# Digital function generator

(57) Abstract:

The invention relates to automation and computer engineering and can be used for processing two-dimensional signals and images, as well as in systems spectral analysis and information-measuring complexes. The purpose of the invention is the increased robustness of the generated signals by improving their correlation properties by reducing the amplitude of the side peaks of the autocorrelation functions of these signals. Digital function generator includes first and second counters 1 and 2, the element OR 3, delay element 4, the function generator Walsh 5, the shift register 6, a memory unit 7, item NO 8, a group of XOR 9, the first and second control inputs 10 and 11 of the generator, a first frequency divider 12, a second frequency divider 13, the key 14, the modulo two 15. The invention allows to create generating equipment for processing of two-dimensional signals and images, which generates a signal with improved correlation characteristics and high noise immunity generated signals. 4 Il., table 1. The invention relates to automation and computer engineering and can be used for oberbach complexes.Known generator of discrete orthogonal functions, containing the master oscillator, frequency divider, the power generation of the Walsh function, the element is NOT, the multipliers and the switch [1]However, this generator that generates functions with improved correlation characteristics and thereby increase the noise immunity of the signals generated in the basis of the output of the function generator cannot be used to generate discrete orthogonal functions with two arguments (two-dimensional discrete orthogonal functions), which does not allow to use it for processing two-dimensional signals and images.The closest in technical essence of the present invention is a digital function generator containing two counter element OR delay element, the function generator Walsh, the shift register unit of the memory element is NOT, and XOR, and control input account generator connected to the first input member OR the output of which is connected to the input of the write shift register, the synchronization input of which the counting input of the first counter connected to the clock input of the generator, the output of the overflow of the first counter is connected to the counting input the address input of the memory block, the output of which is connected to the information input of the shift register, the output of which is connected to the input element, the output of which is connected to the first n inputs of XOR, the second inputs of which are connected to the outputs of the respective bits of the generator of the Walsh function, the control input of which is connected to the output of the overflow of the second counter, the outputs of the XOR outputs are digital function generator [2]

However, two-dimensional signals generated by this digital functional generator, possess a poor correlation properties, because the amplitude of the side peaks of the autocorrelation functions of these signals are high, which leads to low noise immunity generated signals.The aim of the invention is to increase the noise immunity generated signals by improving their correlation properties by reducing the amplitude of the side peaks of the autocorrelation functions of these signals.The objective is achieved by the fact that the digital function generator containing two counter element OR delay element, the function generator Walsh, the shift register unit of the memory element is NOT, and XOR, and the entrance is and the shift register, the synchronization input of which the counting input of the first counter connected to the clock input of the generator, the output of the overflow of the first counter is connected to the counting input of the second counter and through a delay element to the second input member OR the output of a second counter connected to the address input of the memory block, the output of which is connected to the information input of the shift register, the output element is NOT connected to the first n inputs of XOR, the second inputs of which are connected to the outputs of the respective bits of the generator of the Walsh function, the control input of which is connected to the output of the overflow of the second counter, the n outputs of the XOR outputs are digital function generator, we have introduced two frequency divider, the key and the modulo two. Thus the inputs of the frequency dividers connected to the clock input of the generator, the output of the first frequency divider connected to the information input key, the output of the second frequency divider connected to the control input key output key connected to the first input of the modulo two, the second input of the modulo two is connected to the output of the shift register, the output of the adder modulo two is connected to the input element.In Fig.1 shows a block diagram of a digital function generator of Fig.2 the first sixteen discrete orthogonal functions; Fig.3 the autocorrelation function of the signals generated by the prototype (for dimension N=4); Fig.4 the autocorrelation function of a signal generated by the proposed generator (for dimension N4).Digital function generator includes first and second counters 1 and 2, the element OR 3, delay element 4, the function generator Walsh 5, the shift register 6, a memory unit 7, item NO 8, a group of XOR 9, the first and second control inputs 10 and 11 of the generator, a first frequency divider 12, a second frequency divider 13, the key 14, the modulo two 15.Control input account generator connected to the first input element OR 3, the output of which is connected to the input of the write shift register 6. The synchronization input of the shift register 6 and the counting input of counter 1 is connected to the clock input of the generator 11, and also to the inputs of the frequency dividers 12 and 13. The outputs of counter overflow 1 is connected to the counting input of counter 2 and through a delay element 4 to the second input element OR 3. The output of counter 2 is connected to the address input of the memory unit 7, the output of which is connected to the output of the frequency divider 12 is connected to the information input key 14, and the output of the frequency divider 13 is connected to the control input of the key 14, the output of which is connected to the first input of the modulo-two 15. The second input of the adder 15 is connected to the output of the shift register 6. The output of the adder 15 is connected to the input of the element 8, the output of which is connected to the first n inputs of XOR 9, the second inputs of which are connected to the outputs of the respective bits of the function generator Walsh 5, the control input of which is connected to the output of the counter overflow 2. The n outputs of the XOR 9 are the outputs of the digital function generator.Digital function generator works as follows.In the original point on the outputs of the generator 5 is formed, the function Wal (O, y), which for N 4 equal

