SU1691770A1 - Method of spectral analysis with linear prediction - Google Patents

Abstract

The invention relates to a radio metering technique and can be used to analyze the energy spectrum under conditions of small a priori information about the class or parameters of random processes under study. The purpose of the invention is to improve the accuracy of spectrum estimation. The method consists in that the analog signal is converted into digital form, the result is memorized and at the same time the input variance is determined, N iterative calculations are performed, each p. The invention relates to radio measuring technique and can be used to analyze the energy spectrum small a priori information about the class or parameters of the random processes under study. The purpose of the invention is to improve the accuracy of spectrum estimation for a limited sample. The drawing shows a linear prediction spectrum analyzer diagram implementing the method. The iteration includes the computation of forward and backward prediction errors, partial correlation coefficients, variance, and linear prediction coefficients. Fourier transform is performed at each iteration, obtaining squares of the amplitude-frequency characteristics of the prediction filters Kn (f) from the first to the N-ro inclusive, after which a number of step-by-step calculations of the mass coefficients are performed using the above formula. Then, the resulting weights are multiplied by the corresponding squares of the transfer functions of the prediction filters, summarize these products and estimate the spectrum by the inverse function of the sum result. Due to the use of additional information about the process being analyzed, a multitude of realizations of spectrum estimation, which have unacceptable deviations from the true spectrum, is discarded from consideration, which results in an increase in the accuracy of the estimate, of the spectrum at the limited time of analysis.1 Il. The linear prediction spectrum analyzer contains an input analog-to-digital converter (ADC) 1, the output of which is connected to the first inputs of the elements OR 2 and 3, the outputs of which are connected to the information inputs of memory blocks 4 and 5. The outputs of memory blocks 4 and 5 are connected to the first and second inputs of the prediction trellis filter 6, and to the third input to the output of the calculator 7 private correlations. The outputs of the lattice filter 6 are connected with the second inputs of the elements Os s VJ o

Description

OR 2 and 3, 1 and 2 inputs of the calculator 7 private correlations. The outputs of the dispersion meter 8 and the quadr 9 are connected to the corresponding inputs of the recursion unit 10, the control inputs of which are connected to the corresponding outputs of the micro-command generation unit 11, to the corresponding outputs of which the control inputs of the grating filter 6 are connected. The first output of the unit 10 is connected to the Fourier information input- converter 12. whose output is connected via a quadrant 13 to the information input of memory block 14, whose control and address inputs are connected to the corresponding outputs of block 11. Output Lok 14 is connected to the input of the weighing unit 15 and the first input of the calculator 16 weight coefficients. The weighing unit 15 may be performed on standard multiplier chips. The second output of recursion unit 10 is connected to the information input of the memory unit, the control and address inputs of which are connected to the corresponding outputs of block 11. The output of block 17 is connected to the second input of calculator 16, the output of the latter is connected to the second input of weighing unit 15, the output of which is connected to the second input of the adder 18. The output of the adder 18 is connected to the information input of the memory block 19, the control and address inputs of which are connected to the corresponding outputs of the micro-command generation unit 11 The output of the memory block 19 is connected ene to the first input of the adder 18 and data input unit 20 converts, whose output is connected to the third input calculator 16 weight coefficients. The conversion unit 20 can be performed on standard microcircuits — permanent memory devices.

The spectrum analyzer that implements the method works as follows.

In the initial state, initial conditions were established in the micro-command formation unit 11. Previously, in block 10 recursions, the coefficient of joint-stock company 1 is permanently recorded in the register.

