SU1599850A1 - Generator of basic function systems - Google Patents

Abstract

The invention relates to automation and computing and can be used, for example, for the spectral analysis of signals when they are decomposed into formed systems of basic functions. The purpose of the invention is the extension of the class of tasks to be solved due to the possibility of forming the class ⋄ = T ^{N / 2} systems of complex basic functions taking T values, the class ⋄ = T ^{N / 2} systems of real basic functions, and the class = 2 ^. T ^{N / 2} systems of real basic functions. The generator contains N-bit pulse counters 1.6, And 2, N matrix matrix shift registers 3,4,5, N 7 HE elements, N bus repeaters 8 with gating, N direct-to-additional converters 9, N two-input ( M + 1) -display bus switches 10, N-input adder 11, code converters 13,15,16, shaper 17 N time gates, detector 12 near standing units, two-input N-bit bus switch 14, N / 2 information inputs, N-bit input of setting the number of the generated function, N-bit output of the number code of the generated function and a control input, a clock input, functional output synchronization output. The goal is achieved by introducing an AND 2, N-matrix registers 3,4,5 shift, (N-1) elements NOT 7, N bus repeaters with gating, N converters 9 direct code to an additional, two-input N-bit bus switch 14, detector of 12 near standing units, code converters 13,15,16, driver 17 N time gates. 7 il.

Description

The invention relates to automation and computing and can be used, for example, for spectral analysis, signals, information transmission systems, etc.

The purpose of the invention is the extension of the DA of the class of tasks to be solved due to the possibility of forming the class T of systems of complex basic functions,

class systems of valid

- orpN / g

basis functions, class r 2T, sie-, those real basis functions. The generator of systems of basic functions forms the class T of systems of complex basic functions that take T values (the values of the basis Q functions T are determined from the condition

sampling function e where

eO, T / 2-T), by specifying N / 2 samples of the generator function G, class dz of systems of real basic functions, the values of which are determined by the algebraic addition of the values of the real and imaginary components of each complex basis functions, .Q and the class of systems of real basic functions formed by decomposing each complex system of basic functions into two systems of real basic functions.

, Plan the essence of the basic functions implemented by the generator of systems of the method of forming systems of discrete basic functions

55

system of discrete exponential functions (DEF) for

System (2) has the symmetry property with respect to the generator functions 64.64 and

G (2, p) (G (0, p) a (2, p)) mod T / 2;

G (2, p) G (1, (2 p) tnort N);

G (4, p) (G (0, p) -G (4, p)) T / 2;

G (4, p) (G (1, p) .G (3, p)) niod T / 2;

G (4, p) G (1, (4-p) r.od N);

G (8, p) (G (0, p) -G (8, p)) mod T / 2; (3)

G (8, p) (G (1, p) -G (7, p)) mod T / 2;

G (8, p) (G (2, p) -G (6, p)) mod T / 2;

G (8, p) (G (3, p) -G (5, p)) mod T / 2;

G (8, p) G (1, (8 "p) raod N);

where p is the reference number of the function,, N-1;

() niod T / 2 - addition operation

mod T / 2 over signed binary numbers (the coded values of the exponents of Grades D and the sign of the degree W),

when executed, the input data

D (K, S), where S is the data size, is converted to output as follows:

F (1, S) (a3 (K, S)) mod T / 2, (4)

14

where, t + 1, in which a significant part of the result (deduction modulo T / 2)

determined by bits, t,.

F (1, x) (a) (K, xWd T / 2,

v

(five)

sign of the result - bit F (1, m + 1) (5.D (K, m + 1)) mod2 ® p, (6)

e p is the transfer from the significant part to the sign bit formed during the execution of the operation (5), O, if the selection of the whole T / 2 has occurred an even number of times.

(7)

R

1, if the selection of an integer T / 2 occurred an odd number of times. The symmetry property (3) can be used to define an arbitrary system of discrete basis functions in accordance with the expression

c. (n (K) .p). (enti2; -2) ffi4., - s, t / 2,

(about)

(7)

where, loBgN; , G (0, p)

G (N, p) l 1 1. .. l; G (1, p) | A-Ajf,,, L72-1, D eo, T / 2-1.

Thus, for a selected T and a given N, in accordance with (8), it is possible to determine a set of systems i discrete basis functions uniquely determined by enumerating all possible values of W at the first N / 2 positions of the system-forming function G ,. For example, for and A W W ° W ° W J, we obtain the system of functions WOL1; 1A-PELI; for and A is the system of functions (2), in which the forming

About i

C, W W

w, w - -w -w -w

five

98506

Systems of basic functions, formed in accordance with (8), have the following properties:

1.Systems of functions are orthonormal,

2. The function systems are complete.

3. Complex systems of functions can be decomposed into two adjoint

Q: subsystems of complex functions, each of which forms a complete orthonormal system of N real basis functions.

