SU1748146A2 - Generator of systems of basal functions - Google Patents

Abstract

The invention relates to automation and computing, can be used, for example, in digital information transmission systems. In order to expand the functionality of the generator by forming M systems of functions defined by the N / 2 elemental system-forming vector and invariant to the base of a power base, the generator contains an input for specifying a system of functions, an input for clock pulses, n shift registers, a modulo M / 2 modulator (M - number of values accepted by functions, M - even integer), n elements NOT, nN key elements, two n-bit counters, element OR - NOT, functional output, output of the end of the period of generated functions, output of the gene number iruemoy function yl 3.

Description

The invention relates to automation and computer technology, can be used, for example, in digital data transmission systems and is complementary to the basic one by author. Mg 1603360.

The prototype contains two n-bit counters (- the size of the system of functions), n shift registers, n elements NOT. blocks of elements And, modulo modulator M / 2, clock input, function setting input, function output, output of the end of the period of generated functions, output of the generated function number, in which the input of the first counter is connected to the clock input of the generator and the synchronization inputs of the shift registers , the overflow output of the first counter is connected to the counting input of the second counter, to the control inputs of the recording and the shift registers and to the output of the end of the period of the generated generator functions, the discharge outputs of the second counter are connected with the output of the number of the generated generator function and with the control inputs of n blocks of elements I, the input of the 1st group of the 1st shift register, N / 2, ..., n, m is the size of the group determined by the number of bits in the binary representation of the number M / 2-1 (M is an even integer), connected to / 12m / -and the bit group of the input of the set of functions of the generator, the first output / M / 2 / -th bit group of the 1st shift register through the i-th element connected to the first input of the sequential input group of the 1st shift register, the outputs of the second (t - + - 1) -th (N / 21) - bit group of the i-ro shift register respectively, are connected to inputs 2, t + 1 of the sequential input group of the i-ro shift register, outputs l, mM (M / 2) -th bit group of the 1st shift register are connected to the group of information inputs of the i-ro I block , outputs of blocks of elements AND

cl

with

h

N with

uh

4 o

 GO

connected to the inputs of the adder mod by M / 2

The disadvantage of this generator of systems of basic functions is its inability to form systems of functions with different from d ° values of the first element of the backbone vector A

D {d,} (the value of the hardware is formed

), which leads to a reduction in its functionality (in fact, a system of functions is formed)

The purpose of the invention is to expand the functionality of the generator of systems of discrete basis functions due to the formation of M systems of functions.

The goal is achieved in that the generator of systems of basic functions, containing two n bit counters (- the dimension of the system of functions), n shift registers, n elements NOT, n key elements, modulator M / 2, the input of the function system, input clock pulses, function output, the output of the end of the period of the generated functions, the output of the number n of the generated function, in which the input of the first counter is connected to the clock input of the generator and the synchronization inputs of the shift registers, the overflow output of the first counter is connected to the even input p of the second counter, with the control inputs of the recording p of the shift registers and with the output of the end of the period of the generated generator function, the outputs of the bits of the second counter are connected to the output of the number of the generated generator function and with the control inputs of n key elements, the input of the 1st bit groups of i-ro shift register (, N / 21,. п, group size is t-5-1, t is the number of bits in the binary representation of the number M /, M is the number of values accepted by the functions, M is an even integer connected to the (.2m) th digit group of the input of the task of the system of functions Generator, the first output (M / 2) -th bit group of the 1st shift register through the i-th element is NOT connected to the first input of the group of the sequential input of the corresponding shift register, the outputs from the second (t + 1) -th (N / 2) -u of the bit group of each shift register is connected to the corresponding inputs of the sequential input group directly, the group output (№ / 2) of the th bit group of the 1st register is connected to the group input of the 1st key element, the group outputs of the n key elements are connected with n inputs of adder mod by M / 2, output to first connected to the functional output of the generator, the element is introduced

n-OR-NOT, (n + 1) -th key element, with the inputs of the element OR-NOT connected to the n outputs of the second counter, the output of the element n-OR-NOT. connected to the control input of the (n + 1) -th key element, the group input of which is connected to the N / 2-th bit group of the input setting of the system of generator functions, the group output of the (n + 1) -th key, the element connected to (n + 1) -th input

adder mod by M / 2.