At the first stage of operation, the signal under study is fed to the analyzer input, and in block 11, a clock signal is generated at the first output, which is fed to the control input of the ADC 1. The resulting series of samples goes through the OR elements 2 and 3 to the information inputs (B) of the respective blocks 4 and 5 memory. Simultaneously, from the third output of block 11, recording resolution pulses are received to the corresponding inputs of blocks 4 and 5. Synchronous inputs

and the address inputs of the latter are received pulses - microcommands from the 4th and 5th outputs of block 11. Block 11 can be performed on standard electronic elements along

the known serial circuit of the sync generator, the counter and the persistent storage device in which the codes of micro-instructions are recorded

At the same time, the signal from the output of the A / D converter 1 is fed to the dispersion meter 8, in which the dispersion of the input signal is determined. The meter 8 can be made according to the scheme of the serial connection of the quad and the accumulating adder. From the second input of block 11, a signal is sent to the control input of the meter 8, from the output of which the dispersion signal is fed to the first input of the recursion block 10. In the second stage, the linear prediction coefficients anm are calculated (n 1.N is the order of the filter, m is O , N is the number of the coefficient in the nth order filter) and the amplitude-frequency characteristics of the prediction filters from the 1st to the Nth order inclusive are determined from them. In this case, each n-iteration contains four calculation steps: filtering linear prediction errors in the trellis filter 6, calculating

partial correlation coefficient in calculator 7, determination of linear prediction code in block 10 recursions and calculation of amplitude-frequency characteristics of prediction filters in a Fourier converter 12 In the first iteration (n 1), the sequence of samples X (I) recorded in blocks 4 and 5 of memory ti are considered respectively the sequence of linear prediction errors fo (l) X (l)

and a sequence of linear prediction errors back bo (l} x (().

The clock pulses from the fourth output of the microcontrollation unit 11, from the output of blocks 4 and 5, read the sequences of the codes fo (l) and bo (l), respectively, to the first and second inputs of the grating filter 6 of the prediction fi (l) fo (l), bi (l) bo (l-1). These sequences are again recorded in clock pulses and addresses (the third and fifth outputs of block 11) in the same cells of blocks 4 and 5, and simultaneously fed to the first and second inputs of the calculator 7 private correlations.

In the calculator 7, the error sequences fi (l) and bi (l) are summed, squared and summed up again in pairs, forming a new sequence:

Si.i (l) -f bi (l) 2 - {-4fi (l) bi (l)};

fi (0-bi (i) n

S2.l (0 + bl (l) f (l) -bi (l) 2}

- (l) - ()}.

A command from the seventh output of block 11 at the output of calculator 7 generates the value of the partial correlation coefficient pn, corresponding to iteration n 1; qi -Si, 1 / 32.1. The coefficient 1 from the clock pulse (the eighth output of block 11) goes to the third information input of the trellis filter 6, is simultaneously fed to the second input of the recursion block 10 and through the quad 9 to its third input. To the first input of the recursion unit 10 comes from the output of the meter 8 dispersion estimate F0. In block 10 recursions, linear prediction coefficients apt and dispersions Pp are generated according to the relations:

Ept Sn-1, t + O, n Ep-1.n-t Pn (bqn-i2) Pn-i,

1, where Zpt Cp, t p.

Oh, tn

At the same time, at the first iteration (p 1), the linear prediction coefficients are equal: a o aoo + qiaoi aoo 1.

ai zo1 + qiaoo qi.

The address code from the twelfth output of block 11 to the address input of block 10 from the first output of block 10 to the information input of the converter 12 receives linear prediction coefficients. The Fourier transducer 12, operating, for example, by the well-known fast Fourier transform subroutine or by the hardware-oriented principle, calculates a set of Fourier coefficients. Thus, from the first output of the transducer 12 to the input of the quadrant 13, a code corresponding to the amplitude-frequency characteristic of the prediction filter Ki (f) from the output of the quadrant 13. The resulting code is fed to the information input of the memory block 14, the control and address inputs of which receive the resolution pulses and the address from thirteen , the fourteenth and the fifteenth command generating unit 11 outputs. From the second output of the recursion unit ng, the information input of the memory unit 17 receives the estimate of the variance PL At the same time the nineteenth, twentieth, and twenty-first outputs of the block 11 receive recording resolution pulses, clock pulses and the address to the inputs of the block 17. These operations complete the first iteration ( n 1) of the second stage. Po0

The following iterations (n - 2.3N) are carried out in a similar way. The values of the variances and amplitude-frequency characteristics of the error prediction filters are obtained from the 2nd to the Nth order inclusive.