A. Complex systems of functions

15 are transformed into systems of real basis functions by algebraically adding the values of the real and imaginary components of each complex function.

5., Tl systems of functions the ratio is true

20

(С, (R + С „(11)

((P

25

where Su | {,, - is, respectively, the real and imaginary components of the nth complex signal transform coefficient for a given system of basis functions.

FIG. 1 shows a functional diagram of the generator of basic systems

,

 The functions for FIG. 2 - times

Diagrams explaining the operation of the generator of systems of basis functions in the formation of basis functions G, G and GY of a system of basis functions determined by the vector A m and 1 1 W J; Fig. 3 shows the functional scheme of the detector (two or more) of a number of standing units in the binary data code; in fig. 4 - the same, the driver of the time gate in FIG. 5 - the same as the first code converter; in fig. 6 - the same, the second converter codes; FIG. 7 is the same as the third code converter.

45 „

Basic function systems generator

for the case (FIGS. 1-1) contains a n-bit counter of 1 pulses, an element of And 2, a matrix shift register 3

50 with parallel parallel inputs for receiving information, matrix register 4 shift with two parallel inputs for receiving information, matrix register 5 shift with one parallel input

55 receiving information, p-razdnv; counter 6 pulses, p. of elements NOT 7, bus repeater 8 with gating, p converters. 9th direct code in additional, n two-way

1599850

(m + l) -disc bus switches 10, p-input cc 1ator 11, detector 12 near standing units, 13 codes converter, two-input n-razor Bus switches 14, 15 codes converter, 16 codes converter, shaper 17 n time gates, information inputs A (0, h), A (1, s), - A (2, s), A (3.8), input of clock pulses TI, task input

the numbers of the generated function Bj, the control input V, the function output F,

ten

15

output Nj code of the number of the generated function; exit C sync.

The voltage plots (fig. 2 a-p) are shown in: (a) the input of clock pulses TI; (b) the output of the element 2; (c) the output of the low-order bit of the first matrix register 3 shift; (d) the output of the high bit of the first matrix register 3 shift; Cd) the output of the lower order bit of the second matrix register 4 shift; (e ) the output of the high bit of the second matrix register 4 shift; 25 (g) low-order output of the third matrix shift register 5; (h) the output of the most significant bit of the third matrix register; 5 (6); (and) the first output of the driver 17 n time, Q gates; (k) the second exit of the former 17 p. temporary gates; SL) the third output of the driver 17 n time gates; CM) the output of the first bit of the third converter 16 codes; (m) the output of the second on the discharge of the third converter 16 codes; (o) output of the third bit of the third transducer of 16 codes; Cn) output of the lower bit of the functional output; (p) output of the higher bit of the functional output F — for example, the formation of functions 0 {, Oz and Gt7 input and1tnh with icTe complex baseline functions corresponding to the WJ vector for and. The transformation matrix for this case, formed in accordance with (8), has the form

until yes that

we are not ros st qi

pnaro obva 20 forra up ni pr ing him mi in

IL SD El

(f by mi

op ich 3 ra woo n h

with with

40

45

S8

Where

i.

eight

0

five

5, Q

The detector circuit (two or more) of the number of standing units in the binary data code (Fig. 3) is implemented by elements 2I, (p-ORIL.

A driver circuit for 17 p time gates for (FIG. 4) is implemented by a binary decoder and a set of logic elements for combining the outputs of the decoder in accordance with the compression determining the function of the driver.

Data from converter D of 13 codes (Fig. 5) receives data from a six-pulse pulse counter, and to the control input receives data from the driver 17 n time gates. The converter converts the input data D in the specified 0 format (the number of convertible bits is determined by the control signal code) from the direct code to the additional one. The OR-NOT elements in the converter circuit perform the function of inverting the signal and permitting its transmission, the adder SM sums up the unit to the result of the inversion operation.

The code converter circuit 15 (Fig. 6) performs the convolution function on the OR of two binary sequences shifted by 1 bit, and is implemented by the elements of 2Sh1I.

The 16-converter circuit, (Fig. 7), performs the function of convolution mod2 of bits of a binary sequence and is realized by two-input modulo 2 elements.

The p-input adder, which performs the modulo T / 2 addition operation on binary numbers with a sign for and, consists of a half-adder for raod2, which forms the significant part of the result in accordance with (5) and the transfer in accordance with (7), and the adder with mod2, which forms the sign part of the result in accordance with (6).

We encode the values of the basis functions in (9) as follows: 00 W 01,, -w 1l2 and feed the vector 00 01 Ol3 formed in this form to the information inputs AfS.sJ, A (2, s), A (1, s), respectively. , А (0, s), (, 2) generator of systems of basic functions.

The generator of systems of basic functions works as follows.