< / BR>

Counters 1 and 2 are in the state "0" and the frequency divider 12 having a division ratio of 2, and the frequency divider 13 having a division ratio of 2, and the frequency divider 13 having a division ratio of 2

^{N-1}are in their original state.Because the counters 1 and 2 are in the state "0" of the block 7 is selected recorded at address zero of the function Wal (O,x), the value of which is

[1 1 1 1] which is recorded in the register stvlyaetsya the first value "1" of the function Wal(O,x). With the input clock pulses 11 for the first N/2 cycles of operation of the generator at the output of the frequency divider 13 is formed "0" (the division ratio of 2

^{N-1}), resulting in the first half forming the function Wal(O,x) appears at the output of modulo-two 15 without changes.In the next N/2 cycles of operation of the oscillator output divider chastity formed "1", resulting in a second half period of the formation of the function Wal(O,x) the switch 14 is open. At the exit key 14 receive the pulses from the output of the frequency divider 12 (division factor 2) corresponding to the even-numbered elements of the function Wal(O,x) received at the first input of the modulo-two 15. Thus, even elements of the second half-period of the function Wal(O,x), supplied to the second input of the modulo-two 15 are inverted.Consequently, at the output of modulo-two 15 within N clock cycles will be generated signal Z (O,x):

[1 1 1 -1]

So, during the first cycle at the output of the modulo two, you receive the first value "1" of the function Z(O,x), which is inverted into a signal of a "0" element 8 and is fed to the second inputs of the n elements is R> Upon receipt of the remaining clock pulses to the input 11, producing a serial shift output register 6 values written to it functions, pulse counting is performed by the counter 1. As a result, the outputs of XOR 9 previously described manner are sequentially formed, the remaining N-1 columns, and the function Z (O,x,y) has the form

< / BR>

Simultaneously there is an overflow of the counter is 1, the output of which appears the pulse overflow. This pulse is recorded in the counter 2, and the new contents of the counter 2 is supplied to the address inputs of the block 7, perform a subset of the functions Wal(1,x), the value of which is

[1 1 -1 -1]

In the result of the receipt of the pulse overflow output of counter 1 on delay element 4 and element OR 3 in the shift register 6 is written to the function Wal(1, x). The delay element 4 is necessary for the process to decode addresses and a sample of block 7 of the regular functions of the Walsh occurred earlier than you are recording functions Wal in the register 6.In the serial passage of these characters through the modulo two 15, at the first input of which during the second half-cycle of the received pulses corresponding to odd is Described a process of forming a column repeats, this will generate a function Z (1,0,x,y) (see Fig.2). Similarly generates the rest of the function Z (k,0,x,y).As soon as the ending of the process of generating columns for the function Z, generated from the last function of the Walsh-kechmara recorded in the memory unit 7, the counter 2 is reset, and its output pulse appears overflow, which enters the generator 5 and causes its outputs another Walsh functions Wal(1,y)

< / BR>

The block 7 is again selected function Wal(0,x), which is recorded in the register 6 pulse counter overflow 1 (through the elements 4 and 3), and converted using the frequency dividers 12 and 13, the key 14 and the modulo two 15 in the function Z(0,x).Next is shaping function Z(k,1,x,y).Similarly, formed the N

^{2}function Z(k,m,x,y). It must be emphasized that the Kronecker product is the element 8 and the group of XOR 9.The system of two-dimensional Walsh functions is defined as follows:

Wal (k,m,x,y) Wal (k,x) x Wal (m,y), (1) where Wal (k,x) is a vector-string;

Wal (m,y) is a column vector;

* the Kronecker product of functions.Consider the example of a function Wal (3,2,x, y):

achem N

^{2}matrices of the form (2) [2]

Thus, the two-dimensional Walsh functions consist of direct or inverted one-dimensional Walsh functions. The number of different one-dimensional Walsh functions for dimension N = 2N.It is known that the autocorrelation function of the signal s(t) is determined by the expression