At the third stage, a set of (N + 1) -ro weights is calculated, based on the N – P system of equations:

15

/ G (f) Ko2 (f) df P0 / G (f) Ki2 (f) df Pi

(one)

/ G (f) KN2 (f) df PN

The calculation is carried out in the calculator 16 iteratively by the ratio

Ano + i) An (i) + r (i)

g 1

Ј LP (OK,

n 1

with

five

0

(2)

where p I.N, i 1,1

At time i 1, the initial values of 0 and AN (1) 1 / Ro are specified. Al (1) 0 (n - 2.N), and the value of / is fixed constant from the condition of convergence of iterations to the desired root of the system of equations (1).

The clock pulses from the thirteenth output of the microcommand formation unit 11 from the output of the memory block 14 to the input of the calculator 16 receive counts of amplitude-frequency characteristics quadratures of the prediction filters Kn2 (f) (n 1, N). In this case, the synchronous input of the calculator 16c of the output 18 of the block 11 receives a clock pulse. After the arrival of the sync pulse from the nineteenth output of block 11 to the exit of blocks

17, the i / i input of the calculator 16 at its information output forms the coefficient A, -, (i), which is fed to the second information input of the weighing unit. At the 1st iteration, the calculation of the mass coefficients is completed.

At the fourth stage, calculate the current spectrum estimate from iterations i - 1,

G (f) 1 / Ј A ,, (O K, 2 if).

n - 1

5 By this computation

An (0 Kn (f) occurs in the weighing block 15, the amount with accumulation is in the sum of

18 and memory 19, circulation in block 20. According to a clock pulse coming from the nineteenth output of micro-command generating unit 11 to the calculator's input 16 mass coefficients, the coefficients An (I) from the information output of the last one are weighed. At the same time, from the fourteenth output of the block 11, the sync signal is fed to the input of the memory block 14 and the synchronous input of the weighing unit 15. From the output of block 15, the product An О) Kn2 (f) is fed to the input of the adder 18, and from its input to the information input of the block. 19, the control and address inputs of which receive pulses from the fourteenth, sixteenth, seventeenth outputs of the microcommand formation unit 11. The combination of the adder 18 and block 19 forms a accumulating adder. From the output of block 19, the result of summation of 2 LL () Kp (O goes to

n 1

the second input of the adder 18 and the information input of the circulation unit 20; The control input of the block 20 receives pulses from the sixteenth output of the block 11; the output of the block 20 forms the spectrum estimate

G (f) 1 / (2 (1-1) Kp2 (f)), which is on pop - 1

The last 1st iteration is the resulting estimate of the spectrum G (f). At the moment of termination of the Nth iteration after I computations according to scheme (1), the obtained spectrum estimate with high accuracy corresponds to the a priori data of relation (2), thereby ensuring a high degree of proximity to the true spectrum G (f).

Claims (1)

DETAILED DESCRIPTION OF THE INVENTION A linear prediction spectral analysis method, comprising the analog signal being digitized, the result is stored and the input variance is determined at the same time, N iterative calculations are performed, and each n-iteration involves calculating forward and reverse errors predictions, partial correlation coefficients, variance P and linear prediction coefficients, Fourier transform linear prediction coefficients, characterized in that and the accuracy of the spectrum estimate, the Fourier transform is performed at each iteration, the squares of the amplitude-frequency characteristics of the prediction filters Kn2 (f) from the first to the N-ro inclusive are determined, after which step by step calculation of the mass coefficients by the ratio 25 (1 m (f) -RO f 1 §M) Ki2 (0 for given initial values of An and a constant coefficient for all numbers n is from 0 to N, then the obtained mass coefficients are multiplied by the corresponding squares of the transfer functions of the prediction filters, summarize these products and estimate the spectrum by inverse function of the sum result. 777