Figure 1 shows the functional diagram of the generator of systems of discrete basic functions that are invariant to the base of the power basis; for Figure 2, time diagrams explaining its operation; in FIG. 3, systems of basic functions corresponding to the system-forming vector A g g Vg} dl.

The proposed generator of systems of discrete basis functions that are invariant to the base of a power basis, implements a method of forming systems of functions, for-; data backbone vector, through the product n modified

Rademacher functions / n log2N /

, (KP) modN)) modgM / 2, GLVT

ABOUT)

G (r.p) - f (

0 (1.0). p-0.

where g is the index of the function being formed (.M-1); p is the reference number of the function (, N-1); K - index of the modified function

Rademakher (, 212P 1);

dK (t) is the exponent of the Kth modified Rademacher function, equal to the value of the 1st bit in the binary representation of the index g;

, n, {-} mod gM / 2 is the operation of multiplying degrees for mod M / 2; d - the basis of the power basis;

G (1, p) -A-A; D

A is the backbone vector (i}; 0, N / 2-1, M is the number of values accepted by the functions;

M is an even integer, 4bO, M / 2-1.

Systems of functions (1) do not depend on the base of the power basis d (invariant with respect to it). Therefore the same

The system of functions formed by the proposed generator can be used to carry out various transformations. For example. A {g ° g1g2g3}, with () - conversion

5 Fourier, with the Fermat transform. under Walsh transform.

As an example, consider the construction of a system of functions d2d1d °},

G (8) gjgftgytfg o g3g gy-p-g-g °

-gfg3 / 3-g1 / 3-g33-g30g3

gy / -0gy-g3g3-0g3 -g g -g -g 9 -g g g

2 „0„ 2 „0„ 2 JL2 „0

(2)

 GO,

2G, .G,

INJ-J,

(3)

.G (8) (4)

S (r, p) - (2 S (K.p)) mod 2 I;

D

(6)

where s

Oh, if the sign of degree g is positive;

-g g a -q -g g g -g

 / gig2g3-g-g-g-g g The system (2) is orthogonal for any values of g (real, complex, vector, matrix, and their extensions) in accordance with the orthogonality condition

where GI is a conjugate function whose elements are inverse elements of the function GJ (in the sense of group operation). The system of functions associated with system (2) has the form.

"X VriV 1

-g

 TOlТт з

yV Xg39o9i

wraYgX

g3guV-gyc-g3 g2-g-g 9 g g g

Inverse G (8) matrix For the inverse transformation, the general rule for orthogonal transformations is:

1. The forward transformation matrix G (8) is transported.

2. The elements of the transported matrix are replaced by their conjugate (inverse in the sense of group operation) values. Encode the function values in system (2) with binary code.

,,,

. ,, ..

In this form, the operation of multiplying the degrees in system (1) is reduced to arithmetic operations on the codes of indicators and the signs of the degrees and does not depend on the base of the degree g

D (r) (ЈD (K, p)) mod M / 2; (5)

1 if the sign of degree g is negative; I is the transfer formed when executing expression (5),

GO if the selection of an integer I j M / 2 occurred an even number of times, / 1. if the selection of an integer M / 2 occurred an odd number of times.

