the formation of a three-level sequence obtained by analog subtraction, and the corresponding XK, after the last pulse of the two-level input pulse sequence For example, let the decimal number x, 0 7, then the binary direct representation x2 0111 and the additional representation with the number of bits k 0111 о Then

01110 011t

 (+1) 00 (-1) 100-1

1.23

mod g 4 + 0-2 - 1

2e 7

"

173583612

Similarly for 7, i.e. - From and UZO ,, 1001. Accordingly

to

"M

-101-1 -1-23 + -8 + 2-1

termination of the formation of a three-level sequence (taking moda4)

We show that the representation of the alternating number x dog, g as a number with alternating digits x% satisfies the algorithm for multiplying the numbers by means of calculating the discrete convolution. Indeed, let XK and yk be two N-bit alternating numbers in the canonical form of polynomials, ts.

thirty

x „

Then the product

ZKHK U; Lvuh

Xj and yk can be calculated as

ZK

0

N- HC U | S S X

1-SO

tg mZIz S Cx,.) J J

where z (i)

N-1

; -2) (Zly)

1- “about 2M-2. ,

S),; -o

x

; © y; - discrete convolution of three-level pulsed

S

sequences x representing numbers xk and

and

y; ancestor

It is known that for a binary (two-level) representation of xj and yj, under the condition and y.0, such a multiplication of numbers is called an algorithm of discrete convolution. Consider the implementation of the algorithm for multiplying alternating numbers xk and y,% by means of a discrete convolution using the example LET a numeric value

Suppose that the decimal number is x () 7, its additional representation is hfg4i and 0111 and xk (+1) 00 (1), and yw is -7, its additional representation is yg0pt4 1001 and CC (1)). Then multiplying the numbers xk and uk for

13

obtaining ZK хц Ук by means of the discrete convolution algorithm is equivalent to the well-known multiplication column with analog addition of the results of partial products, i.e.

one

0

(+1) 00 (-1)

N) o (s) N)

-1001 +1 00-1 0000 -10 O -I

-10100-11 (-T) VET (-1) 1 -1-2b + 1-2 +

+ (-D-2 + 1-2 ° -6D +16 - -2 + 1 - -49 - х „у 10

To form radio signals that uniquely correspond to alternating numbers, use the transformation of each two-level pulse sequence, corresponding to the digital representation of the alternating number in an additional code with logic levels 0 and 1, to a three-level pulse sequence with logic levels -1, 0, +1, and then carried out. balanced manipulation of the harmonic carrier signal in accordance with the logic levels of the three-level sequence. At the same time, there is a one-to-one correspondence between the sequence of amplitudes and phases in the generated radio signal and the sequence of logic levels in the three-level pulse sequence corresponding to the alternating number, which allows determining the results of vector-matrix transformations in a parallel acousto-optical processor regardless of the signs of the processed numbers. To enter the generated three-level pulse sequences corresponding to the alternating numbers into the acousto-optic processor, it is necessary to convert them into radio signals. This is necessary because for the input of signals into the acousto-optic cells of the acousto-optic processor, piezotransducers are used, which are axis35836

14

They convert electrical signals into acoustic waves. Due to the resonant nature of the piezoelectric transducer, the possible input signal for an acousto-optic processor is a modulated harmonic carrier signal with a frequency f „corresponding to the resonant frequency of the CO piezoelectric transducer

 an acousto-optic processor, i.e.

S (t) S (t) ,, t + q (t),

ts where S (t) and Cf (t) determine the modulation law of the amplitude and phase of the carrier. one

In addition, in accordance with the rule for converting the number x from

20 additional representation (code) X9onzk B representation xk with alternating digits formation xk can be represented as simultaneous input of two-level impulse

25 sequences matching

xEpg1c-2 psh g) c and t-xgon J, since xk ixaon, k1 -Jinodtk L-Xg00ikJ, and the values of 0 and 1 in one two-level sequence, and 0 and -1 in the other. It is known that among the set N of signals of the form) Aksin (u) (, t + С ,,), where A | characterizes amplitude modulation, a Cfj phase, only two signals are linearly independent, and the remaining N-2 signals are linearly dependent. Therefore, the signal S (t) can be represented as the sum of two quadrature components

S (t) S0I (t) cosq, t + S0Q (t) x x sinOJHt,

where S0 is some constant coefficient; Koi

Q (t) - modulating functions);

Kt) gep (t - nT);

Tg ° n

Q (t) -SlVi t - nT

P

where ip and 1p are information symbols corresponding to two possible linearly independent pulse sequences; T is the clock interval in pulse sequences;

151735836

(t) and q (t) are the elementary modulating signals in pulsed sequences

pulse shape and usually rectangular functions. Depending on which values the information signals g n and 1 can receive, various combinations of possible signals S (t) are formed, i.e. S; (t),

to the carrier signal, and to the logical nu-1 in the three-level pulsed sequence, the recorded amplitude 1 corresponds to the phase value of 180 ° in the harmonic carrier signal. It can be shown that with this representation of alternating numbers by radio signals, and also on the basis that in a coherent acousto-optic processor, the light is pulsed according to the complex amplitude of the light, i.e. the amplitude and phase of the light oscillation

where s; (t) S0 | 21g; p (t - iT) cosu) Ht + J5 is not modulated according to

with the amplitude and phase of the radio signal introduced into the acousto-optic process, it is possible to determine the results of the vector-matrix

one; q (t - iT) sinG3Mt,

If we put in correspondence g; p (t - iT) the pulse sequence DL xEpgK. 2 then & l a for l; q (t - iT) is the impulse sequence C xEpgO and Taking into account that xk x9otHk. 2jmojzk +

