# Walsh functions generator

FIELD: automatics and computer science, possible use in information compression equipment in television, multi-channel communications, telemetry for representing varying messages and signals in Walsh basis.

SUBSTANCE: generator has set-point element, NOT element, shift register, function number register, AND element, trigger, n-digit counter and additional AND element.

EFFECT: simplified generator due to decreased number of triggers, used as shift register digits.

3 dwg, 4 tbl

The invention relates to automatic control and computer engineering, in particular to the generators of discrete functions, and can be used in hardware data compression in television, multichannel communications, telemetry for presentation in the Walsh basis of different messages and signals.

Known generator of the Walsh function, comprising a generator of clock cycles, the n-bit counter (2^{n}the number of generated functions Walsh), n elements And n-shadowy modulo two, the block number generation functions Walsh and the group of n-1 adders modulo two (see USSR author's certificate No. 1091145, CL G 06 F 1/02, 1982).

However, this generator has significant complexity and limited performance due to use in his scheme of the inertial element of the summation modulo two.

The closest in technical essence of the present invention is the generator of the Walsh function, contains a master oscillator, a shift register, the register number function, item NO, item And trigger, and the output of the register function rooms connected to the parallel information input of the shift register, the output of the master oscillator connected to the clock input of the shift register and to the input element, output element and a serial output of the shift register through the element And is connected to the counting input of the trigger (see copyright is the certificate of the USSR No. 1076892, CL G 06 F 1/02, 1982).

However, this generator has significant complexity due to the large number of digits used in the shift register (2^{n}-1 if 2^{n}the generated Walsh functions), since each bit of the shift register is a trigger.

The aim of the invention is the simplification of the generator of the Walsh function by reducing the number of triggers that are used as bits of the shift register.

This objective is achieved in that in the known generator of the Walsh function, contains a master oscillator, a shift register, the register number function, item NO, item And trigger, and the output of the register function rooms connected to the parallel information input of the shift register, the output of the master oscillator connected to the clock input of the shift register and to the input element, output element and a serial output of the shift register through the element And is connected to the counting input of the trigger, put n-bit counter (where 2^{n}the number of generated functions Walsh) and an additional element And, moreover, the shift register is closed in a ring feedback circuit via the auxiliary element And the second input is connected to the output of the high-order bit of the counter counting the output of which is connected to the output of the master oscillator.

Figure 1 shows the block diagram of General the RA of the Walsh function, figure 2 - timing diagram illustrating the process of forming the generator functions Wal (5, θ), figure 3 - timing diagram illustrating the process of forming the generator functions Wal (6, θ).

The function generator Walsh contains the master oscillator 1, element 2, the shift register 3, register 4 function rooms, the And gate 5, the trigger 6, the n-bit counter 7 and the additional element And 8.

The function generator Walsh works as follows.

Binary code number of the Walsh function, which must be recorded in the shift register 3, is defined by the following tables:

Matrix, the rows of which are the binary codes of the rooms of the Walsh function, symmetric with respect to the column with the sequence number 2^{n-1}marked in the tables by an arrow. Therefore, the initial conditions for modeling the desired Walsh function can be set, specifying writing in the shift register 3 is not a whole number is binary functions, only the symbols of the 2^{n-1}and next in order in the row corresponding to the number of the desired function. The number of these symbols is equal to 2^{n-1}.

The number of characters equal to the number of bits in the shift register 3. Before you begin the high-order n-bit counter 7 must be installed in one state and the other bits - in the zero state, the trigger 6 must be installed in a single state.

Code combination representing a truncated code having the number of digits in two times less than the full number is binary options Walsh (see tables 1, 2, 3), rewritten from the register 4 function rooms in the shift register 3.

For example, for the case N=16 when forming function with sequence number 7 in the prototype (see USSR author's certificate No. 1076892, CL G 06 F 1/02, 1982) used the shift register 3 having 15 bits (triggers) to write binary code function rooms Walsh 010101010101010. And the proposed generator for forming the same function uses the shift register 3 having only 8 bits (triggers) to record a truncated binary function rooms Walsh 10101010 (see table 3).

