SU1709291A1 - Device for generating matched systems of discrete basal functions - Google Patents

Abstract

The invention relates to the field of automation of computer technology and can be used in the spectral analysis of signals. The purpose of the invention is to expand the functionality of the generator by forming 2M ^ systems of discrete basis functions consistent with an arbitrary waveform. The generator contains a block 1 of forming 2M systems of discrete basis functions, an n-bit counter 2 (N = 2 "is the dimension of the generated systems of functions. M = 2 ^ r is an arbitrary integer), (N / 2) is an unequal shift register 3, adder 4 modulo M / 2. The coordination of the system of basic functions with an arbitrary waveform is achieved by inserting additional blocks into the generator: counter, shift register, modulo adder M / 2. 3 or FP G Invention relates to the field of automation and computer technology and can be used with spectral analysis e signals. The purpose of the invention is to expand the functionality of the generator by forming 2M systems of discrete basis functions consistent with an arbitrary waveform signal. Fig. 1 shows a functional diagram of the generator for N = 8; Fig. 2 shows timing diagrams explaining its operation; in Fig. 3 — the system of functions formed by the proposed generator. The generator comprises a block 1 of a form-2 of 2M systems of discrete basis functions, an n-bit counter 2, N / 2-bit register-shift 3, an adder 4 mod by М / 2, first input 5 task system we have functions, input 6 clock pulses, second input 7 of setting the system of functions, output 8 of the number of the generated function, output 9 of the end of the period of the generated function, functional output 10. Voltage patterns (Fig. 2, 1-12) refer to the following items: input 6 - FIG. 2-1; output 9 - FIG. 2-2; the output of the third bit of counter 2 — FIG. 2-3; the bit inputs of the first operand of the adder 4 — respectively, FIG. 2-4,5,6; the bit inputs ^ of the second operand 4, respectively, FIG. 2-7,8.9; generator bits 10, respectively, FIG. 2-10, 11.12. The generator implements a method of forming 2M systems of discrete basis functions, coordinated with an arbitrary signal. In order to clarify the essence of such a method, we consider iterative co-V4.