+ kj Ll transform of the three-level pulse sequence corresponding to xk, in the decomposition we obtain the following set of signals S (t):

qn o +1

About with S0cosGOHt with

1ts - O, -1;

x; kx; k

0;

one;

S0cos (coHt + fr) with x; k -J

whether in complex form

ib3Mt

S; (t) - x; k-e1

;

where x; -1.0, +1 is the logic level in a three-level pulse sequence corresponding to xk.

Thus, to unambiguously convert a three-level pulse sequence into radio signals, it is necessary to carry out a balanced modulation of the harmonic carrier signal with a frequency (x) n in accordance with the logic levels of the three-level pulse sequence corresponding to xk. In this case, the logical level 0 of the three-level pulse sequence corresponds to the zero value of the amplitude of the harmonic carrier signal, the logical level 1 in the three-level pulse sequence corresponds to the normalized value of the amplitude 1 and the value of the phase P ° in the harmonic

sixteen

the carrier signal, and the logical level -1 in the three-level pulse sequence corresponds to the normalized amplitude value 1 and the phase value 180 ° in the harmonic carrier signal. It can be shown that with such a representation of alternating numbers by radio signals, and also on the basis that in a coherent acousto-optic processor, light is modulated according to the complex amplitude of the light, i.e. the amplitude and phase of the light oscillation is modulated according to

with the amplitude and phase of the radio signals introduced into the acousto-optic processor, it is possible to determine the results of the vector-matrix

transformations based on multiplication and addition operations on arrays of alternating numbers based on the operation of convolution of radio signals. In this case, the complex envelope of the radio signal represents the value of alternating digits x -,) ,,, i.e. the amplitude of the radio signal represents the absolute value of the digits x; and the phase is the sign of the digits x; in the acousto-optic processor cell with acoustic

which wave the radio signal is converted into

S (t) A (t) ej4 W eicu "t

icfW

V P

0 where A (t) e

- complex radio signal envelope; A (t) nCP (t) is its amplitude and

phase, light is generated

E (t)

 x

A (t) e-i4 (l1. EJ (c0c + 04lH JfUetWuH

"K

The light is modulated by the complex amplitude of the field in accordance with the complex envelope of the radio signal S (t), i.e. in accordance with A (t),

At the same time, in a coherent acousto-optic processor based on a discrete convolution algorithm, when entering radio signals corresponding to alternating numbers

17

s

 J

m

 k

those. radio signals

 (t) - x.v-e

Sg; (t) y, k.e

ju, rt. jtoHt

where the values of the digits xjx and y; are the values of the complex envelope of radio signals, in carrying out optical calculations on the complex amplitude of the light field, a multichannel calculation of the discrete convolution is performed on the complex amplitude of the light field, i.e. the formation in each mn-th channel of the optical signal of the form

to e

2n-2

(Z:

Center + gunn

NI

S

„

/ then

de 1 0,1,2, ..

(5-ene

(c) e5 (SEE + gv) mP 25, N-1;

.and

E. Ш - complex amplitude

K I fMW

mn light signal

No

followed by two-dimensional or one-dimensional (depending on the type of vector-matrix conversion performed) by summing the optical signals on all channels, i.e. formation of signals of the form

E either

III

with

. Yu

(t) 2XWft (0) e :(, RHmw

which can be summarized as

EI (t) -Ek),

.IV Kft

where E (t)

EKAWn (

lio E Ґ. (t)

E

Nn

Kamn

(t)

For

IV

registration signal (t). presented in the form of the complex amplitude of light, it is possible to use the method of heterodyne photodetection, in which, due to interference at the photodetector site of the unmodulated light photodetector E (t) e from the coherent source 10

t zrpo

П 25

I73583618

 light of an acousto-optic processor and its optical output signal E (t) E Ј „(t)) in the photo detector a radio signal is generated with a carrier frequency of 2 C0 ″ and a complex envelope equal to), It is known that the heterodyne photodetection is based on the nonlinearity of the photodetector with respect to to the light field.

If the sum of two harmonic signals undergoes non-linear quadratic transformation, then harmonics with both sum and difference frequencies will appear as a result. Detection of an optical signal is nothing more than quadratic conversion of the radiation field. Therefore, when two optical CHI signals with different frequencies are simultaneously detected, an electrical signal is generated at the difference frequency at the output of the photodetector. Therefore, the electrical CHI-NAL at the output of the photodetector will look like

15

20

EV (t)

| E (t + E, ;; (t) i

0 + B, (.

+

IV

 i2COHt

1 + Е (t) -e (КГ. (T)).