Under the influence of the clock frequency supplied from the output of the master oscillator 1 to the clock input of the shift register 3, the information recorded in it, shifted and applied to one of the inputs of the element 5, the second input of which receives the inverted signal of clock frequency. Information from the output of the shift register 3 is supplied also to one of the inputs of the additional element And 8, to the second input of which receives a single potential output high-order bit of the counter 7. The output of the additional element And 8 will do what and the input of the shift register 3 as long
while the high order bit of the counter 7 will be located in a single state. Since the counter 7 has n bits, and before beginning his work in his eldest discharge was recorded as "1", it will happen in 2^{n-1}cycles of operation of oscillator 1. Thus, in the shift register 3 in the feedback circuit can be written 2^{n-1}-1 characters left out of it, and, therefore, they will re-fed to the input element And 5, i.e. to the input element And 5 will eventually do not truncated and the full code of the function rooms Walsh.

The voltage on the output element 5 is strobilaceum with each binary interval minimum duration has one gate, and the duration of each of the gate is equal to half the duration of the clock interval. The signals from the input element And 5 proceed to the counting input of the trigger 6 pre-installed in a single state. The moments of occurrence of logical units on the output element And 5 correspond to the points of change of sign of the generated function, Walsh, therefore, at the output of the trigger 6 is formed corresponding to the Walsh function.

Figure 2 and figure 3 presents diagrams illustrating the process of generating functions Wal (5, θ) and Wal (6, θ).

The graphs depict a temporary state outputs:

a) master oscillator 1;

b) item NO 2;

C) old is his digit counter 7;

g) register 3 offset;

d) an additional element And 8;

e) item 5;

W) trigger 6.

The proposed function generator Walsh the number of bits in the shift register 3 is equal to 2^{n-1}and the number of digits in the counter 7 is n, then the total number of digits:

N_{1}=2^{n-1}+n.

In the prototype the number of bits in the shift register 3 is:

N_{2}=2^{n}-1.

Thus, the proposed scheme generator of the Walsh function contains much smaller than the prototype, the number of triggers (bits of the shift register 3 and the counter 7). The gain in the number of triggers is:

N_{2}-N_{1}=2^{n}-1-(2^{n-1}+n)=2^{n-1}(2-1)-1-n=2^{n-1}-n-1.

Table 4 presents estimates of the number of triggers included in the shift register 3 and the counter 7 of the proposed generator of the Walsh function and a prototype for a different number of generated functions N=2^{n}.

Table 4 | |||||||

Used scheme | The number of triggers for different numbers of generated functions Walsh | ||||||

16 | 32 | 64 | 128 | 256 | 512 | 1024 | |

The placeholder | 15 | 31 | 63 | 127 | 255 | 511 | 1023 |

The proposed generator | 12 | 21 | 38 | 71 | 136 | 265 | 522 |

The proposed generator is provided, the gain in the number of triggers that are used to build the shift register 3 and the counter 7 in comparison with the prototype for a variant form 16 of the Walsh function is 20%, for forming 128 functions 44%, for forming 1024 functions - 49%.

Increasing the number N=2^{n}form of the Walsh function win increases and in the limit equal to 50%.

The use of the invention allows to significantly simplify the generator structure of the Walsh function by reducing the number of triggers that are used as bits of the shift register.

The function generator Walsh, contains a master oscillator, a shift register, the register number function, item NO, item And trigger, and the output of the register function rooms connected to the parallel information input of the shift register, the output of the master oscillator connected to the clock input of the shift register and to the input element, output element and a serial output of the shift register through the element And is connected to the counting input of the trigger, wherein, with the purpose of simplification of the generator by reducing the number of triggers used in quality is the firmness of razryadov of the shift register,
it introduced the n - bit counter, where 2^{n}the number of generated functions Walsh, and an additional element And, moreover, the shift register is closed in a ring feedback circuit via the auxiliary element And the second input is connected to the output of the high-bit counter, the counting input of which is connected to the output of the master oscillator.

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