RU2321053C1 - Serial-parallel device for processing signals - Google Patents

Abstract

FIELD: informational and measuring devices, possible use in computer engineering, systems for managing and processing signals.

SUBSTANCE: the device contains input realization storage register, control block, clock generator, block for generation of a matrix of coefficients, clock impulse counter, registers for storing a row of matrix, comparison register, multipliers, adders, storage registers, output realization storage register.

EFFECT: extraction of useful component under conditions of insufficient a priori information about statistical characteristics of additive noise and useful component function.

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Description

The present invention relates to information-measuring devices and can be used in computing, in control systems and signal processing.

.The proposed device is based on the presence of a single discrete implementation of the investigated process Y _i , Y ₂ , ..., Y _N , where Y _k = Y (t _k ),

.

A simplified mathematical model of the measurement results is presented in the form:

where S _k is a useful component; u _k is the additive noise component.

With respect to the random component, we also assume that Mu _k = 0, Du _k = σ ² and, moreover, its values at different instants of time are uncorrelated (i.e., cov (u _k , u _s ) = 0, k ≠ s) although these conditions are not essential.

The main problem to be solved is the selection of the useful component in conditions of insufficient a priori information about the statistical characteristics of additive noise and the function of the useful component.

принадлежит к известному классу функций и определяется конечным числом параметров, используются параметрические методы оценивания (сюда входят методы регрессионного анализа, основу которых составляет классическая теория наименьших квадратов). В тех же случаях, когда отсутствует информация о функции полезной составляющей, для оценивания полезной составляющей используются непараметрические методы, такие как сглаживание.A similar problem may arise: 1) in the operation of transceiver devices for long-distance or space communications; 2) in radio engineering when processing signals; 3) in digital image processing systems; 4) in meteorology and economics when processing measurement results. In cases where the useful component S _k ,

belongs to a well-known class of functions and is determined by a finite number of parameters, parametric estimation methods are used (this includes regression analysis methods, which are based on the classical theory of least squares). In those cases where there is no information about the function of the useful component, non-parametric methods, such as smoothing, are used to evaluate the useful component.

For the practical implementation of existing parametric and nonparametric processing methods, it is necessary to use high-performance digital devices (digital signal processors, programmable logic arrays) or hybrid processor circuits. In the simplest case, digital filters implement digital filters with a priori specified characteristics, since their construction is less resource-intensive and simpler than the implementation of adaptive digital filtering, approximation, or interpolation algorithm.

The known method of the moving average [Anderson T. Statistical analysis of time series. - M .: Mir, 1976. - 765 p.]. This is one of the easiest methods to smooth out measurement results. To use it, one implementation of Y ₁ , Y ₂ , ..., Y _{N of the} original process is sufficient.

, определение длины m отрезка ряда Y_k,

(или ширины «скользящего окна»), для которого производится вычисление среднего арифметического,

значений Y₁, Y₂, ..., Y_m, замену центрального из значений Y₁, Y₂, ..., Y_m найденным средним

, сдвиг «скользящего окна» на одно значение вправо (т.е. выбор вместо отрезка Y_k, Y_k+1, ..., Y_k+m-1 другого отрезка Y_k+1, Y_k+2, ..., Y_k+m), вычисление среднего арифметического выбранных значений реализации, и так до тех пор, пока не будет достигнут правый конец исходной дискретной реализации результатов измерений.For the initial discrete implementation of the measurement results, the smoothing interval m is determined, i.e. natural number m <N. The moving average method involves storing the initial discrete implementation of the measurement results Y _k ,

, Determining a number m of the segment length Y _k,

(or the width of the "sliding window") for which the arithmetic mean is calculated,

values of Y ₁ , Y ₂ , ..., Y _m , replacing the central of the values of Y ₁ , Y ₂ , ..., Y _{m by the} found average

, shift of the “sliding window” by one value to the right (i.e., instead of selecting the segment Y _k , Y _{k + 1} , ..., Y _{k + m-1,} another segment Y _{k + 1} , Y _{k + 2} , .. ., Y _{k + m} ), calculating the arithmetic mean of the selected implementation values, and so on, until the right end of the original discrete implementation of the measurement results is reached.