Ka

 1 +

| E. (OG)

+ (V KA

five

,,. „T 2Re XVA (t)

The 2Re E KVft term in the photodetector output current is extracted by band-pass filtering with the center frequency of the pass-band 0 &) (). Therefore, the signal after performing band-pass filtering S, (t) will look like

IV

five

S, (t)

Ka

cos 263.t

Further, to highlight the complex envelope, i.e. signal E kA (t), synchronous detection of the signal Sf (t) by radio signals

at the double frequency of the harmonic carrier signal, i.e. on frequency 2nd) c. It is known that a synchronous detector is called a frequency converter, operating

under the condition Qr Oc, where the frequency (Og is the generation frequency, () s is the frequency of the signal, and a low-pass filter is turned on for output of the useful signal, for example, a parallel RC circuit. Therefore, by means of the synchronous detection operation, the signal E is extracted). . (t), to represent which in digital form, the subsequent operations of analog-digital conversion and digital weighting and summation, i.e., while performing operations on alternating numbers of processed arrays without The independent computation channels used to take into account the signs of the numbers are the result of vector-matrix transformations performed in the acousto-optic processor, which are alternating sign values that use heterodyne photodetection of the output optical signals of the acousto-optical processor to produce radio signals at twice the frequency of harmonic carrier signals. carrier and synchronous detection of radio signals at twice the frequency of the harmonic carrier signal with the subsequent analog-digital conversion of the detected two-polar analog signals and their digital weighting and summation with the presentation of the results of calculations in the additional code.

The proposed method for determining the results of vector-matrix transformations in parallel acousto-optical processors is implemented by the following sequence of operations.

Three-level pulse sequences are formed from input-two-level pulse sequences, in the process of obtaining which each input two-level pulse sequence is delayed by a time interval corresponding to the pulse following sequence in the input two-level pulse sequence, the input three-level pulse sequence is subtracted from the delayed signal and the formation of a three-level pulse sequence is deducted after it arrives last pulse to the input two-level pulse sequence and then in the process of forming radio signals | the input to the acousto-optic processor is performed by formed three-level pulse sequences.

five

0

five

But with a balanced modulation of harmonic carrier signals with the same frequencies and initial phases. Thereafter, the formed radio signals are introduced in parallel into an acousto-optic processor, in which parallel optical generation of discrete convolutions of pulse sequences is performed followed by summing optical signals corresponding to the results of obtaining discrete convolutions and parallel heterodyne photodetection of the output optical signals with radio signals being doubled with respect to harmonics carrier frequencies, and synchronous detectors are performed. Received signals by radio signals at the doubled frequency of harmonic carrier signals, and then subject the result of detection to analog-to-digital conversion and perform digital weighing and summation with alternating signals presented on the conversion result

0

five

0

Fig. 1 is a functional diagram of the device for determining the result of the scalar product of vectors with alternating vector elements represented by alternating numbers in an additional code implementing the proposed method; Fig. 2 shows timing diagrams illustrating the process of forming three-level pulse converters; in FIG. 3, timing diagrams illustrating the process of multiplying alternating numbers represented by three-level impulse sequences by means of discrete convolution of these sequences

The device contains a block 1 - a harmonic signal generator connected by its output to the input of block 2 - a harmonic signal frequency divider by a factor M and a pulse sequence generator with the resulting division of the pulse frequency connected to its output from input 5 of block 3 - a pulse frequency divider by two The output of which is connected to the first clock output of the entire device, as well as to the clock inputs of blocks f and 5 multi

O

21

channel converters of input two-level impulse sequences corresponding to the numerical representation of the alternating elements of multiplied vectors in the additional code into three-level

one

pulse sequences, while the numerical inputs of the C and 5 blocks are the two multi-channel inputs of the entire device, and the multi-channel outputs are connected to the multi-channel modulation inputs of blocks 6 and 7, respectively, of the multi-channel amplitude-phase manipulators, in which the inputs for the harmonic carrier signal are connected to the outputs of block 8 is a frequency divider of the harmonic signal by a factor of two with the formation of a harmonic carrier signal, the input of which is connected to the output of block 1 with multichannel moves blocks 6 and 7 respectively with multi-input units 9 and 10 - spatiotemporal multichannel acoustooptic light modulators (MPVAOM) aligned with one another and having opposite directions of propagation of sound in modulators similarly known. On the optical input, blocks 9 and 10 are optically coupled through block 11 — the shaper of the input light beam to the optical output of block 12 — the coherent light source (laser); and on the optical output through block 13, the focusing lens of the diffracted light beam is optically connected Ik - photodetector, the output of which is connected to the input of block 15 of the bandpass filter with the center of the passband at a frequency equal to twice the frequency of the harmonic carrier signal. Herewith, the output of block 15 is connected to one of the two inputs of block 16 - a analog multiplier, the second input of which is connected to the output of block 1, and the output of block 16 is connected to input 17 of a low-pass filter, the output of which is connected to the input of block 18 - a parallel analog-to-digital converter of two-pole signals, whose first clock input (input - output) is directly connected to the output of block 2, and the second clock input is connected to block 2 via a delay line 19 for analog-digital conversion time, while

3583622

The bit outputs of block 18 are connected to the corresponding bit inputs of block 20 — a digital accumulator with the introduction of weighting coefficients and the presentation of the result in an additional code, the clock output of the entire device, and the output is the numerical output of the whole device.

