SU940169A2 - Function generator - Google Patents

Description

(B) FUNCTIONAL TRANSFORMER

one

The invention relates to automation and computing and can be used, in particular, in devices intended for piecewise quadratic approximation of arbitrary functions, and is an improvement of the known functional converter.

According to the main author. St. No. 879603, a functional converter is known comprising two groups of keys, an inverter, a shift register, a group of VI integrators (where n + 1 is the number of members of a number of approximating functions) and a group of basic analog blocks of weighted summation, each of which is connected by inputs to the outputs of integrators, each i-th (liS) key of the first group of keys is connected by a signal input to the input bus of selected values of the input signal and to the input of the inverter, and the output is connected to the input

i-ro integrator, each i-th key of the second group of keys is connected by a signal input to the inverter output, and the output is connected to the input (-f1) -ro of the integrator, and the shift register is connected to the IWS bus of clock pulses, and the output of each -th bit - with control inputs of 1 keys of the first and second groups of keys Ci.

A disadvantage of the known device is the reduced accuracy of the functional transformation due to the piecewise linear nature of the function approximation.

The purpose of the invention is to increase the languor of the functional transformation. .

This goal is achieved by the fact that a group of m additional is introduced into the functional converter. Weighted analog blocks of weighted summation (where m is the number of simultaneously formed values of the or39 0169 dinat functions), each of which is connected by inputs to the outputs of the main analog blocks of weighted summation, and the output to the corresponding output of the functional one. converter The drawing shows a block diagram of a functional converter for the case of n-m-. The converter contains the first and second groups 1 and 2 keys, inverter 3, shift register k, a group of n integrators 5 (where fc-1 is the number of code members approximating functions), a group of basic analog blocks 6 weighted summation and a group of m additional analog blocks 7 weighted summation (where m is the number of simultaneously generated values of the ordinates of the function), Each of the additional blocks 7 is connected by inputs to the outputs of the main blocks 6 of the weighted summation, and the output is connected to the corresponding output converter. Each of the main blocks 6 is connected by inputs to the outputs of integrators 5 “Each i-and (1 i € n) key 1 of the first group of keys is connected by a si-nal input to the bus 8 input of selective values of the input signal and the input of the inverter 3, and output. the input of the 1st integrator 5. Each I-and key 2 of the second group of keys is connected by a signal input to the output of inverter 3, and the output is connected to the input (if f1) -ro of the integrate 5. The shift register k is connected by an input to the E input bus of clock pulses, and the output of each 1st bit is with the control inputs ix of keys 1 and 2 of the first and second groups of keys whose. The analog blocks 6 and 7 of the weighted summation can be implemented, for example, on operational amplifiers with weighting resistors. The proposed functional converter implements a piecewise quadratic representation of the input signal instead of the piecewise linear one used in the known. The decomposition of the signal f (t) using piecewise linear Walsh basis functions can be represented as f (t) .pci, t ;, (1) where P (i, t) are the integral Walsh functions, which are defined as five . fu “o in 5 gd ku qi for Rk Ma from Citi, i) -IwAHi) (, | (2), 1,2, ...; P (0, t) 1; W.t) are the Walsh functions; T is the interval of the given argument t. cut quadratic basic rations of P (i + 2, t) are obtained by grinding P (i + l, t) + 2.4.) - cJpti4i, i) dr, (3) o C is a constant of P (0 , t) - f; p, t) p (i, t) signal decomposition with the help of square-quadratic basis functions PJ C-H, t) can be represented by Si) -., PKti, t). the transformation Atrix P, (1 + 2, t) I 8 8 has the form 4 9 16 25 36 TsE 6 16 23 28 31 32 О 8 9 12 15 72в 0121 О -1 -2 -1 321 1 5 6 J itza (5 can be represented as the extension of two matrices, (6) V / is the Walsh transformation matrix.) the elements of the upper triangular matrix are defined as follows;

ci

o (a.

 ЯZ

The inverse matrix Z will have

View Z is an nmzhe-triangular matrix, the elements of the main diagonal are equal to one, the first subdiagonal is -3, the second is 1, the third is 4, the fourth is 4, and so on. In the matrix form, the equation () is written in the form of a 5-cX / row vector of an approximated function, the row vector of the coefficient of expansion in piecewise quadratic basis functions P. -tp -R - K At the same time, from (b) P; - Then, substitution ((} and (S) in C8) with regard to transportation (6), (we get -h; j-. X is a vector- column of a given discrete sequence f (t). Thus, to obtain an approximated value of a function at any time, it is necessary to compute the decomposition coefficients by transformation and multiply the coefficients by the matrix Z. At the same time, 1 can be represented as the product of two matrices гг. )

-one

is a matrix

the deg elements of which on the main diagonal are equal to 1 and on the first subdiagonal are equal to -1;

-f

7. “the lower triangular matrix, whose elements on the main diagonal are 1, on the first subdiagonal is -2, on the second 2,

to

15

 -g 1

Claims (2)

, - lV, Za, X. The converter works in a consistent manner. Inu 8 with a clock frequency enters the process X (t), which, depending on the type of matrix 1, goes directly to the signal inputs of keys 1 or, in an inverted form, to the signal inputs of keys 2. The operation of keys t and 2 controls the shift register, the outputs of which are depending on the type of matrix 2, they are connected to the control inputs of the corresponding keys 1 and 2. After arriving from the bus 9 to the input of the register C p pulses, the output of the integrators 5 generates conversion coefficients i that are summed in blocks 6 in accordance with the weight the values of rows of matrix 2 (zero weights in the matrix correspond to infinitely large values of the weight resistors, i.e. disconnecting the corresponding inputs of blocks 6), with the result that the outputs of the main blocks 6 of weighted summation will have voltages proportional to the expansion coefficients. These voltages are fed to the inputs of additional blocks of 7 weighted summation, which are used to multiply the coefficients of the columns of the matrix Z and summation .. i To obtain intermediate values, fno relative to the input sample (TaM) of the approximated function, you need a smart line vector of coefficients Shu on Z, Dl 1111 1 1-1-1 Z - V (/ PK (1-1-1 1 1-1 1-1 1i Э162536 96 4 1i 91623283132 1it787 1 0 1 4789121516 1Л123 567 001Л1 00001Л1 2 3 0000 0 .0 l / i 1 where PK (upper half of the matrix, t) is long. In this case, it is necessary to double the number of additional blocks 7 and choose write weight resistors in these blocks in accordance with matrix columns 2. Thus, the proposed functional converter, in relation to the well-known one, allows realizing a piecewise quadratic approximation, which increases the accuracy of the functional transformation. Claims of the invention Functional converter according to the author. St. If 879603, which is based on the fact that, in order to increase the accuracy of functional development, a group of additional analog blocks of weighted summation wi is entered into it (where m is the number of simultaneously generated values of the ordinates of functions, each of which are connected by inputs to the outputs of the main analog blocks of weighted summing, and output to the corresponding output of the functional converter. Sources of information taken into account during the examination 1. USSR author's certificate No. 879603, class G 06 F 15/332, G About G 7/36, 10.0 3.80.