The 3-bit counter of 1 pulses counts incoming 40 at its input

45

91599850

TI pulses (Fig. 2-a) and such

ten

forms an interval. that determines the duration of the period of the generated function G.y ,. A three-time - ordinary pulse counter 6 counts the pulses overflowing the pulse counter 1, generated by an AND 2 element (fig. 2-6), arriving at its input, and

From the outputs of the converters, the 9 values of the generator functions in the additional code arrive at the second inputs of the two-input bus switches 10, from the outputs of which are direct (the signal at the control input of the two-input bus switches is 1) or in the additional (otherwise) code

forms at its outputs a parallel- | Q, they arrive at the inputs of the p-input

code of the number of the generated function N j. At the beginning of each period T, on the trailing edge of the pulses N-1, and in this case 7, the status of information inputs is polled - f5 A (0, s) .A (3, s) of the generator of basic function systems, which is fixed in the shift matrix registers 3-5, and the registers switch (according to the recording control signal 20 (FIG. 2-6) at the control inputs V of the shift registers) to the shift mode of the information recorded in them, forming on the parallel outputs Q (3, s), Q (1, s) and Q (0, s), respectively, codes 25 form the functions C ((Fig. 2c, d), G (Lig. 2d, e) and d, (Fig. 2 Well, h). With parallel in the outputs of the matrix registers 3-5 shift the higher bits () are fed to the inputs of elements JQ NOT 7 and from their outputs to the inputs of the higher bits of the inputs of the sequential reception of information I) of each matrix shift register. The inputs of the least significant bits () of the inputs of the successive reception of information of each matrix shift register information from the outputs of the lower bits enter without change. Simultaneously signals

adder 11 performing an addition modulo t / 2 operation on them. Depending on which code receives the values of the generating functions at the inputs of the adder 11, they are either summed up (the function values are sent to a specific code of the adder in the direct code), or they are subtracted (the function values are given in the additional code), which is equivalent to either multiplying degrees with the same bases W, or dividing them according to (8). From the output of the p-input adder 11, the codes of the values of the generated function, P f, are fed to the functional output F of the generator of systems of basic functions. In this way, a given system of basic functions is periodically formed. To set the mode of periodic repetition of a given function from the formed system of basic functions, the control input V of the generator of systems of basic functions is transferred to state 1 and in this case the set code of the function number from the output BJ is transmitted to the internal potential triggers of the n-bit counter 6 pulses and generator systems The bass parallel outputs Q (p, S) of each up to each function periodically forms

matrix shift register is fed to the inputs of the corresponding bus repeater; gating sensors 8, where an operation is performed on them, is equivalent to raising to degree 1 (dZ signals are passed without changing, provided that 1 signal is equal at the gate input) or O (prohibit the passage) and then to the first inputs n a two-input function. The outputs of the code of the number of the generated function Nj and the output of the synchronization are intended to synchronize the proposed generator of systems of basic functions when working with external devices.

Claims (2)