The device for determining the result of the scalar product of vectors with alternating vector elements represented by alternating numbers in the additional code works as follows. In block 1, an output harmonic signal is produced, which can be written as

ten

15

20

W °

(

Where

(2fH) - harmonic frequency

signal. The signal U8bUl (t) from the output of block 1

enters the input of block 2 - the harmonic signal frequency divider by the coefficient M and the pulse sequence former with the received pulse frequency division. Therefore, the output signal of block 2 is the signal

and,

(t) (i + 1) T 3

five

0

five

Out

where i is 0,1,2, .00, oo and - - (i +1) T 3 is a unitary rectangular function, i.e. rectЈ, .. 3 1 with | t- (i + 1) to

xT T / 2, where T is the pulse following period (the clock interval) in the generated pulse sequence, moreover (2), and rect.H 0 with It - (i + DT j T / 2 o

The signal UBb) (2 (t) from the output of block 2 is fed to the input of block 3 — the frequency divider — pulse train by two. Therefore, the output signal of block 3 is the signal

SO

UB ,, x5 (t rect

t - (i + 1)

Where T 2T Signal U

five

W0

comes in first

from unit 3 output

a clock output of the entire device, connected to a clock input of external (not included in the device) memory blocks of alternating elements of multiplied vectors, i.e. alternating numbers represented in the additional code. When a UBb ((t) signal arrives at the clock inputs of these external memory blocks, two-level pulse sequences are formed at their numerical outputs, corresponding to multiplying vector elements, i.e., numbers in the additional code that go to the inputs of the k and 5 blocks of the multichannel converters respectively input two-level pulse sequences corresponding to the numbers multiplied in the additional code into three-level pulse sequences. The numeric inputs of the blocks and 5 are the numerical inputs of the elements of the two multiplied vectors for the entire device, and the clock inputs of blocks A and 5 are connected to the output of block 3, i.e., they receive a signal (i), therefore, taking into account the fact that the inputs of block 4 receive two-level pulsed sequences corresponding to the elements of the vector

CX3 Cxi X4XЈ, .., xb of dimension L, and the input of block 5 is a two-level pulse sequence corresponding to the vector SU Y, Ug., Ug .... of dimension L, the following expressions can be written for the total input signals of blocks k and 5 :

 i, N-i) S §E CHEOPD

- (i + 1)) i-N-f

uws (0 - 2 C y; sog,

X (i + 1)

GLEHH59OPGY

and; avp, "g

Eopgm e

- values of bits of N-bit alternating numbers in the additional code, corresponding to the 1st elements of the vectors -.

At the channel output of the block, a signal is generated) Ovihf Jag representing a three-level pulse sequence

IV, x

I .v

VT-P

0

five

: ivyhgg ({: -Cow (t) c

 StifleB. - (i + 2) lj -f% С

x; Eop 1SS C - «+ DT S: CxC 3onlN -x.-8on, Nlrectx i + DT,

Г е Гх (1 -оэопгМ - xJ3ontNlle TAKES the values -1.0, + 1. At the same time, the formation of a three-level pulse sequence corresponds to the sequential formation of the representation of the alternating element of the vector, i.e. coefficients with power x, i.e.

G1 M

 JS Lx (43ontN

 x5Eol4n e- reStft-a + OT -SCx; r «« t-) T.

0 e Cx (i -,) goniN Х59оп1м3 is the scaling variable coefficients taking the values -1.0 and +1, corresponding to the alternating coefficients at powers of two for the unit of the element (number) x in the canonical form of the polynomial, i.e. THEM

xe S; kV21

0 Described the process of forming the output three-level pulsed

the sequence (-) in the locale 4 of the input two-level pulse sequence $ fc is illustrated in the time diagrams of figure 2, where CuBX4 (t) 3 corresponds to the element (number) x. -7, i.e. in additional with respect to .. 16 code

0 Cx9ot, g 100K THIS OUTPUT, the output signal LUgbijr Ct i of the 1st channel of the block k represents the number xj, in the canonical form of a polynomial, i.e.

t t -1 0 +1 - j "-Ь23 + 0-22 +

+ B2

1-2

6

-7.

Similarly, the 1st channel of the multichannel block A (figure 1) works

25

The 1st channel of the multichannel block 5. Therefore, the output signal D ekDf lc of the 1st channel of block 5 can be written as

N-1

tWe (t) e, .Ozopgm eom 1

s

 .KV (i + 1) T,

-o and

S IXV2

about

Therefore, the set of output signals of blocks k and 5 can be represented as

  i f x; Vecti - (i + DT,

Willow5) SZ Ou erectl - (1e from.

