SU1748147A1 - Parallel generator of matched systems of basal functions, invariant to a base of power basis - Google Patents

Abstract

The invention relates to automation and computing and can be used, for example, in digital information transmission systems. In order to expand the functionality of the generator by parallel formation of MN matched systems of basic functions, the generator contains two inputs of a system of functions, clock input, output of the end of a period of generated functions, N function outputs, an n-time counter (dimension of the system of functions, -n integer), n + 1 shift registers, n elements NOT, key element, N - modulators M / 2 (M is the number of quantization levels, M is an even integer). 1 il.

Description

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The invention relates to automation and computing and can be used for spectral analysis of signals when they are decomposed into systems of functions.

The prototype contains two n-bit counters (- the dimension of the system of functions), n shift registers, n elements NOT. n blocks of elements And, modulo modulator М / 2, clock pulse input, function setting system input, function output, period output of the generated functions, output of the generated function number, in which the input of the first counter is PDB to the clock input of the generator and inputs synchronization n shift registers, the overflow output of the first counter is connected to the counting input of the second counter, to the control inputs of the recording n of the shift registers and to the output of the end of the period of the generated generator functions, the bit outputs of the second counter are connected s with the output of the number of the generated generator function and with the control inputs of gg units of elements I. the input of the 1st group of the 1st shift register (, N / 21, ..., n, m is the size of the group defined by the number of bits in the binary representation of M / 2-11, M - even tce 1 st rank

number), connected to

the group of the input of the task of the system functions of the generator, the first output of the N / 2 and the bit group of the 1st shift register through the 1st element is NOT connected to the first input of the group of the sequential input of the 1st shift register, the outputs from the second to m + 1 N / 2-and bit groups of the 1st shift register are connected respectively to inputs 2, t + 1 groups of the sequential, input of the 1st shift register, outputs 1, t + 1 N / 2 -u of the discharge group 1- go shift register connected to

2

00

J

Xi

a group of information inputs of the i-ro block of elements And, the outputs of the blocks of elements And connected to the inputs of the adder modulo M / 2

The disadvantages of this generator are the inability to form consistent systems of basic functions, a limited class (2M) of systems of basic functions formed by the generator, and the inability to simultaneously form basic functions in a system of functions.

The purpose of the invention is to expand the functionality of the generator by increasing to MN the number of concurrently formed consistent systems of basic functions.

The goal is achieved by the fact that the generator containing the counter, n shift registers, (is the dimension of the system of functions), n elements NOT, the block of elements I, the first modulo M / 2 adder (M is the number of values accepted by the functions) (2m J) -H (.p, 1.2pN) the input of the first group of tasks of the generator function system is connected to the j-th bit information input of the i-ro shift register. the bit information output of the 1st shift register is connected to the serial information input of the 1st shift register, while the sign output of the 2H section of the 1st shift register is connected to the serial sign input of the 1st shift register through i element NO, the counting counter input is the clock input of the generator and is connected to the synchronization inputs of all shift registers; the counter overflow output is the output of the period of the generator function and connected to the control write inputs of all the shift registers, entered (n + 1) th shift register and from the second to the n-th modulo m / 2 adders, with 2n 1 bit information inputs of the (n + 1) th register with the view being the inputs of the second task group of the generator function system , the bit information output of the (n + 1) -th shift register is connected to the serial information input of the (n + 1) -th shift register and the information input of the AND block, the control input of the AND block of the elements the single output of the counter, the output of the block of elements And is connected to the corresponding input of each adder modulo M / 2, p The potential information output of the 1st shift register is connected to the inputs of those adders modulo M / 2. the numbers in the binary representation contain a unit in the 1st bit, the outputs of modulo M / 2 adders are information outputs of the generator, the synchronization input and the control input of the (n 1) -th shift register are connected to the clock input of the generator and the output respectively overflow of the counter, the 2nd input of the first group of the task of the generator function system is connected to the input of the first modulo M / 2 adder.

The drawing shows the functional diagram of the generator ().

The generator contains input 1 of the first group of the function system set, input 2 clock pulses, input 3 of the second group of the function system set, counter 4, shift registers 5-8, block 9 elements I. NOT elements 10, adders 11-18 modulo M / 2 , functional outputs 19-26, output 27 end of the period of the function.

The generator forms M systems of discrete basis functions that are invariant to the base of a power basis and are consistent with an arbitrary signal that accepts M values.

The generator implements a method of forming systems of discrete basis functions through the product of n modified Rademacher functions in accordance with the expression

fnGdl% (k.p) rriodgM / 7, g-W-1.

GfaHk |

 4G (1,0), (1)

where r is the index of the function, .n-1:

p is the reference number of the function,, М-1;

K is the index of the modified Rademacher function,, 2Т2 ,:

dk (i) - (exponent i of the k-th modified Rademacher function, equal to the value of the 1st bit in the binary representation of the index g, .p,

G (1, p) A-A, A - backbone vector.