The width of the "window" is chosen odd, because the smoothed value is calculated for the central value. The expression for calculating the smoothed values of the initial discrete implementation of the measurement results is written in the form:

where p = (m-1) / 2 (m is an odd number).

Often, smoothing based on a moving average transforms the implementation of the measurement results, so that small but important parts for the analysis of the useful component (waves, bends, etc.) are not highlighted.

The features of the analog device, which coincide with the features of the claimed technical solution, are as follows: storing a discrete signal, highlighting time periods, finding the arithmetic mean of the signal that fell into the selected time periods, replacing the original discrete implementation of the measurement results with smoothed values.

The disadvantages of the known device is the following:

- the first p and last p values of the measurement results are not smoothed; this drawback is especially noticeable in the case when the volume of implementation of the measurement results is small, or if it is necessary to extrapolate beyond the considered time interval;

- the moving average method causes autocorrelation of residues, even if it was absent in the original useful component (Slutsky-Yul effect).

The reasons that impede the achievement of the required technical result are as follows:

- if the width of the “window” of smoothing is 2p + 1, then the first p and last p values of the initial implementation of the measurement results are not processed;

- since the central value of the “window” of smoothing is calculated as the arithmetic average of the neighboring ones, the values of the estimation of the useful component become dependent.

The structural diagram of a device that implements the considered method contains a pulse generator, a switch, a control unit, first and second registers, an adder whose output is connected to the information input of the first register, the output of which is connected to the first information input of the switch, the second input of which is the input of the device.

используется выражение:There is a method of weighted moving average [Economic and mathematical methods and applied models: Textbook for universities. / Ed. V.V. Fedosova. - M .: UNITI, 1999. - 399 pp.], Which differs from the simple sliding smoothing method in that the values of the initial discrete implementation of the measurement results included in the smoothing interval are summed with different weights. To calculate the score

expression is used:

where the weights p _{k are} determined using the least squares method.

For a weighted moving average, the disadvantage is the inability to smooth the values of the initial discrete implementation of the measurement results at the ends of the implementation. In addition, the use of this method without negative weights causes autocorrelation of residues, i.e. the Slutsky-Yule effect takes place.

A known method of least squares and a device for piecewise linear approximation [Bendat J., Piersol A. Applied analysis of random data: TRANS. from English - M .: Mir, 1989. - 540 p., Copyright certificate No. 1624479]. To use this method, one implementation of Y ₁ , Y ₂ , ..., Y _{N of the} original process is sufficient.

, минимизируя целевую функцию вида:The least squares method allows to obtain an estimate for the measurement results Y ₁ , Y ₂ , ..., Y _{N of the} original process,

minimizing the objective function of the form:

представляет собой полином первой степени

, коэффициенты а и b можно найти, минимизируя целевую функцию вида:In the case when

is a polynomial of the first degree

, the coefficients a and b can be found by minimizing the objective function of the form:

Differentiating expression (2) with respect to a and b and equating to zero, we obtain a system of linear equations:

The solution of the system is:

, сумма квадратов отклонений значений оценки от значений реализации измерений является минимальной (2).When evaluating

, the sum of the squares of the deviations of the evaluation values from the implementation values of the measurements is minimal (2).

The features of the analog device, which coincide with the features of the claimed technical solution, are as follows: storing a discrete signal, approximation by the least squares method, replacing the original discrete implementation of the measurement results with approximated values.

The disadvantages of this method is the following:

- when using this method requires a priori information about the function of the useful signal;

- the error of the useful component along the implementation, in the general case, is non-linear and reaches its maximum values at the boundaries of the approximation interval;

- with a non-polynomial model for estimating the useful component, a strict solution to the problem of minimizing the objective function of the least squares method does not always exist due to the nonlinearity of the system of equations being solved;

- limited method of least squares to parallelize and build a multi-channel processing system.

The reason that impedes the achievement of the required technical result is as follows:

- the effectiveness of the estimation of the useful component depends on the volume of sales, the statistical characteristics of the additive noise and the availability of a priori information about the functional dependence of the model of the useful component.