In accordance with FIG. 1, the three-level pulse sequences UByx4 (t.) And Ueb | Jt (t) formed in blocks I5 from the outputs of blocks k and 5 arrive at the modulation inputs of blocks 6 and 7, respectively, of the multichannel amplitude-phase manipulators, in which the harmonic carrier signal t ebixg arrives at the inputs of the harmonic carrier signal from the output of block 8 - divider the frequency of the harmonic signal by a factor of two to form a harmonic carrier signal, that is, the signal formed by dividing the frequency into two signals (t) cos2n H) t post Payuschie from the input unit 1 output unit 8. The output signal of the block 8 will

cos2ftfHt,

where f and is the frequency of the harmonic carrier signal. In blocks 6 and 7, the multichannel generation of radio signals is carried out by means of balanced modulation in each channel of the harmonic carrier signal Ueb) g (t) in accordance with the input i to the modulation inputs of blocks 6 and 7 by three-level pulse sequences U Ј 1, (t) and iyykh5

ten

3583626

from the outputs of blocks k and 5. At that, in the formed channels of blocks 6 and 7 radio signals the logical level O in the three-level sequence corresponds to the null value of the amplitude of the harmonic carrier signal, to the logical level 1 in the three-level pulse sequence corresponds to the normalized value of amplitude 1 and the phase value 0 in harmonic the carrier signal, and the logical level (-1) in a three-level pulse sequence corresponds to the normalized amplitude value 1 and the phase value 180 ° in harmon a common carrier signal. T „e„ radio output signals Ufcbixg t) and output About blocks JQ 6 and 7 have the form

Wt 2 в, x4 (0 E e 2; & iyykh5Sh ee1 27.

15

25

The radio signals Ueb) x $ (t) HUeb)) f7 (t) from the outputs of blocks 6 and 7 are fed to the electrical inputs of blocks 9 and 10, respectively, of multichannel space-time acousto-optic light modulators (MPWLM), which are combined with each other and have the opposite direction of sound propagation in modulators, the S and 10 blocks being optically coupled through the optical input through a block 11 —the shaper of the input light beam with the optical output of the block 12 — a coherent light source (laser), and through the optical output

40 block 13 — the focusing lens of the diffracted light beam is optically coupled to the input of the photodetector unit “When radio signals Ueb | Xe (t) and URbh, 7 (t) are received on

45 the electrical inputs of blocks 9 and 10 - MPVAOM by means of a piezoelectric transducer MPVAOM, connected to the electrical inputs of blocks S and 10, are converted into crisscross

50 blocks of blocks 9 and 10 towards each other Acoustic (ultrasonic) waves with amplitudes (W.tjQp and. Where 1 is 1.2, ..., L is the channel number in blocks 9 and 10, W 55 is the coordinate along the direction of propagation Fannies of sound in one of blocks 9 or 10, for example, in the direction of sound propagation in block 9 with the origin in the middle of the entrance 27

optical aperture. Taking into account the fact that blocks 9 and 10 are aligned with each other and have a counter direction of sound propagation, the expressions for sound waves traveling through them

Г81Ы (У ° З. е. Corresponding to the radio signals (t) lt. Supplied from the outputs of blocks 6 and 7) and Omw Ze when selecting the W coordinate along the direction of sound propagation in block 9 can be written as:

v, ".,

xrect (W / W0);

WHe-b4- f l

xrect (W / We)

17

and

73583628

form acousto-optic convevers (devices for determining the result of a convolution operation) with a heterodyne one. photodetection and RF output at a double frequency of harmonic carrier signals.

In addition, block 13 performs tO optical summation of the results of determining the convolution operation over all available L channels. Therefore, the output signal of block 15 will be a signal of the form

UWIX (t) (2f | l) (t -20) f.

S LKpchIeCH,), b

2 (t-2.)

fl w

The signal Uguy,) from the output of block 15 is applied to one of the inputs of block 16,

where W0 is the size of the input optical aperture along the direction of sound propagation in blocks 9 and 10;

V.B is the speed of sound in the crystals of blocks 9 and 10; rect (W / W $) is a rectangular function that takes into account the optical aperture of blocks 9 and 10, i.e. rect (W / W0) - 1 with fW / W0U "in / 2 and rect (W / W0) t 0 with (W / W0 | w, / 2,

Taking into account the fact that (W0 / 2V b), Q0 represents a constant delayed second input of which receives the signal U8b, x, (t) (2ffl) t from the output of block 1. After the analog transceiver

and U.kw. (t

signal multiplications Ueb, j, 5 (t)

samu

in block 16 at its output we get

U signal

thirty

S 1X16

iW0

(t), i.e. , 5Ct) 6PCS 4

(t)

(2fH) (t) (2fM) t

eGCHiv "4) 1e (iv 5 5 (K) the passage of sound to the middle of the optical aperture of blocks 9 and 10,

 out5

2 (tV.

  "Fcos 2t (2fh) 0

+ (2fh) (t) + 2fr (2f ,,)

and also substituting the expression for 6 "b p-g

"WO and Ueb) X7 (t), (W, t) e 4e" St No. tt) J "lU iC8 | B, 1g we get t, i

FsfB, (w, t) e {u, mo - (w / v, -,

+ o - (W / V, 6) + Op - rect (W / W0);

, t3je {uRblXg t -e, - (W / V) e exp {j2tf - “, - - (W / Vjft) j rect (W / W0),

where trigonometric d is used. Formula 2cosA.cosB cos (A - B) + + cos (A + B). Signal U -.- y.-Ct) with you -fBbl 16

the stroke of block 16 is input to block 17t. Therefore, the signal ,,. (t) on you the course of block 17 has the form

50

 (ABOUT

| r (,

)) Je (UBb, (wave -tJl, "rt.

