SU1354205A2 - Device for computing digital convolution - Google Patents

Abstract

The invention relates to computing and information technology and can be used for digital processing of signals and images, as well as in 9o-10 encoding devices, the principle of which is based on the theory of finite fields (Galois fields) and rings. The purpose of the invention is to expand the range of lengths of the t-sequences to be processed. The goal is achieved by the fact that the device includes an n-bit register (-1, M is a conversion module), a multiplier modulo M 2, a convolution calculation unit 3, an input of a correction multiplier 4, a first input 5 of a multiplier, a task input sequence of samples 6, the first 7 and second 8 inputs of the convolution calculation unit, the recording resolution input 9, clock input 10, control inputs 11, 12 and 13, information output 14. 1 Il. (L N)

Description

The invention relates to computing and information technology, can be used for digital processing of signals and images, as well as in coding devices whose principle of operation is based on the theory of finite fields (Galois fields) and rings, and is an improvement of the device according to Aut. St. No. 1295415,

The length of the impulse response should not exceed in the known device one-half of the value of the number-theoretic transform (PTS) N, which must satisfy the condition

N

NOD (Р -1, Р, -1,, .., Р „-1) (1)

where is the vertical line a | S means; and divides & GCD - the greatest common divisor and module of PTS

M. R

Y-2 1

. (2)

The purpose of the invention is to expand the range of lengths of the processed sequences.

The drawing shows the functional diagram of the device for calculating digital convolution.

The device contains a p-bit register 1, a multiplier 2 modulo M convolution calculation unit 3, an input 4 specifying a correction multiplier, the first input 5 of the multiplier, input 6 specifying a sequence of samples, the first 7 and second 8 information inputs of the convolution calculation unit 3, input 9 recording resolution, clock input 10, control inputs 11-13, information output 14.

In most of the known methods for calculating convolution, the module M is assumed to be simple. For the case of composition-pO (

.Mn P7 P

) W.-Z

volume of PM N

must satisfy (1) and for numbers -1 is too small for practical use of the indicated modules.

Let us consider the requirements for the values of elements of collapsible sequences and parameters of PPP, it is possible to calculate the digital convolution of the volume N using the composite mode .oi

Liu R,. . .. for N, which does not satisfy condition (1), but divisors of some, at least one of the numbers ().

Let in the ring of integers modulo M, 1,.,. , M-l, there exists an element N opposite to N and a root of unity of order N TeZ. The product of the matrix (e) of the inverse PST and the matrix Hu, (e) of the direct PTP (X | (e) 6 °, l ,, N-1) is not equal to the unit modulo M matrix, since the cyclicity condition does not hold.

Matrix (e) -Xj (e)

15

modM

except the unit modulo M diagonal, contains nonzero elements. In the worst case, the off-diagonal elements are not zero, for which we have:

. N-i .... ,,

- (: -it it

; .. N) -b modM

 -1 JLL (N) g modM,

(3)

30 a also g;. | J., G,; j, and. From relation (3) it follows that the matrix D contains no more than N-1 different elements between each other, which allows us to denote them by g ,, g,

 8n-1 V Convolution is calculated by the scheme

35,

(x) PM (b),

where OTCHP - reverse PTS.

In the matrix form we have:

(e) -X, (e) -h

one

(four)

45

Usch (x®H) x (e) x (e) x

(x®h) Dy.

. The symbol ® denotes multiplication in the ring Yg - the value of convolution, computed. 50 according to (4), which may differ from the true value of y.

The convolution cyclicity condition is satisfied for the modulus F, defined as

L.

 t

(five)

where f is equal to those of those defined in the decomposition of M for which 31354

The condition N I () (for even N it is necessary to clarify the conditions for choosing the root 5).

It follows that g or g2 i-FniodM,, N-1.

Let us bring the matrix D to a diagonal modulo M. For this, multiply (4)

on R such that, where Pd is a row of lines, direct matrices and inverse numbers from the decomposition of M, for there are no repetitive elements, the condition N | (Pg -1 -1) is not met and which -on all g,, N-1.