R(q) S(t)S(t-q)dt

(3) where q is the magnitude of the time difference signal.From the expression (1) shows that R(q) characterizes the degree of connection (correlation) of the signal S(t) with its copy shifted by the value of q along the time axis. It is clear that the function R(q) reaches its maximum at q 0, since any signal is perfectly correlated with itself. If this

R(O) S

^{2}(t)dt E

(4) i.e., the maximum value of the autocorrelation function is equal to the signal energy (see Gonorovski I. S. Radio circuits and signals. Moscow: Soviet radio, 1971, S. 68).For the case of signals, normalized by the energy given E=1, the autocorrelation function consists of a Central peak with an amplitude of 1, is hosted on the interval (-q,q) and the side peaks, distributed on the interval (-T, -q) and (q,T). The amplitude of the side peaks take on different values, but the signals with good correlation properties they are small, i.e., substantially smaller than the amplitude of the Central surrounding smaller the amplitude of the lateral peaks of AWKAF, are more robust.Correlation properties of one-dimensional signal that comprises a two-dimensional signal characterizes the measure of distinctiveness (PR), defined as the difference of values of the autocorrelation function corresponding to the main and lateral peaks. Obviously, the greater the PR, the better the signal (see Dixon, R. K. Broadband system. M. Bond, 1979, S. 85 and 66, Fig. 3.11).The calculation of the autocorrelation functions of the signals, which are the rows of the matrices describing the two-dimensional Walsh functions generated by the prototype show that they have large side peaks, which leads to low noise immunity generated signals.Using EDCM was synthesized system of two-dimensional functions Z (k, m,x,y) generated by the proposed generator having much better autocorrelation function and performance distinction (PR), increases the immunity generated signals.The system of two-dimensional discrete orthogonal functions generated by the proposed generator is defined as follows:

Z(k,m,x,y) Z(k,x) Wal(m,y), (5) where Z(k,x) is a vector-string;

Wal(m,y) is a column vector;

* the Kronecker product of functions.For example, for N=4 the system of the Walsh function is

(6)

After inverting the even-numbered elements of the second half of the period will receive a new system of orthogonal functions

(7)

Consider the example of a two-dimensional function Z (3,2,x,y)

(xy (,Wly=

(8)

For dimension N we get N

^{2}matrices of the form (8). For signals which are rows of the matrices describing the two-dimensional Walsh functions generated by the prototype, and signals, which are the rows of the matrices describing the two-dimensional functions that are generated by the proposed generator were calculated autocorrelation function and performance distinction (PR).The results of the calculations are presented in the table.We offer digital function generator generates a signal in which the measure of distinctiveness (PR) is greater than the signal generated by the prototype of 75% for any dimension N of functions (see table and Fig.3 and 4).Because of the symmetry of the graphs of the autocorrelation functions of the signals is asany respectively the values "+1" and "-1" of the function Z(k,m,x,y), and the function itself is located at the intersection of the column defined by the function Z(k,x), and the line defined by the function W (m,y).In block 7 (ROM), as in the prototype [2] has consistently recorded the functions of the Walsh-kechmara. In this case, the value "+1" function corresponds to the signal "1" and the value "-1" signal "0" at the outputs of the ROM.The use of the invention allows the generator to create the equipment for processing of two-dimensional signals and images, which generates a signal with improved correlation properties, because the autocorrelation function of signals which are rows of the matrices describing the two-dimensional functions have small amplitude of the side peaks, which leads to a high noise immunity generated signals. DIGITAL function GENERATOR containing two counter element OR delay element, the function generator Walsh, the shift register unit of the memory element is NOT, and XOR, and control input account generator connected to the first input member OR the output of which is connected to the input of the write shift register, the synchronization input of which the counting input of the first counter connected to the clock input of the generator, the output of preponement OR the output of the second counter connected to the address input of the memory block, the output of which is connected to the information input of the shift register, the output element is NOT connected to the first inputs of the XOR group, the second inputs of which are connected to the outputs of the respective bits of the generator of the Walsh function, the control input of which is connected to the output of the overflow of the second counter, the outputs of XOR group are the outputs of the digital function generator, characterized in that it introduced two frequency divider, the key and the modulo two, and the inputs of the frequency dividers connected to the clock input of the generator, the output of the first frequency divider connected to the information input key, the output of the second frequency divider connected to the control input of the key, the output of which is connected to the first input of the modulo two, the second input is connected to the output of the shift register, and the output to the input element.

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