Each individual 1st channels of blocks 9 and 10 in combination with block 11, block 12, block 13, block 1 and block 15 with a bandwidth center at a frequency of 2fH equal to twice the frequency of the harmonic carrier signals

the second input of which receives the signal U8b, x, (t) (2ffl) t from the output of block 1. After the analog switch U.kw. (t)

signal multiplications Ueb, j, 5 (t)

samu

in block 16 at its output we get

U signal

S 1X16

iW0

(t), i.e. , 5Ct) 6PCS 4

(t)

(2fH) (t) (2fM) t

eGCHiv «4) 1e (iv 5 5 (K) out 5

2 (tV.

) J

where the trigonometric formula 2cosA.cosB cos (A - B) + + cos (A + B) is used. Signal U -.- y.-Ct) with you -fBbl 16

The stroke of block 16 is applied to the input of block 17t. Therefore, the signal ,,. (t) on you the course of block 17 has the form

 (ABOUT

| r (,

)) Je (UBb, (wave -tJl, "rt.

Thus, block 16 and block 17 allow synchronous detection of the signal Ueb) Xls (t) by radio signals Uftbnt ((t) at a doubled clock

Tote of harmonic carrier signals Since Ј0 (W0 / 2) / Vib, then when choosing (2fu) О W / Ъ

 &

H - 1V AJBH P GDE P an integer, sound wavelength at the frequency of the harmonic carrier signal, i.e. when choosing the optical aperture of the WQ blocks 9 and 10 along the direction of sound propagation multiple of the sound wavelength in the crystals of blocks 9 and 10 at the frequency of the harmonic carrier signal fH, for UBblx (t) we get the following expression:

 l ° g

U6bIM7 (t) 2 JotUBbl4 (0) e,

TO.

Y.-.L y-y

 2 Kb, 4) (t- -Uo,

i o - ".),

d

(t)

Thus, the signal U6b) X at the output of block 17 - a low-pass filter represents the sum of convolutions of three-level pulse sequences flJBb, M (t) „, (t) g with a doubled time scale (2 times accelerated by events) and a constant delay t 2 (t - $ e). Since the three-level impulse sequences {and (t) g and | ГИВЬ | represent the alternating numbers in the conical form of polynomials in powers of two with alternating (-1.0, + 1) coefficients for powers of two, m.

N-t LuBb.) Je g x-.J ,,

xrect t - (i + 1) T, N-i

where x6 s v 2

and similarly

sh

Cu-x5 jSfr e tN-l

where is ye S y .k% 2

Jeo

then the expression for (t) can be written as

 um-z NUMeo (t) .1 Z xsj € ГIffiTi A / - i (° 2 () 1

NC (+ (1} (TiUt J

3583630

where i and j are integer variables, i

 0,1,2N-1 and j 0,1,2, ...,

(2N-2);

5 G,. /.) 2 (t -C0) 1

L (eDiNal positive triangular function (saw function, resulting from the convolution function of the function 10 - (i + 1) T,

® is the sign of a convolution operation. Provided that PT, where n is an integer, the expression for Uftbty (t) can be converted to the form 2N-2 N-

n6Yh „(t) g, Z: S x; k-y (j -,) k

 , („

(j + From

20 where T T / 2. The condition 2 2ft pT, taking into account the previously imposed condition (2Јts) 0 n, means that the frequency of the harmonic carrier signal must be a multiple of the following frequency

25 pulses in pulse sequences corresponding to the elements of the vectors, i.e. the numbers x and y ", or 1 / fj, pT. Therefore, the pulse frequency (clock frequency)

30 must be formed by dividing the frequency of the harmonic carrier signal, which is accomplished by blocks 2 and 3 (FIG.).

The signal U6b | Xn (t) from the output of the low-pass filter block 17 is fed to the input of block 18, in which, when pulses with a pulse period T1 arrive at the first clock input connected to the output of block 2, the signal U B | x, 7 is gated (t), m3e. converting it to the signal Ujg (jT), and then converting the signal (jT) to a digital (two-level signal) Ufcbu, 8 (jT1) and converting to a digital signal is carried out separately for positive and negative values of U1g (jT), which control a clock CHI is used that arrives at the second clock input of block 18 from the output of block 19, the input of which is connected to the output of block 2. At the same time, the gates of the EXC1 signal in block 18 at times t jT / 1 result in the formation

55 ignals U18 (jTf)

 2N-2 M-

u, 8 (ji) -S S Ho. °

40

45

31

It can be shown that the signal U (jTr) obtained after gating is a bipolar pulse sequence with amplitudes of pulses equal to the coefficients at powers of two when representing the number z, the result of the scalar product of the vectors VJ and fyj,

those. (V УД z, where z is a scalar p (number), the designation of the transposed vector “In accordance with the well-known definition, the scalar product of the vectors Ј 1 and the dimension n is the number T,, +

 + wasp the number formed by the matrix product of the row наt by the column {, in the canonical form of a polynomial in powers of two with alternating coefficients at powers of two It is known that for two-level pulse sequences representing the numbers xbfl and yb 0, this multiplication is10

173583632

villages are called discrete convolution algorithm

In fact, the multiplication algorithm by discrete convolution is equivalent to the analog addition of partial products when successively multiplying numbers by a column.

