SU1753465A2 - Basis function system generator - Google Patents

Abstract

The invention relates to automation and computing and can be used, for example, in digital data transmission systems. In order to expand the functionality of the generator by the formation of M systems of functions. determined by the N / 2-x elementary system-forming vector and invariant to the base of the power basis, the generator contains two n-bit counters (N 2 is the dimension of the system of functions), n elements NOT, n (t + 1) -discal switches (t - the number of bits in the binary representation of the number M / 2 - 1, M - the number of values taken by the functions, M - even integer), modulo M / 2, n shift registers, n + 1 key elements, n formers additional code, n-bit switch, a detector of standing units, three code converters, ovatel n time gates, input specifying functions of system clock input, functional output numbers generated output function, the output end of the period the generated functions. Table 1 .. Zil. "W e

Description

The invention relates to automation and computing, can be used, for example, in digital data transmission systems, and is an improvement of the device according to the author. St. ISb 1753465.

A Walsh function generator is known that contains an element NOT, four AND elements, two n-bit counters, two OR elements, an n-input mod 2 modulator, n-1 modulo modulators 2 of the first group, n-1 adders no mod 2 second groups, n switches.

This generator forms Walsh basis functions, taking values i 1, which is its disadvantage, so

VI

as it does not allow to form other systems of basic functions.

The closest to the proposed technical entity is the O system of basic functions, containing (Jp | two n-bit counters (N-2 - the size of the system of functions), n elements HE, P n (m + 1) -bit switches (t is the number of hO bits in the binary representation of the number M / 2-1, M is the number of values accepted by the functions, M is an even integer, modulo M / 2, l shift registers, n key elements , additional driver shapers, n-bit switch, detector of a number of standing units, three code converters, driver n time gates, input specifying system

functions, clock input, function output, output of the generated function number, output of the end of the period of generated functions, in which the count input of the first counter and the synchronization inputs and shift registers are connected to the input of the generator clock pulses, the discharge outputs of the first counter are connected to the inputs of the And element, the output of which is connected to the control input of the write p shift registers, the counting input of the second counter and the output of the end of the period of the generated generator functions, the bit outputs of the second counter are connected to the detector input of a number of units, the data input of the first converter, the first information input of the n-bit switch, the input of the shaper n time gates and the output of the number of the generated generator function, the output shapers n of the time gates are connected to the first information input of the second code converter and the control the input of the first code converter, the output of which is connected to the second information input of the n-bit switch, the control input of which is connected to the output of the detector p units, the output of the n-bit switch is connected to the second information input of the second code converter, the outputs of bits from the 1st to the nth of which are connected respectively to the control inputs from the 1st to the nth key elements, the outputs of the bits The first to second (n + 1) second converters of the codes are connected to the input of the third code converter, the outputs of the bits from the 1st to the nth of which are connected to the control inputs from the 1st to the nth (t + 1) -disk switches, the outputs of which are connected to the corresponding inputs of the adder no mod M / 2, the output of which is connected to the functional output of the generator, the 1-bit bottom group of the parallel input of the 1st shift register (I - 1, N / 2, i 1, n) is connected to the (I 2m) -th bit group the input of the task of the generator function system (the group size is m + 1), the output of the N / 2 -th bit group of the 1st shift register is connected to the data inputs of the i-ro key elements, the outputs of which are connected to the inputs of the corresponding additional code drivers and primary / informational inputs of the corresponding (t + 1) -discal switches, the second information inputs otorrhea connected to the outputs of respective formers additional code, the first output of M / 2-th discharge group 1 st shift register through the 1-th element NO

connected to the first input of the group of the corresponding shift register in series, the outputs from the 2nd rfo (m + 1) -th N / 2-th bit group of the 1st cdeig register are connected to the corresponding inputs of the sequential input group of each shift register directly.

The disadvantage of this generator of a system of basic functions is its inability to form systems of basic functions with different from d ° values of the first element of the system-forming vector A (N / 2) (the value of d ° 1 is formed in hardware), which leads to its narrowing

5 functionality (in fact, a system of basic functions is formed).