Description

relation, with which you can form a system of basis functions of dimension 2 d (2 9 (2..,), d ((yes, A А (2h-) where 9 () ,. g () 2 different orthogonal matrices, elements which are the values of the function exp (-g D) W /, M 2 - the number of values of the function exp (j-jTT-D j in the interval (0.2 J, r-arbitrary integer number A 6 (0, M / 2-1 ), A (211-1-vector multiplier of the elements W, X is the operation of the scalar (element-wise) product of the vectors of matrices) FROM the vectorA (2pch). Matrices d (2 "-) can be formed, for example, by setting N / 2-x the famous G A - A, where A {a |}. 1 O, N / 2-1, ai ± WN. 3 giving the N / 2-x value; the research institute forming the function Gi with the vector A means approximating the 1/2 period of an arbitrary signal S (t) (with any desired accuracy by selecting the corresponding parameters M and / (. Approximating the second half of this signal and building the system of functions matched to it (the signal is an eigenfunction of the system being tendered) is carried out by noj; 6opoM elements of the vector multiplier A / jn-i) in (1). For example, we construct a system of functions matched with the signal S (A T) given by its samples S (AT) (-1; 0.707; -one; 0; -one; -0.707; -0.707; 0.707). 1. Having defined the generator Gi A - A -WB We - We We We We - Wef where M 8, W8 1; W8 0.707+ jO.707; W8 j; Ws -0.707 + 0.707), build the matrix -W -W -W - W ° -W ° -W ° -W tll o d / 2 n / 0, lnO, i, 2 W -W w W -ww -ww - w ° -wwww -W -w ° w -www ° -w -NA / ° W ° -W w -W w -w ° wwwww -W -w -W -w .w -w ° w ° -W -ww ° -w ° - w ° www -w ° w The left submatrices (2) are matrices. 2. Define the vector A () V-t -w ° -w2-w w3. 3. form the system d (2) according to (1) When forming matrices (2) and (3), the operations of multiplying the powers of WM are reduced to elementary operations on the codes of the exponents (5 and signs (S) degrees ...; ... W, 5 (Si Φ S2) ® p - WM, where Si, 82 are the signs of the powers of WM and WM; Go, e (if the sign of the degree is positive, if the sign of the degree is negative; p is the transfer formed during the operation of addition degrees in (4): (0. if the selection of a whole M / 2 proP) has elapsed an even number of times, I 1, if the selection of a whole M / 2 proI has elapsed an odd number of times. The generator works as follows. the coded values of the vector A -W ° W - W ° W are fed to the input 5 of the task of the system of functions, to the input 7 of the generator the coded values of the vector A are fed (2л-1 fW ° - W - W W. The block 1 forms (in cycles 0-7) Fig. 2-4.5,6) intermediate system of basic functions (2) and the pulse of the end of the period of the generated function (Fig. 2-2), which goes to the output 9 of the generator and to the reset input (set to O on the falling edge of this pulse) counter 2. Counter 2 counts the clock pulses arriving at its input (FIG. 2-.1) and forms the N / 2-clock interval (FIG. 2-3). which controls the operation of shift register 3 according to the following algorithm: on the leading edge of clock pulses 5. 6, 7, O (if there are 3 signal 1 values at the control input of the control), the information recorded in the register in previous clocks is shifted and outputted to the output of the last bit group (Fig. 2-7,8,9) during the 4, 5, 6, 7 cycles; on the leading edge of the clock pulses 1, 2, 3, 4 (if there is a register of assignment O on the control input), the register is written to the information on the parallel input and the information output to the register output is blocked during the O, 1, 2, 3 cycles. Thus, the values of the functions of block 1 are passed to the output of the adder 4 and then to the output 10 of the generator without changing during the cycles O, 1, 2, 3, and in the cycles 4, 5, b. 7, elementwise trans. arriving at both inputs of the adder 4 vectors (unlocking the output of the shift register 3). FIG. 3. The system of basic functions is provided, which is formed by the proposed generator, which is matched with the signal S (Д Т) (-1; 0.707; -1; 0; -1; -0.707; -0.707; 0.707).

Claims (1)

Claims of the Matched Systems Generator diskHMx basic functions containing a block forming 2M systems of discrete basic functions (M 2 N 2 the dimension of the system of functions, r n - integers), the information input of which is the input of the first vector set by the system of functions of the generator, clock input, output the function numbers and the output of the period end of the function of the block forming 2M systems of discrete basis functions are respectively the clock input, the output of the function number and the output of the end of the period of the function of the generator, differing it. what. in order to expand the functionality of the generator by forming 2M discrete systems of basic functions that are matched with an arbitrary waveform, it contains an n-bit counter. (Y / 2) -discharge shift register and modulo M / 2 adder, moreover, the output of the period end of the function block of the 2M system of discrete basis functions is connected to the installation input of the n-bit counter, the output of the n-th (senior) bit of the n-bit counter is connected to the control input of the (L / 2) -digit register the shift, the parallel information input (N / 2) -pa3r of the common shift register is the input of the second vector of the function system set generator, information output of the block forming discrete basis functions and serial output (M / 2) -discharge shift register connected to the inputs of the modulo M / 2. the output of the modulator M / 2 is the functional output of the generator, the counting input of the n-bit counter and the clock input (M / 2) -discharge shift register are connected to the clock input generator. fe / 7 About i Z b. H S -6 4 five . " e f s 10 C iS g, -.- y / o -V (7-W ° -W ° W W W -SPL (y) yO J -y / o ld / W o 3 J  J  ji / ° -W -W W W (S w. W - w w  .. ,, I “,,, glX C NX / D -.t .. (,, W ° W --- 0 (7 ° -W