Starting from the structure of the matrix D, followed; . ,,

blows that all elements of g,, n-1

equal to each other:

We have:

R R5, F R :), F R R, F

I f

R.HM -F F

R N-v-F

L /

R

0 0 R 0 0 R

"

0 0 0

0.0 0

R

, R.y; (R.y;) modM,, N-1. Since R | M, the inverse of R modM does not exist, which does not allow one to uniquely restore the value of y. It may differ from

you h

on

a multiple of FmodM. We write this as follows:

W; Y; VSE + p; FmodM,, (6)

where p; - unknown coefficient, taking one of the values O, T, 2, ..., (M | F-1).

Determine what should be a coefficient of 1 to be equal to

STVO y (2 X, b) U11CH (b)

y (.x, h) 2 y {x, h) 2 (y ,,,, (x, h) +) modM (2-y8 «, i4 (x, h) + 2 pF) (modM).

At. (ModM) y (g. X, b) (t. X, h).

So, if all the elements of one of the arrays (x or h) have a factor jJmodM (hereinafter referred to as a correction factor) such that g, using a PPP, you can calculate the true cyclic digital convolution of volume N such that not all components of the decomposition M satisfy condition NJ (Pj- 1),, m.

The requirement for module F is significant. depending on whether even or odd N is chosen. Let N be odd.

In the rows, except for the first, one, there are no repeating elements,

Starting from the structure of the matrix D, followed; . ,,

blows that all elements of g,, n-1

equal to each other:

15

N

20

.

. (...- e) modM N (e-1G (eSOmodM. We write the module M as. Now S modF () (modF) and gmodF N (-1) () modF 25 0 (modF).

So, for odd N, the F-module can be determined from (5).

Consider the case of even N. 30 For the nondegeneracy of the PMP matrices, an additional condition is imposed on 6:

g KmodM).

35

The values of g,., N-1 are not all equal. It can be shown that there are only three different values of g. Denote them by g (, 40 §N / 241 according to the position in the first row of the matrix D.

We write the elements g,, g, gf ,, 2 +,

g, (... +) modM g4.2.N (be + ... +) modM

gH f Γ (H-) modM.

f-n

As shown above, (modF) for the module F defined by (5).

g2modF ((l + ...) modF 2 -N () - (-1) 0 (modF),

if a

  1 (modF); e 1 (modF).

To fulfill the requirement of g

0 (modF) root 6 must satisfy the condition:

(2 (modM)) - (+1) 0 (raodF).

So, in the case of an even N to choose

the root C of the LP Z is superimposed on the following. conditions:

6: 1 (modM) i 1 (modM)

 (modF).

When designing and creating a device for calculating the convolution, the parameters of the PST of M, are selected, from which they are calculated using (2), (7), (8), the correction of the given factor h and the possible values of N are determined.

A device for calculating a digital convolution operates as follows.

Before starting work, register 1 records the value of the correction multiplier using inputs 4.9 and 10 of register 1. Further, the time diagram of the device operation does not differ from the time diagram of the known device, with the only difference that all control signals are sent with a delay equal to the delay introduced by the multiplier 2.

Editor N. Tupitsa Order 5695/44

Compiled by A. Baranov Tehred A. Kravchuk

Corrector

Circulation 671 Subscription

VNIIPI USSR State Committee

for inventions and discoveries 113035, Moscow, Zh-35, Raushsk nab., 4/5

Production and printing company, Uzhgorod, Projecto st., 4

th

3542056

The values of the input sequence S ,, supplied to the inputs 6 of the multiplier 2, are sequentially multiplied by the correction factor raodM and together with the values of the sequence 5 arrive at inputs 7 and 8 respectively of the convolution calculation unit. ten

20

Claims (1)

Invention Formula Device for calculating digital convolution auth. St. No. 1295415, 15 characterized in that, in order to expand the scope of application by expanding the range of lengths of processors of the sequences, the n-bit register (-1, M-modulus of the transducer) and the multiplier modulo M are entered into it to the information input of the Fourier – Galois transform unit, the first input of the multiplier modulo M is connected to the output of the n-bit register, the information input of which is the input of the setting of the correction multiplier of the device, the input of the setting of the sequence of counts l a second input of the multiplier modulo M, a clock input and write enable input of the n-p-stand different registers are respectively the clock input and write enable input of the device. 25 thirty Proofreader L. Pilipenko