Setting N / 2 — the values of the function G (1.p) that forms the system with the vector A (N / 2) means approximation of the 1/2 period of an arbitrary signal S (t) with any desired accuracy by selecting the corresponding parameters in (A (N / 2) . p, M) according to expression (1). Approximation of the second half of this signal and the construction of a consistent system of functions (the signal is the function of the system of functions itself) is carried out by selecting the elements of the vector multiplier B (N / 2) in the interaction relation (2), which forms the system of functions of dimension 2P

G2n

g () i B () x g (2

g () 2 -B (2n-1) xg (2

 one

) 2 J,

(2)

where g () i. g (2n 1) a - two different systems of basic functions of dimension, formed according to expression (1), whose elements are the values of the power function where the g is an arbitrary number (real, complex, vector, matrix, or their extensions); DЈ0, M / 2-1, M is the number of values accepted by the functions, M is an even integer.

The product of the degrees g in expressions (1) and (2) and the formation of the values of the basis functions in the generator is performed according to the rule gi xg4 () P g () modM / 2, (3)

where Si and $ 2 are signs of degrees.

(Oh, if the sign of the degree dy is positive,

/BUT

(1, if the sign of the degree of two is negative,

p is the transfer formed when performing the operation of adding the exponents in the expression (3):

O, if the selection of the integer M / 2 occurred an even number f. time.

1, if the selection of the integer M / 2 occurred an odd number of times. The systems of basis functions formed in accordance with equations (1), (2) and (3) do not depend on the base of the power basis g and can be used to perform various transformations (with different values of g).

The generator works as follows.

 The coded values of the vector A (N / 2) are fed to the input 1 of the first group of the task of the system of functions. The input 2 serves a sequence of clock pulses. To the input 3 of the second group of the task of the system of functions, the coded values of the vector B (N / 2) are supplied. Counter 4 counts the clock pulses arriving at its input and thus forms the period of the following basic functions, where t is the period of the following of the clock pulses. At the beginning of each period T, at the front of the 0th clock pulse, the states of inputs 1 and 3 of the generator are interrogated and the corresponding information is recorded in registers 5, 6. 7. 8 shift. The leading edges of clock pulses 1-7 shift this information in the shift registers and generate a modified Rademacher function RI at the output CU of the shift register b, function R2 at the output Q2 of the shift register 7 and function R4 at the output QI of the shift register 8. Additional modified Rademacher RO function

formed at the output of Cm shift register 5. Elements 10 form the sign bit of the modified Rademacher functions RI, R2, Rn. Adders 11-18 modulo M / 2 are used to form samples of basic functions according to expressions (1) and (3). From the outputs of adders 11-18 mod

M / 2 samples of the basis functions in parallel arrive at the functional outputs 19-26 of the generator.

In contrast to the prototype, the proposed generator forms MN matched systems of basis functions with an arbitrary base of a power basis, moreover, all functions in the system of functions are simultaneously (parallel) formed.

Claims (1)

Invention Formula Parallel generator of matched systems of basis functions invariant to the base of the power basis, containing a counter, n shift registers (is the dimension of the system of functions), n elements are NOT, the block of elements is And, the first adder modulo M / 2 (M is the number of values taken by the functions), with 2 j-th (, n,.) input of the first task group of the generator function system is connected to the Jth bit information input of the 1st shift register, the bit information output of the 1st shift register is connected to the serial information input of the 1st shift register, while the sign output of the 1st shift register is connected with consecutive sign input of the 1st shift register via the i-th element NOT, counting input of the counter is the clock input of the generator and connected to the synchronization inputs of all shift registers; the overflow output of the counter is the output of the end of the period of the generator function and is connected to the control the write inputs of all the shift registers, about the fact that, with the aim of expanding the functionality of the generator by increasing the number of concurrently formed matched systems of basic functions to M, it contains (n + 1) -th register the shift and from the second to the n-th adder modulo M / 2, with 2 bit information inputs of the (n + 1) -th shift register being the inputs of the second task group 5 of the generator function system, 2n-1-th bit information output (n + 1) -th shift register is connected to the serial information input of the (n + 1) -th shift register and the information input of the block of elements I, the control input of the block of elements AND connected to the n-th bit output of the counter, the output of the block of elements AND connected to the corresponding input by each generator outputs, the input of the synchronizing adder modulo M / 2, ratios and the control input of the recording of the (n + 1) -th sequential information output of the i-rotor shift are connected respectively to the register the shift is connected to the inputs of the generator input and the output of modulators M / 2, the number of which is 5 replenishment of the counter, 2P and the input of the first group in the binary representation contain the setting of the system of functions of the generator unit in the i-th bit, outputs totalizers connected to the input of the first adder on Modules M / 2 are information-modulo M / 2.