The block diagram of a device for piecewise linear approximation, contains a group of series-connected registers, first and second subtracters, an adder, first and second accumulative adders, delay elements, a clock, two multipliers and two dividers by a constant coefficient.

Closest to the invention is a method for highlighting a trend by multiplying estimates of its only initial implementation (ROSOTs) and a device for its implementation (patent No. 2207622, IPC 7 G06F 17/18).

The prototype device under consideration involves: 1) remembering the input implementation Y ₁ , Y ₂ , ..., Y _n ; 2) dividing the input implementation into sub-intervals by random numbers having a uniform distribution law; 3) checking the condition that the sub-intervals include at least L values of the original implementation, if the condition is not met, then random partition numbers are regenerated; 4) finding in each subinterval input implementation the coefficient estimates approximating polynomial and + bk + ck ² using the method of least squares; 5) repetition of the procedures described in paragraphs 2-4 K times; 6) finding the smoothing function as the arithmetic mean of “piecewise quadratic” approximating functions at each moment in time.

The disadvantages of the known prototype device are:

- the impossibility of implementing the known method Razots in real time;

- lack of practical recommendations on the choice of the number of partition intervals and the number of multiplication estimates;

- high computing costs.

The reason that impedes the achievement of the required technical result is as follows:

- to use the method of reproduction, it is necessary to remember the entire input implementation.

A device for highlighting a trend by the method of multiplying estimates of its only initial implementation (Razots) contains a block for storing measurement results, switches, a random number generator, a block for eliminating related values, a ranking block, a register for storing random numbers, approximation blocks, register for storing estimates, an arithmetic summing device , storage unit estimates useful component, a clock generator.

The essence of the proposed serial-parallel signal processing device is as follows. A simplified mathematical model of the input sequence of measurement results is presented in accordance with expression (1).

на m интервалов:The essence of the method of multiplying estimates is to multiply the estimates of the useful component by repeatedly dividing the original implementation into intervals of random length and estimating the useful component on them by approximating the linear or quadratic function by the least squares method. Partitions are formed by dividing the interval (1, N) by random numbers α _i ,

on m intervals:

- вариационный ряд случайных чисел, каждое из которых имеет равномерный закон распределения; значения α₀ и α_m - фиксированы (α₀=1; α_m=N).where Δ ₁ , Δ ₂ , ..., Δ _m are the lengths of the intervals of the partition,

- a variational series of random numbers, each of which has a uniform distribution law; the values of α ₀ and α _m are fixed (α ₀ = 1; α _m = N).

The main disadvantage of the method of multiplying estimates is the complexity of real-time processing and the large computational costs when implemented as a device.

In the General case, the assessment of the useful component can be represented as a convolution of the form:

:Expression (4) can be considered as the multiplication of a square matrix of weight coefficients of dimension N × N by an input column vector

:

The matrix of weights is a set of impulse responses that are a response to an input effect of the form:

In matrix form (5) is a unit matrix.

In order to find the impulse response of the method of multiplying estimates, it is necessary to determine the impulse response of a device implementing the least squares method.

, коэффициенты а и b находятся, минимизируя целевую функцию вида:In the case when the estimate of the useful component is defined as a polynomial of the first degree

, the coefficients a and b are found, minimizing the objective function of the form:

The expression for estimating the coefficients of the approximating polynomial is as follows:

Since the values of the discrete sequence of the source signal are obtained at equidistant time instants, then:

тогда

then

представляет собой единичную матрицу размерностью N×N, то отклик системы, реализующий метод наименьших квадратов имеет вид:If the original sequence

is a unit matrix of dimension N × N, then the response of the system that implements the least squares method has the form:

являются отсчетами линейной аппроксимирующей функции.Thus, if we substitute expression (6) into expression (4), then the values

are samples of a linear approximating function.

To obtain the impulse response of a device that implements the method of multiplying estimates, it is proposed to obtain the following matrix of coefficients for each set of partitions (reproduction):

- матрица размерности Δ_i×Δ_i, Δ_i - длина интервала разбиения,

- номер интервала разбиения, m - количество интервалов разбиений, t - номер размножения. Для каждого i-го интервала разбиения формируется импульсная характеристика

с помощью выражения (б):Where

- a matrix of dimension Δ _i × Δ _i , Δ _i is the length of the partition interval,

- partition interval number, m - number of partition intervals, t - breeding number. An impulse response is generated for each ith interval of the partition

using expression (b):

Since the intervals of the partition Δ _i have a random length, the matrix (7) is different for each set of partitions (3).

