SU1327134A2 - Device for determining characteristic function - Google Patents

Abstract

The invention relates to the measurement technique and is an improvement of the invention according to the author. No. 1163340. The purpose of the invention is to expand the functionality (L

Description

1327134

devices by determining the statistical points. In the operation of the device, the properties of the Walsh function are used, which make it possible to calculate the derivatives by adding modulo two and shift. The device contains a block of 1 memory and 2 channels, in each of which n blocks of 2 multiplication and blocks 3 of memory, generator 4, sum 1

The invention relates to a measurement technique and can be used for statistical analysis in data transmission systems, digital tracking systems and in adjacent areas in which random processes are represented as a binary-number vector, and is an improvement of the known device according to the basic algorithm. .sv. No. 1163340.

The purpose of the invention is to expand the functionality due to the possibility of determining moments.

The operation of the device is based on the following relationships.

The Walsh characteristic function is defined as

) „, (X)

where .. () is a functional transformation of the input data vector according to the basic system of discrete Walsh functions. Operator

(S) t (k) 1 iCk) - ti (k 2 2).

is the j-M component of the gradient of the vector i (k).

Here © is the operation of modulo two.

In the general case, the rth moment is determined by the tensor

 P ,, 1 ,. E (x, x., ... x;)

ak-T4T :: jk-; ® iK -,. o

The drawing shows a diagram of the yc solution.

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torus 5, converter 6 amplitude to the number of pulses, trigger 7, waiting for blocking generators 8, 9, reversible counter 10, in channels - a group of 11 AND-NOT elements, a group of 12 AND elements and a group of 13 AND-NOT elements, as well as an adder 14 modulo two, formers 15, 18 pulses, shift registers 16, 17, adder 19. 1 Il.

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The device for determining the characteristic function contains a block of 1 memory of a binary-number vector of input data and channels, in each of which n blocks of 2 multiplication, blocks of 3 memory (binary code of the parameter of the Walsh function), generator 4 of the reference frequency, in each of the channels adder 5, converter 6 amplitude to the number of pulses, trigger 7 (parity), two waiting blocking generators 8 and 9, reversible counter 10, and in (2 -1) channels - the first group of 11 NAND elements, group 12 elements AND, the second group of 13 elements NAND, adder 14 modulo two, p rvy pulse generator 15, registers 16, 17 shift, the second pulse generator 18, an adder 19.

The device works as follows.

In the input data memory 1, a bit binary number is stored, which is stored therein in accordance with the rate of arrival of information. Each bit of a binary number with a certain probability can be 1 or 0. In blocks 3 of the memory parameters of the Walsh functions in each of the (2-1) channels are written in binary code n-bit numbers corresponding to the frequency of a specific Walsh function. For example In the fourth channel, which has four sign changes in the definition interval, the n-bit number stored in the memory will be 100.

Multiplication unit 2 is carried out by a multiple multiplication of two n-bit binary numbers using the reference frequency generator 4, the role

which is to improve the accuracy of the multiplication operation and at the same time the reliability of the results from possible interference due to the introduction of high frequency pulses.

As a result of multiplying two binary numbers, a new code-pulse number appears at the inputs of adder 5, which is then summed bitwise and as a result, a pulse of a certain amplitude is formed at the output of adder 5.

Converter 6 amplitude in the number of pulses is designed to convert the amplitude of the pulses at the output of the adder into a sequence of standard pulses, the number of which is proportional to the amplitude. These pulses are then counted by a parity trigger 7.

In case the number of in-pulses turns out to be even, at the zero output of the trigger there is a potential that starts the waiting blocking generator 8, from the output of which the pulse generated by it will go to the reversible counter 10 through its direct input.

otherwise, i.e. when the number of pulses turns out to be odd, the blocking generator 9 is triggered and the pulse generated by it goes through the inverse input to the reversible counter 10. At the outputs of the reversible counters 10 of all channels, as a result of averaging, an estimate of the first two multidimensional statistical moments is formed.

1) Definition of the first multidimensional statistical moment (mathematical expectation).

Blocks 1-11, 15, 16, 19 are working. A single signal is prerecorded in the first register register 16. To determine the expectation of the jth binary variable, it is necessary to apply a number of pulses from a single-pulse generator the tenth equivalent of the jth binary variable. As a result, a binary number is formed in register 16, corresponding to the j-th power of the number two. For example, to determine the mathematical expectation x- (for j 3), it is necessary to start the pulse shaper 15 times.

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then in register 16. the toco binary code is generated.

The generated binary code is a key that, if a Walsh function parameter coincides in one of the channels with the same binary code, coming from blocks 3 of the memory of the parameters of the Walsh function to the inputs of groups 11, 12, 13 of the AND-NOT elements AND provides the passage to the input summation, 19 of the corresponding direct or inverse component by the characteristic of the function ti ((k). In the considered example, this would be jjrCkg.). At the output of the adder 19, an estimate of the mathematical expectation is obtained, which is obtained by adding the decrypted component of the characteristic function with the number 2 and the component calculated from the zero Walsh function, i.e. h j (k).

2) Definition of the second multidimensional statistical momentum CECxjX-).

All units of the device are working. Single signals are pre-recorded in the first bits of registers 16 and 17. The indices i and j are set by applying pulses i + 1 from the driver 15 pulses and j + 1 from the driver 18 pulses, as a result of which in register 16 a binary number 2 is formed , and in register 17 - the number 2. These binary numbers are bitwise summed modulo two in the adder 14, forming the binary number 2 Ф 2. The generated binary numbers 2,2, 2 ® 2 j go to the corresponding inputs of the AND-NOT and AND elements groups 11, 12 and 13 to decrypt the component characteristics cal function with the same parameters of binary codes of Walsh functions. The decrypted components with the corresponding characters are fed to the inputs of the adder 19 of the respective groups, where they are summed from the components by the characteristic of the function calculated from the zero-Walsh function fed to the inputs of the n-th group to form the second statistical moment at the output of the adder 19.

Claims (1)

Claims. Device for determining the characteristic function of avt.ev. No. 1163340, Different 513 By the fact that, in order to expand the functionality due to the possibility of determining the moments, two pulse shapers, two shift registers, a modulo adder two, an adder, are entered into each jth (J 1,2 ,,.,) the channel has two groups of AND-NOT elements and a group of AND elements; in the JM channel, the bit outputs of the reversible counter and the memory block are connected respectively to the first and second inputs of the corresponding AND-NOT elements of the first and second groups and the corresponding AND elements of the group, the third inputs elements AND IS NOT the first group oedineny dnymi with respective discharge outlets of the first register, the third inputs of AND-NO elements are connected to the second group Compiled by, Orlov Editor M, Bandura Tehred V. Kadar Corr Podpi 3393/47 Circulation 672 VNIIPI USSR State Committee for inventions and discoveries 113035, Moscow, Zh-35, Raushsk nab, 4/5 Production and printing company, Uzhgorod, st. Project, 4 46 with the corresponding bit outputs of the second register, the third inputs of the AND elements of the group are connected to the corresponding bit outputs of the adder modulo two, the outputs of the AND-N elements of the first and second groups, and the outputs of the AND elements of the group are connected to the corresponding inputs of the j-th group of the adder the inputs of the pth adder group are connected to the corresponding bit outputs of the reversible channel counter, the outputs of the first and second pulse formers are connected to the shift resolution inputs of the same name registers, the outputs of which are. connected to the same inputs of the modulo two adder, the output of the adder is the output of the device's moment values. Proofreader G, Reshetnik Subscription