The purpose of the invention is to expand the functional capabilities of the generator of systems of basic functions due to the formation of M systems of basic functions invariant to the base of a power basis.

The goal is achieved by the fact that

5 into the generator of systems of basic functions, containing two n-bit counters (N 2n-dimensionality of the system of functions), n elements NOT, n (m + 1) -bit switches (m is the number of bits in the binary representation of the number M / 2-1, M is the number of values accepted by the functions, M is an even integer), modulo M / 2 modulator, n shift registers, n key elements, n additional code generators, n-bit d switch, detector near units, three code converters, shaper n time gates, the input of the task of the system of functions, the input of clock pulses owl, functional output, output

0 the number of the generated function, the output of the end of the period of the generated functions, in which the count input of the first counter and the synchronization inputs of the shift registers are connected to the clock input of the generator, the overflow output of the first counter is connected to the write control inputs of the shift register n, the count input of the second counter and output end of period of generated generator functions, parallel

0, the output of the second counter is connected to the detector input of a number of standing units, the data input of the first code converter, the first information input of the n-bit switch, the input of the driver

5 time gates and the output of the number of the generated function of the generator, the outputs from the 1st to the nth shaper and the time gates are connected to the first information input of the second code converter and the control input of the first

code converter, the output of which is connected to the second information input of the n-bit of the Dny switch, the control input of which is connected to the detector output of a number of standing units, the output of the n-bit-5 switch is connected to the second information input of the second code converter, outputs of the digit The 1 st through 1 st dows are connected respectively to the control inputs from the 1 st to the n th key 10 elements, the bits of the second converter of the 1 st to (n + 1) th codes are connected to the input of the third converter codes, outputs bits 1-g the nth one is connected to the control inputs, respectively, from the 1st to the nth (m + 1) -disk switches, the outputs of which are connected to the n inputs of the modulo modulator M-2, the output of which is connected to the functional output of the generator, the input of the 1st bit group 20 of the 1st shift register (I 1, N / 2, I 1, n) is connected to the (I 2i) th bit group of the input of the generator function system (the size of the group is equal to m + 1), output N / 2 - and the bit group of the 1st shift register - 25 keys to the data input of the corresponding key element, the outputs of the key elements are connected to the input of the corresponding additional code formers and the first information inputs of the corresponding (t + 1) -electric switches, the second information inputs of which are connected to the outputs of the corresponding additional code formers, the first output of the N / 2 -u bit group i- ro shift register through the 1st element is NOT connected to the first input of the sequential input group of the corresponding shift register, the outputs from the 2nd to (t + 1) -th G4-2-th bit group of the 1st shift register are connected with the corresponding group entries after entering each register directly, a (n + 1) -th key element is inputted, with the n-th output of the time generator n connected to the control input of the (n + 1) -th key element, n / 2-bit of the task input group the generator function systems are connected to the data input of the (n + 1) -th key element, the output of which 50 is connected to the (n + 1) -th input of the modulo modulator.

FIG. 1 shows a functional diagram of the generator for the N 8; in fig. 2-55 timing charts explaining generator operation; in fig. 3 - the system of basis functions corresponding to the vector A «{gg g1g °} and the base of the power basis d 1.5.

The proposed generator of systems of basis functions invariant to the base of a power basis implements a method of forming systems of basis functions by dividing the modified Rademacher functions.

G (r (k) .p) us% Јffi s f .t.fbtt

G (1. (2k p) -modN) ,.

where k is 0.1p. G (1, p) A-A; A - System A

spreading vector, A {gi}, I O, N / 2-1; g is the base of the power basis; M is the number of values accepted by the functions. M is an even integer; D € O, M / 2-1, (1) mod dm 2 - the operation of dividing the degrees g & no mod M / 2.

Systems of functions (1) do not depend on the basis of the power basis d (are invariant with respect to it). Therefore, the same system of functions formed by the proposed generator can be used to perform various transformations. For example, A {g ° g1g2g3}.