The resulting impulse response of the method of multiplying the estimates is determined by averaging the impulse responses obtained for each partition option.

The method of multiplying estimates allows you to parallelize the calculations and implement it in a serial-parallel processing system.

The serial-parallel signal processing device is an N-channel device, where N is the maximum size of the input implementation, and contains the storage register of the input implementation 1, which is the information input of the device, the output of which is connected to the first inputs of the multipliers 8.N, the outputs of which are connected to the first inputs adders 9.N, respectively, the output of each of which is connected to the Nth input of the storage register of the output implementation 11 and the inputs of the storage registers 10.N, the outputs of which are connected to the second inputs of the adders 9.N; the output of the control unit 2 is connected to the input of the unit for generating the matrix of coefficients 4, the output of which (1, 2, ..., N) is connected to the inputs of the storage registers of the row of the matrix 6.N, the outputs of which are connected to the second inputs of the multipliers 8.N; the output of the clock counter 5 is connected to the input of the comparison register 7, the output of which is connected to the input of the clock counter 5 and the enable input of the storage register of the output implementation 11, the output of which is the information output of the device, the synchronism of the operation of the device is set by the clock generator 3.

Serial-parallel signal processing device is implemented as follows. The values of the input implementation go to the input of the device and are recorded in the storage register of the input implementation. In the block for generating the matrix of coefficients, an impulse response matrix is formed, where each row of this matrix is a response to a single input effect. The parameters of the method of multiplication of estimates are set by the control unit. Each row of the matrix of coefficients is written line by line in the corresponding register of storage of the row of the matrix. To calculate the convolution (4) in the multipliers, each row of the coefficient matrix is multiplied by a row of the input implementation. Using cyclic adders, the resulting sum of multiplying all values of the row of coefficients by the results of the input implementation is found. The result is sequentially written to the storage register of the output implementation and is output to the device.

Serial-parallel signal processing device operates as follows. The values of the input implementation are recorded in the storage register of the input implementation 1, size N. In the control unit 2, the parameters of the method of multiplying the estimates are set, based on which the impulse response matrix is formed in the coefficient matrix generation unit 4. Each row of the matrix of coefficients from the block forming the matrix of coefficients 4 is recorded in the storage registers of the row of the matrix 6.N. Using the 8.N multipliers, the values from the storage register of the input implementation 1 are multiplied by the values stored in the storage registers of the row of the matrix 6.N. The result of the multiplication is transmitted to the inputs of the adders 9.N. Using the adders 9.N and the storage registers 10.N, the sum of all the results of N multiplications of the values of the input implementation stored in the storage register of the input implementation 1 is calculated by the value of the coefficients stored in the storage registers of the rows of the matrix 6.N. The result is transmitted to the input of the storage register of the output implementation 11. The counter of clock pulses 5 carries out the count of the clock pulses of the clock generator 3. The result of the count of the clock pulses is compared using the comparison register 7 with the value N + 3, if equal, the enable pulse is transmitted to the enable input to the register storing the output implementation 11 and the clock counter 5 is reset. The device is synchronized by the clock 3.

Claims (1)

A serial-parallel signal processing device, containing the input implementation storage register, the input of which is the information input of the device, the output implementation storage register, the output of which is the information output of the device, characterized in that the output of the input implementation storage register is connected to the first inputs of the multipliers, the outputs of which are connected to the first inputs of the adders, the output of each of which is connected to the Nth input of the storage register of the output implementation and the inputs of the storage registers, passages which are connected to the second input of the adder; the output of the control unit is connected to the input of the coefficient matrix forming unit, the outputs of which are connected to the inputs of the matrix row storage registers, the outputs of which are connected to the second inputs of the multipliers; the output of the clock counter is connected to the input of the comparison register, the output of which is connected to the input of the clock counter and the enable input of the storage register of the output implementation, the output of which is the information output of the device, the synchronism of the device is set by the clock.