Consider the form of the signal U (jT1) using the example of multiplying the 1-th element of the vectors corresponding to the alternating numbers XЈ 5, Y {7 represented by three-level pulse sequences corresponding to these numbers in the canonical form of the polynomials of the 2-th power of two with the alternating (-1 , Oh, +1) in numbers, i.e.

(+ 0-23 + 5 and y, (-0 (0) (+0 (-0 - (-0-23 +

V. . in / - V -.L

20

x (+ ONM + OH). . fc

+ (-0 22 + (+0 2 + (-1) -2)

+ P-22 + (+ 0-21 + (-1) "2 ° -7.

The product of these numbers will be equal to

(+ O (-i) (+ 0 (-O (-O (o) (+ O (-O (+0 (-0 (+0 (-0 (-0 (o) (+ 1H-0

(-0 (+0 (-0 (+0 (+0 (-t) (+0 (-0 ° o about x

-0 (+0 (-t) (+ 0 h

h h

(-0 (+ Och (oG (-Sh + 2I-2} (- and)

 (rt) -2 "+ (+ 0-2 - (0) 24 + + (+2)" 22 + (-2) - 2 + (+ 0-2 ° -64 + 32 + 0-8 + 8- 4 + 1 - -35 hgue 5 (-7).

In addition, fu18 (jT) e / b0 1; , (lJ, 8 (JT) f, - f - -2; tlJieUT i / M +2; (jT) | j- -I., {Ui8 (JT) bff4 - 0; ((jT) i; fu48 (jT ) |, -. 6 -1.

The process of forming the signal Ujg (jT) for multiplying the numbers xg 5 and yg -7, represented by the signals, UBblX4 (t) j p and ILX5 (t) e

vectors. Therefore, to obtain a scaled product of the vectors Z txj in the usual digital form in the form of a two-level pulse sequence 45, corresponding to the representation of alternating numbers in the additional code, it is necessary to carry out an analog-digital conversion of the two-polar signal

those. signal shaping UBblx (t) 50 received by strobirov .. ..OUT1

and the signal UieCjT), which is the gated result of the Syvp4 convolution (fc9e® LuBbiys (t) J €, is shown in the time diagrams in FIG. 3). When multiplying all possible numbers, the value Uig (jT) is in the -NL range; U , (jT 5Ј -NL, where N is the number of digits of the multiplied numbers, L is the number of elements

18.

UBWJffeu (jT

corresponding to the alternating numbers, and then weighting the alternating numbers, represented by the 55 signal 9m Ueb | Jr, eu (jT (), coefficients 2 and add up the weighted numbers to get the result of the product Z V.

ten

73583632

villages are called discrete convolution algorithm

In fact, the multiplication algorithm by discrete convolution is equivalent to the analog summation of partial products when successively multiplying numbers by a bar.

Consider the form of the signal U (jT1) using the example of multiplying the 1-th element of the vectors corresponding to the alternating numbers X, 5, Y {7, represented by three-level pulse sequences corresponding to these numbers in the canonical form of polynomials of the 2nd degree two with alternating-sign (- 1, 0, 1) in numbers, i.e.

(+ 0-23 + 5 and y, (-0 (0) (+0 (-0 - (-0-23 +

V. . in / - V -.L

20

x (+ ONM + OH). . fc

+ (-0 22 + (+0 2 + (-1) -2)

+ P-22 + (+ 0-21 + (-1) "2 ° -7.

(-0-23 +

vectors. Therefore, to obtain the scalar product of the vectors Z txj in the usual digital form in the form of a two-level pulse sequence, corresponding to the representation of alternating numbers in the additional code, it is necessary to carry out analog-digital conversion of the two-polar signal

 the resulting strobing of the received strobirov18,

UBWJffeu (jT) digital signal

corresponding to the alternating numbers, and then weighting the alternating numbers represented by the signal 9m Ueb | Jr, eu (jT (), by the coefficients 2 and add the weighted numbers to get the result of the product Z V. From the block 20, connected

Mr. with block 18 to obtain a digital signal in the form

2n-2

ivyh20tsat) -z; and

J6b1V

„O As well as the formation of the signal (JT) obtained by gating, it is also converted to Ugbntiei / JT1) in block 18 (Fig L). The output signal of block 20 and, accordingly, the entire device will be the following signal :

17

U

JT UBWXwu (jT) output

(JT1 2P

J

R

H S U8blX, 8ts

, Mr. and Mr. Mr.

J-o

- (j +

 J3on (S., ° T3 S Z; 9an (2 x rectjt - (j + 1) T.