2) 5

The matrix (2) in coded form (the form in which it is formed by the proposed generator) takes the form

s x,) in and

G (8f

10 V

011 011 011 100 011 110 110 001

011 010 001

011

111

001 000 010

011 001

111

000 011 100 010 011

011 000 101 101

111 111

100 100

011

111

011 010 011 010 110 101

011 110 001

111 111

011 101

111

100 011

101 000 000 010 110 111

011

100 101 001

111

011,100,000

(7)

The generator (Fig. 1) contains the input of a task of the function system 1, the input of clock pulses 2, the first p-bit counter 3, n shift registers - 4, 5, 6, respectively, the second n-bit counter 7, n elements NOT 8, p key elements 9, element p20 OR-NOT-10, (n + 1) -th key element 11, mod modulo M / 2 12, functional output 13, output of generated function number 15, output of end of period of generated functions 14.

25 The voltage plots (Fig. 2) are shown at the input 2 of the clock pulses of the generator (1), the overflow output of the first counter 3 (2), the outputs of the bits of the second counter 7 (3-5), the outputs of the fourth discharge group

30 shift register 4 (6-8), the outputs of the second bit group of the shift register 5 (9-11), the outputs of the first bit group of the shift register 6 (12-14), the outputs of the bits of the functional output 13 of the generator (15-17) on

35 An example of the formation of the function GT. g2g1g},.

The generator works as follows

40 The encoded knowledge of the elements of the backbone vector A (N / 2) is fed to the input 1 of the task of the generator function system, respectively: the input of the fourth bit group is the value of the first

45 elements, to the input of the third bit group - the value of the second element, etc. The first counter 3 counts the clock pulses arriving at its input (Fig. 2.1) and thus forms the period of the generated

50 functions m, where r, the period of clock pulses. The second counter 7 counts the overflow pulses arriving at its input (Fig. 2.3) of the counter 3 and generates at its outputs the code of the number generated

55 functions (Fig.2.3-5). At the beginning of each period, on the leading edge of the 0th clock pulse, the state of the input 1 of the generator is interrogated and the corresponding information is recorded in the shift registers 4, 5 and 6 in accordance with the circuit for connecting the inputs of the registers. In cycles 1–7, the shift registers 4, 5, and 6 operate in the shift mode

the information recorded in them (low signal value at the recording control inputs of all registers), forming the outputs of the bit groups of samples of modified Rademacher functions that go to the group inputs from the 1st to the nth key elements 9, where they are processed, equivalent to raising to the power of 1 (the signals pass without change when there is a high level signal at the control input) or 0 (the signals do not pass). The formation of samples of the modified Rademacher functions is attended by the elements of HE 8, which form the sign (TM) th discharge of the function counts. From the output of elements 9, the samples of the modified Rademacher functions, those of them that are allowed to pass, are fed to the inputs of the adder modulo M / 2 12. To the input n + 1 of the adder 12, there are samples of the additional modified Rademacher RO function from the output-turn (n + 1 ) th key element 11. The function R0 is involved in the formation of functions. therefore, the passage of samples of this function through the key element 11 is allowed only when the generator forms the function G, while all other key elements 9 are blocked, according to, system (1). From the output of the adder 12, the generated samples of the generated functions (Fig 15-17) are fed to the functional output of the generator 13

Fig. 3 shows, as an example, the system of discrete basis functions A {g3g2g1g °}. ,

Unlike the prototype, the proposed generator forms M systems of discrete basis functions defined by all elements of the backbone vector A (N / 2) and independent of the base power basis d, which is its advantage.

Claims (1)

Invention Formula The generator of the system of basic functions on the author.St. No. 1603360, characterized in that, in order to expand the functionality of the generator by forming M systems of functions, it contains the (n + 1) -th block of AND elements and the OR element, and the information input of the (n + 1) -th block of AND elements connected to the N / 2 input of the task of the generator function system, the output of the (n + 1) th block of elements AND is connected to the (n + 1) input of the modulo M / 2 adder, the inputs of the OR element are connected to the data information outputs the second counter, the output of the element OR is connected to the control input (the PM} of the block of elements I. CD t cc "RCVJ her 3 About 1 2 j × 5 6 7 % Figz