In

M N 8, with g expQ -rr) Fourier transform, with g 2 - Fermat transform, with g 1 - Walsh transform. As an example, consider the construction of the system of functions A «{g3g d d0}, M N 8

gVgWflW

3 "2Г1" og. JL -1

g g g a -g rV9i doo d-93-913

9з 9зЧЧ1 9зЧ9з

93-92dG909 3929 190

gVgV-gV-gV

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

E GtGV

IN.I-J.

where GJ is a conjugate function whose elements are inverse elements are functions of GJ in the sense of group operation.

The system of functions associated with system (2) has the form

G (8G

- “UgUo ZU 1

 gy $ 0 -g23g; g; -g13-gfg1p3

-gV-g gVgVg1

W%: d1s2 "

V93 929 39291

gV-g2-g-gWg1

The inverse matrix G (8) for the inverse transformation is the general rule for orthogonal transformations: the forward transformation matrix G (N) is transported, the elements of the transposed matrix are replaced by their inverse values.

In the proposed; generator, the values of the basis functions are represented in binary code as follows:

d ° 000; d1 001; d2 010; d3 011;

- d ° - 100; d1 101; d2 110; -d3 - 111.

In coded form, the division of powers for dl (1) is reduced to arithmetic operations on codes of indicators and signs of degrees and does not depend on the basis of degrees g

A (r (k), p) (A (1, (2k-p) x

x mod N-A (2k-rfk), p)) mod M / 2; S (r (k), P} S (1, (2kP) x xmodN) © S (2k-r (k), p) @l,

Where

Oh, if the degree sign is flax;

g D put1 if the sign of the degree dD is negative; 1 - the transfer formed at performance (5).

0, it allocates an integer M / 2 an even number of times;

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

The matrix (2) in encoded form (in which the proposed generator forms it) has the form

 011 011 011 011011 011 011 0111 011 010 001 000 111 110101 100 011 001 111 101 011001 111 101 G (8) 000101010111100101110011 011 111 011 111011 111011 111 01110111110001 100111 010101000 0101011101111110001 100111 010101000 01010111011111011101110111110111110111110111110111110111110111110111111111011111 input 1 sets the functions of the system, input 2 clock pulses, n (n 3) shift registers - 3-5, respectively, the first n-bit counter 7, the second n-bit counter b, the detector 8 near the standing units in the code

data, the first converter 9 codes, n elements NOT-10, n key elements 11, n-bit switch 12, n drivers of 13 additional code, (n + 1) -th

key element 14, n (m + 1) -discal switches 15, second converter 16 codes, third converter 17 codes, driver 18 n time gates, adder 19 modulo M / 2, functional

0 output 20, output 21 of the number of the generated function, output 22 of the end of the period of the generated functions.

FIG. 2 shows voltage plots; 1 — generator clock input; 2

5 - overflow output of the first counter 7; 3-5 exits of bits of the second counter 6, 6-8 exits of the former 18 temporary gates; 9-11 outputs of the 4th digit group of the first shift register 3, 12-14 - outputs

0 of the first shaper 13 additional code; 15-17 - outputs of the bits of the functional output of the generator 20, - by the example of forming the system of functions 7v {gVg1g} 011 010 001 ooo, m - N 8

5 (g 1.5).

The generator works as follows.

The encoded values of the elements of the backbone vector A (N / 2) are fed to the input of the job of generator 1, respectively, to the input of the fourth bit group — the value of the first element, to the input of the third bit group — the value of the second element, etc. First counter 7

5 counts the clock pulses arriving at its input (Fig. 2 1) and thus forms the period of the generated functions r Nr, where r is the clock pulse repetition period. Second counter 6 counts

0 incoming overflow pulses of the counter 7 (Fig. 2.2) and forms at its outputs a parallel code of the number of the generated function (Fig. 2.3-5). At the beginning of each period on the leading edge

5 0 clock pulse, the state of input 1 of the generator is polled and the corresponding information is recorded in shift registers 3-5. In steps 1–7, shift registers 3–5 operate in the shift mode of the information recorded in them, forming, at the outputs 4, 2 and 1 st of the corresponding discharge groups, counts of the modified Rademacher functions RI (Fig. 2.9–11), R2 and R, which are fed to the inputs from the 1st to the nth key of the 5th elements 11, where the operation is performed on them, is equivalent to raising to the power 1 (function counts are passed without change when there is a high level signal at the control input ) or 0 (prohibition of passage).