Claims of the Invention System Generator. output bus switches 10 and the inputs JQ contain two n-bit counters 9 direct code to additional converters, where the direct code of the values of their functions is converted into an additional one in accordance with the expansion where is the inversion operation of the input data bits. pulses (, 2N, where N is the number of basis functions in the system being formed), the element is NOT, and n is the two-input (t + 1) -discharge bus switches. 55 (t is the number of bits in the binary representation of the number T / 2-1, where T is the value of the basic FUNCTIONS, determined from Ijv -jsloviskekostizatsii functions e, ten From the outputs of the converters, the 9 values of the generator functions in the additional code arrive at the second inputs of the two-input bus switches 10, from the outputs of which are direct (the signal at the control input of the two-input bus switches is 1) or in the additional (otherwise) code they arrive at the inputs of the p input adder 11 performing an add modulo T / operation on them 2. Depending on the code in which the values of the generating functions arrive at the inputs of the adder 11, they are either summed up (the function values are sent to the specific code of the adder in the forward code) or they are subtracted (the function values are given in the additional code ), which is equivalent to either multiplying degrees with the same bases W, or dividing them in accordance with (8). From the output of the p-input adder 11, the codes of the values of the generated function, P f, are fed to the functional output F of the generator of systems of basic functions. In this way, a given system of basic functions is periodically formed. To set the mode of periodic repetition of a given function from the formed system of basic functions, the control input V of the generator of systems of basic functions is transferred to state 1 and in this case the set code of the function number from the output BJ is transmitted to the internal potential triggers of the n-bit counter 6 pulses and generator systems basic functions periodically forms required function. The outputs of the code of the number of the generated function Nj and the output of the synchronization are intended to synchronize the proposed generator of systems of basic functions when working with external devices. Claims of the Invention System Generator. Contains two n-bit counters Contains two n-bit counters pulses (, 2N, where N is the number of basis functions in the system being formed), the element is NOT, n is the two-input (t + 1) -disc bus switches. (t is the number of bits in the binary representation of the number T / 2-1, where T is the values of the basic FUNCTIONS, determined from Ijv -jsloviskekostizatsii functions e, where h 0, T / 2-1), n-input adder, wherein the code-n-input adder is connected to the generator output, characterized in that, in order to expand the class of tasks to be solved by allowing the formation of a class-T system of complex basis functions of class the control input of which is connected, to the detector output of a number of standing units, the output of the two-input n-bit bus switch is connected to the second information input of the second code converter, the outputs of the bits from the first to the nth are connected respectively to the control inputs (, N / 2 .. systems of actual basic Q from the first to the fifth tire repeaters function and class 2T. systems of real basic functions, the element I, n matrix matrix shift registers, the (n-1) -th element NOT, with gating, the outputs of the second converter codes from the first to (n + 1) -th are connected to the input of the third converter of the codes, the outputs of the fault repeaters from the gates 15 from the first to the nth of which are connected, n converters of the direct code In an additional, two-input p-razdnyy.shiny switch, a detector of a number of standing units, three code converters, shaper n time-20 to the current inputs of the n-input adder. control inputs, respectively, from the first to the nth two-input (go + 1) -size bus switches, whose elevations are connected to the corresponding gates, and the counting input of the first n-bit pulse counter and the synchronous inputs of the n shift matrix registers are connected to the clock input of the generator, the output of the first p-time-25 rd pulse counter is connected to the input of the element I, the output of which is connected to the output of the synchronization of the generator, to the inputs for controlling the recording of n matrix shift registers and counting JQ NOMU input of the second p- A pulse counter counter whose recording control input is connected to the generator control input, an n-bit input setting the number of the generated function jj of which is connected to the parallel receive input of the second n-bit pulse counter, the output of which is connected to the detector one hundred units, the data input to the first code converter, the first information input of the two-input n-bit bus switch, the input of the driver n time information information inputs A (i, s) of the generator to the inputs of the parallel reception of information D (l., s) of the k-th matrix shift register A (i, s) -D (l, s) j, where i is the generator input, 2 i is ,, i to O, N / 2-1, 1 - input of parallel reception of information of matrix shift registers,,, S - data width s-1, ra + 1; , n, pth parallel output Q (pjS) of the k-ro matrix shift register (. -1, р еO, N / 2 -1) is connected to the data inputs of the corresponding bus repeater with gating, the outputs of which are connected to the inputs of the corresponding inverters of the second and second information inputs of the corresponding two-input (t + 1) -disk bus switches, the second information inputs of which are connected to the outputs of the corresponding direct code-to-additional converters, bits (, ha) of the serial input the output of the code of the number of generated information receiving 45 of the k-ro matrix generator refunction, the output of the driver n time gates is connected to the first information input of the second code converter and the control input of the first transducer of the code JQ output of which is connected to the second information input of the two input n-bit One of the main switches,. the shift gores are connected to the corresponding bits of the p-th parallel output of the matrix shift register of the same name, the bit of which is not connected to the s (m + -C) input of the corresponding matrix shift register via the k-th element. the control input of which is connected, to the detector output of a number of standing units, the output of the two-input n-bit bus switch is connected to the second information input of the second code converter, the outputs of the bits from the first to the nth are connected respectively to the control inputs from the first to the fifth tire repeaters with gating, the outputs of the second converter of the codes from the first to (n + 1) -th are connected to the input of the third converter of the codes, the outputs of bits from the first to the fifth that are connected to the inputs of the n-input adder. They are connected to the control inputs respectively from the first to the nth two-input (go + 1) -disk bus switches, the outputs of which are connected to the corresponding stations from the first to the fifth, which are connected to the inputs of the p-input adder. information inputs A (i, s) of the generator are connected to the inputs of the parallel reception of information D (l., s) of the k-th matrix shift register A (i, s) -D (l, s) j, where i is the generator input, 2 i - ,, i in О, N / 2-1, 1 - input of parallel reception of information of matrix shift registers,,, S - data width s-1, ra + 1; , n, pth parallel output Q (pjS) of the k-ro matrix shift register (. -1, р еO, N / 2 -1) is connected to the data inputs of the corresponding bus repeater with gating, the outputs of which are connected to the inputs of the corresponding inverters of the second and second information inputs of the corresponding two-input (t + 1) -disk bus switches, the second information inputs of which are connected to the outputs of the corresponding direct-to-additional converters, bits (, ha) of the serial input receiving information of the k-ro matrix shift register is connected to the corresponding bits of the p-th parallel output of the matrix shift register of the same name, whose bit through the k-th element is NOT connected to the s (m + -C) -discharge input of the corresponding information matrix shift register. ha ь “in A) J“ o a: S: ““ x FIG. five FIG. 6