SU1273948A1 - Device for determining initial moments of random process - Google Patents

Abstract

The invention relates to a specialized computing technique and allows determining the starting points of a random process. The purpose of the invention is to increase the determination of the initial moments of a random process, which is achieved by the introduction of blocks for selecting the maximum number, averaging blocks, and scaling amplifiers. In the device, by using the operation of sequential extraction of the largest number from the input (investigated) and the number, the distribution density of which is uniform over a given interval, the I number is allocated, the distribution function is equal to the product of the distribution functions of the compared numbers, which is equivalent to averaging the averaged sequence the sequence obtained by power conversion of the random variable under investigation. 2 hp ff, (L 1 ill.

Description

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Claims (3)

4 00 The invention relates to a specialized computational technique that can be used in the determination of the moment-based statistical characteristics of random processes. The purpose of the invention is to increase the accuracy of determining the initial points of a random process. When a hardware study of a random process X is allowed, the finiteness of its distribution function CJ on the interval X is allowed. The offset of the process X under consideration by the value of X along the X axis: X X X X rno.yi1 m leads to the X process with the distribution function on the X interval .. .m. -chmivi x, x, o1. ; If in a sample of volume N (N-1) SL, tea values are independent and equally distributed on the interval, СХ. , 01, and N- the case under study is distributed by the law F (X) on the same interval, the distribution function F (X) F (X) F, (X) - (1 From here the Nth initial moment of the random process). - (Nl) (H - (-) pi X Vl (x) -IZ XX (, 4 |; li) .V. Ha drawing is a diagram of the proposed device The device contains averaging blocks 1, amplifiers 2, multi-input adders 3 , - 3j |,, inverters 4, max selection blocks 5, constant subtraction block, key 7, random signal generators 8, clock generator 9, delay elements 10, input 11, outputs of the initial moments, adder 13, from the first p to the third delay elements 14-16. The device works as follows: The implementation of the random process X under study from the input of 11 devices through the key 7, the opening pulse and, coming from the output of the clock generator 9 to the control input to 482 cha 7, is fed to the input of the subtraction block 6 of the constant, where the value X is chosen as the constant. From the output of block 6, the random sequence (by a random sequence with a random amplitude) with a distribution on the inter "X. ,, - x:; ,,, about comes to the shaft. To the first input of the maximum allocation unit 5, to the second input of which a uniformly distributed sequence synchronously with it arrives at the interval X ; 0 from the output of the generator 8 of a random signal, and with the arrival of a pulse from the output of the clock generator 9 to the clock input of the i-ro generator 8 (. A random signal at the output of the latter, a pulse is formed with a random (uniformly distributed over the X ... O} amplitude) From the output of the maximum selection block 5, where the selection of the largest of the two compared numbers of the two input sequences occurs:, i th, uniformly distributed on the interval fX. 0, X is removed. The distribution function F (X) (1 - - - :-) which pass through the inverter 4, goes to the third input of the multi-input adder, and the first input of the multi-input adder receives a signal from the output of block 6. From the output of the multi-input adder of the i-ro channel, a signal equivalent to the mean value) -,. (iimiiL) x-. passage through amplifier 2., where the gain is equal to (i + 2), is fed to the first input of the multi-input adder (i + l) -ro channel, the remaining inputs of which receive signals from the output amplifiers where the gain values are T (, 3, .. ., N-II, 4N). From the output of the multi-input adder i-ro channel signal, the passage through amplifier 2, -y, where the gain is equal to n4iiiniil-) J, averages i LO. in block 1, the averaging, from the output of which the value (i-H) of the th initial moment is taken. The values of the delays in the delay elements are chosen to be necessary for synchronizing the signals that have passed. through various blocks. Claim 1. A device for determining the N initial moments of a random process, comprising a random signal generator, a clock generator, an adder, characterized in that, in order to improve accuracy, the first, second and third delay elements are introduced into the device, amplifiers, averaging unit, constant reading unit , key, block of maximum, inverter and N-1 channels, the i-th (..., N-1) channel contains a random signal generator, delay element, maximum selection unit, inverter, multi-input adder, amplifier, block averaging first the second group of (i + I) amplifiers, the information input of the key is the device input, the output of the clock pulse generator is connected to the inputs of all random signal generators and to the control input of the key, the output of which is connected to the first input of the dedicated block nor the maximum, the output of which is connected to the first input of the maximum selection block of the first channel, the output of the maximum selection block of each channel except the last one, is connected to the first input of the maximum block of the next channel, the output The constant subtraction lock is connected to the first inputs of multi-input adders of all channels and through the first delay element to the first input of an adder, the output of which is connected to the input of the first amplifier, the output of which is connected to the second input: a multi-input adder of the first channel and through a chain of series-connected (i- 1). The amplifiers of the first group of the i-ro channel are connected to the second input of the multi-input sum-48 math of the i-ro channel, in each channel the output of the random signal generator is connected to the second input via a delay element the max selection location, the output of which through the inverter is connected to the third input of the multi-input adder, the output of which through the amplifier is connected to the input of the averaging unit, the outputs of the averaging blocks of all channels are the outputs of the (i + l) -x initial moments of the device, the output of the multi-input adder of each i- ro channel, except the last one, through a chain of successively connected ix amplifiers of the second group of its channel is connected to the JM inputs j (i + 3), ... (N-1) 3 multi-input adders of subsequent channels, the output of the random signal generator la through a second delay element coupled to the second input of the peak isolation unit, whose output is connected to the second input of the first channel and a maximum separation unit via series connected inverter and third ele--. delay ment - to the second input of the adder. 2. The device of claim 1, wherein each maximum end unit contains a comparator, a switch and two delay elements, the first and second inputs of the comparator being the same as the maximum allocation unit, respectively, which through the corresponding elements delays are connected to the same information inputs of the switch, the control input of which is connected to the comparator output, and the switch output is the output of the maximum allocation unit. 3. The device according to claim 1, about t l and each so that each i-th: multi-input adder contains an adder and i + 1 delay elements, with the output of each K-th delay element (, ..., i + l) is connected to the K-th input of the adder of the i-ro fflogovy adder, the input of the K-th delay element is the K-th input of the multi-pass adder, the output of the adder is the output of the multi-input adder.