Elements HE 10, which form the sign bit (t + 1) th function counts, form the counts of the functions Ri- R2, and from the output of the key elements 11, the Rademacher modified functions are fed to the inputs of the corresponding drivers of the 19 additional code, in which my code of function counts is replaced by their binary addition, and the first information inputs (t + 1) of bit switches 15, the second information inputs of switches 15 receive function counts in an additional code (Fig. 2,12-14). Depending on the values of the signals at the control inputs of the switches 15, the inputs of the 1-n adder 19 modulo M / 2 samples of the functions Ri, R2, R4 are received either in the forward code (the power exponents are added, which corresponds to the multiplication of powers with the same basis mi), or in an additional code (subtraction of indicators is made, which corresponds to the division of powers). The (n + 1) -th input of the adder 19 modulo M / 2 receives the samples of the additional modified Rademacher function - RO from the output of the (n + 1) -th key element 14, the RO function participates in the formation of the generated functions Gs, Ge, G, Go.

From the output of the adder 19 mod M / 2 samples of the generated functions (Fig. 2.15-17) arrive at the functional output of the generator 20.

Elements 8,9,12,16,17 and 18 of the generator participate in the formation of the necessary control signals.

A detector 8 near the standing units generates a signal at its output, provided that the data of two or more adjacent units is detected in the n-bit code. The detector is implemented by logical elements 2I (p-1) OR.

The first code converter 9 converts the first k bits of the input n-bit code and into their binary addition in accordance with the expression

Q (n) D (nk) + D (k (v) + t, where D (k (Y)) is the inversion operation of the k first bits of the input code D; k toQ2 - 1LG is the binary equivalent of the control signal. Converter 9 is implemented OR elements and the adder rro fnod / 2.

The second code converter 16 performs a bitwise addition on OR of binary data from two inputs shifted by one bit in accordance with the expression

G dip), gi J di-i (1) Vdi (2), l 2, n,

ldn (1). ln + 1,

where di (1), di (2) are, respectively, i-e data bits from the first and second inputs; Y is a logical OR operation.

The converter is implemented by OR logic elements.

The third converter 17 converts the input (p-M) -th bit code into an n-bit output code in accordance with the expression

п + 1 9п (Е di) mod2,

I k

where di is the value of the 1st binary digit (0.1) of the input code, k 1, p. The converter is implemented by logic elements that perform the function of addition mod 2.

Shaper 18 p temporary strobes forms temporary strobes with duration at their outputs

Sk y r, (k)

where r (n) is the period of the following clock pulses; i (k) -ie state of n-paer nogr of the driver input, k 1, n, I 2 + 1.2 Shaper 18 is implemented by a n-bit decoder and OR elements that assemble signals corresponding to a given input state .

The table shows the code values,

formed by converters and generator formers of the generator (positions 6,8, 18, 9, 12, 16, 17), when forming the system of basic functions K- {g g y g}. M N 8. In contrast to the prototype, the proposed

the generator forms all systems of discrete basis functions determined by the cwd-theme-forming vector A (N / 2) and independent of the base of the power basis d.

Claims (1)

Invention Formula The generator of systems of basic functions on the author. No. 1599850, characterized in that, in order to expand the functionality of the generator due to the formation of M systems of basic functions invariant to the base of the power basis, it contains the 1st block of the I elements, and the information input of n + 1 th the block of elements I is connected to the N / 2nd input of the task of the system of generator functions, the output n + 1 of the block of elements I is connected to the n + 1-m input of the modulo M / 2 adder. O .1 3 E. 4 S 6. 7. .AH OK: l / g2 jj- Fig.Z