Thus, the device shown in Fig. 1 performs the determination of the result of the scalar product of the vectors Z Јxj. , where СХ3 and SU of vector of dimension L with alternating elements in the form of alternating N-bit numbers in an additional code, with obtaining a two-digit result in an additional code.

In the device, calculating the scalar product of a vector with alternating elements of vectors represented by alternating numbers in the additional code implementing the proposed method (Fig. 1), blocks 9 and 10 (multi-channel space-time acousto-optic light modulators (MPVAOM)) can be used various types of currently known MWASM, the number of channels MWASM can reach 128 and is theoretically limited to 512, while as elements of digital electronic nodes I can t be used chip series K500, K1500. As channels of blocks 6 and 7 (multichannel amplitude-phase manipulators), as well as for block 16 (analog multiplier), chips of analog multipliers-modulators,, and 526PS1, 526PS2 or “digital,

15

20

735 363J

500 and K1500 series microcircuits for parallel analog-digital converter of bipolar signals - block 18 - microcircuits of parallel analog-digital converters 1107ПВЗ and 1107ПВ can be used, allowing operation with clock frequencies up to 100 MHz in

JQ In comparison with the known method, the proposed method allows to increase by a factor of k the speed of determining the results of vector-matrix transformations while maintaining the dimension of the processed arrays or maintaining the speed of determining the results by a factor of 2 to increase the dimension of the processed arrays. This is explained as follows. In a known method, for operations with alternating numbers, a redundant representation of alternating numbers is used, i.e. the division of numbers into positive and negative is organized and four independent channels of computations are used, followed by summing up the results of the calculations, taking into account the signs,. To organize four independent channels of computations, the frequency multiplexing of the channels, t, e0, is used. generation of radio signals with frequency multiplexing, where part of the frequency band is equal to W / 2, provided that W is the frequency band for each

35 to the input of the acousto-optic processor, is assigned to represent the numbers, one character followed by the input of radio signals into the acousto-optic processor. In this case, if we consider

40 each individual input of the acousto-optic processor, its capacity will be determined by the amount of information transmitted through it per unit of time. However, it is known that, according to the Shannon theorem, the bandwidth C of a channel with a frequency band W in which there is arbitrary noise is limited by the inequality

25

thirty

Wlog

P +

Ni

ЈC "W log

P + N

five

where P N N is the average power of the transmitted signals; average noise power;

K - entropy noise power, i.e. geometric mean noise power at different frequencies in the W band

35

N,

 logN (f) df

where N (f) is the noise power at frequency f.

Claims (1)

Therefore, when using frequency channel multiplexing in the known method to represent positive and negative numbers, the throughput of each of the inputs of the acousto-optic processor is two times less than the proposed one, since each time the acousto-optic processor enters either the positive or the negative number , and for each of them, the W / 2 band is assigned, and the speed of determining the results of vector-matrix transformations in the proposed method, The number of numbers of arrays processed per unit time is four times larger than in the known method, in which the dimension of each of two arrays processed in parallel by an acousto-optic processor must be reduced twice / because, for the same number of parallel inputs of an acousto-optic processor With a fixed bandwidth, it is necessary to form two separate processing arrays taking into account the sign (either only positive or only negative numbers) and use a frequency seal for simultaneous processing of elements formed arrays. Similarly, at a fixed speed of determining the results in the proposed method, the dimension of the processed arrays is increased by 2 times, as in the known method with a fixed value of W, i.e., the bandwidth of the passband along the inputs of the acousto-optic processor, the dimensionality of the processed arrays is two times smaller due to . Invention Formula The method of determining the results of vector-matrix transformations in parallel acousto-optic processors, based on the formation of the input two-level pulse sequences, respectively 10 735Я3636 alternating elements of parallel-processed arrays, radio signals input into acousto-optic  a processor performing parallel optical generation of discrete convolutions of pulse sequences with subsequent summation of optical signals corresponding to the results of obtaining discrete convolutions, parallel photodetection of the output optical signals, analog-to-digital conversion of photo-detected signals and subsequent digital weighting and summation, characterized in that for the purpose of increasing speed of determining and increasing the size of 20 parallel arrays processed sign of the operating numbers, from the input two-level pulse sequences form a three-level pulse sequences, in the process of obtaining j, each input two-level pulse sequence is delayed by a time interval corresponding to the pulse-following sequence in the input two-level pulse sequence, calculated 15 thirty 35 40 45 50 55 From the delayed signal, the input two-level pulse sequence is lost and the formation of the three-level pulse sequence is stopped after the last pulse is received in the input two-level pulse sequence and then, during the formation of the input radio signals into the acousto-optical processor, balanced three-level pulse sequences are balanced by modulating the harmonic CHI signals with the same frequencies and initial phases, and parallel photodetecs Testing the output optical signals is carried out by means of heterodyne photodetection of the output optical signals at twice the ratio in the harmonic carrier signals and then subjecting the detection result to analog-to-digital conversion, performing digital weighting and summing over the result of the conversion to the alternating signals presented in the additional code. /, / C -j--  r / fnodowp pshoi / hoi / : Po, 2  Vttft foxtig / v og V / HitpddU muoshzhhi | $ 0XI9ff