Rapid generation and analysis method for half-cycle matrix of pseudo-random signal

Abstract

The invention discloses a method for quickly generating and analyzing a half-cycle matrix of a pseudo-random signal, which comprises the following steps of: S1, adopting a plurality of frequencies of which the adjacent frequency ratio is 2, and taking the lowest frequency as the fundamental frequency of a 2n-sequence pseudo-random signal, forming a two-dimensional matrix consisting of # imgabs0 # elements according to the column number of the matrix generated by the multiple of the lowest frequency and the highest frequency and the row number of the matrix generated by the used frequency number in the bandwidth range of 2-7 to 214Hz; s2, summing the matrix according to columns by using a three-element self-closing addition principle, performing amplitude correction, and generating a one-dimensional pseudo-random signal time sequence at equal time intervals in a self-closing manner in a ternary number addition group # imgabs1 #; s3, the one-dimensional time sequence is sampled according to the sampling rate and the sampling time, analog-to-digital conversion is achieved, and a time domain discrete pseudo-random signal is formed; according to the method, the 2n sequence pseudo-random signal is rapidly generated without a complex mathematical process, and then spectrum analysis of the pseudo-random signal can be accurately and efficiently realized through mixed-base rapid Fourier transformation.

Description

Technical Field

[0001] The present invention belongs to the field of pseudo-random signal generation and analysis, and particularly relates to a method for quickly generating and analyzing a semi-period matrix of pseudo-random signals. Background Art

[0002] The wide-area electromagnetic method is an artificial-source frequency-domain electromagnetic sounding method, which inherits the advantages of the CSAMT method of using an artificial field source to overcome the randomness of the field source and the advantages of the MELOS method of non-far-zone measurement, expands the observation range of the artificial-source electromagnetic method, and improves the observation speed, accuracy and field work efficiency. In the early 1990s, He Jishan proposed a pseudo-random multi-frequency signal scheme, which has the advantages of a wide frequency range, basically equal amplitudes of each main frequency signal, intensity not decreasing with the increase of frequency, reasonable and uniform distribution of frequency points on the logarithmic coordinate, and wide coverage of the frequency range. In the exploration of the wide-area electromagnetic method, the requirements for the generation and analysis of pseudo-random signals are relatively high. The mathematical process of time-frequency analysis of pseudo-random multi-frequency signals in the existing methods is relatively complex, and it is analyzed as an analog signal. The algorithm calculation requirement is large and it is not easy to promote, and it is difficult to meet the requirements for signal processing in the new round of prospecting breakthrough. Summary of the Invention

[0003] In order to solve the above technical problems, the present invention proposes a method for quickly generating and analyzing a semi-period matrix of pseudo-random signals, which solves the problem of quickly generating a 2 n sequence pseudo-random signal by avoiding a complex mathematical process, and then through a mixed-radix fast Fourier transform, it can accurately and efficiently realize the spectrum analysis of the pseudo-random signal.

[0004] The technical solution provided by the present invention is as follows:

[0005] A method for quickly generating and analyzing a semi-period matrix of pseudo-random signals, comprising the following steps:

[0006] Step S1: Adopt multiple frequencies with adjacent frequency ratios of 2, use the lowest frequency as the fundamental frequency of the 2 n sequence pseudo-random signal, and generate the number of columns of the matrix and the number of frequencies used to generate the number of rows of the matrix within the bandwidth range of 2 -7 to 2 14 Hz by the multiple of the lowest and highest frequencies, forming a two-dimensional matrix composed of elements;

[0007] Step S2: Use the three-element self-closed addition principle to sum the matrix by column and perform amplitude correction, self-closed in the ternary addition group to generate an equal-time-interval one-dimensional pseudo-random signal time series;

[0008] Step S3: Sample the one-dimensional time series based on the sampling rate and sampling time to achieve analog-to-digital conversion, forming a discrete pseudo-random signal in the time domain;

[0009] Step S4: Generate a spectrum through a mixed-radix fast Fourier transform to analyze the power characteristics of the pseudo-random signal.

[0010] Preferably, step S1 includes the following sub-steps:

[0011] Sub-step S11: Select n adjacent frequencies with a frequency ratio of 2, and use the lowest frequency among them as the fundamental frequency of the 2 n sequence pseudo-random signal;

[0012] Sub-step S12: Assign values to each frequency component from high to low to obtain each row of the matrix, and obtain a generation matrix of the one-dimensional pseudo-random signal time series with n rows and 2 n columns where the number of signal cycle repetitions for each row is the ratio of its frequency to the lowest frequency.

[0013] Preferably, the one-dimensional pseudo-random signal time series in step S2 is:

[0014]

[0015] Preferably, the specific three-element self-closed addition principle in step S2 is:

[0016]

[0017] Sum the half-period matrix column by column and perform amplitude correction through the following formula;

[0018]

[0019] In the formula, n is the frequency of the selected signal, and e n is an n-row all-1 vector, is the generation matrix of the one-dimensional pseudo-random signal time series;

[0020]

[0021] Preferably, step S3 includes the following sub-steps:

[0022] Sub-step S31: Sample the one-dimensional pseudo-random signal time series based on the sampling rate f s and the sampling time t s ;

[0023] Sub-step S32: Repeat each element in the one-dimensional pseudo-random signal time series f s / 2 n times, and repeat the new sequence after repetition t sNext, perform analog-to-digital conversion to form a discrete pseudo-random signal in the time domain.

[0024] Preferably, step S4 includes the following sub-steps:

[0025] Sub-step S41: Mix the discrete pseudo-random signal in the time domain obtained by analog-to-digital conversion according to the sampling rate f s and the sampling time t s ;

[0026] Sub-step S42: Obtain the spectrum according to the mixed-radix fast Fourier transform. The highest frequency of the spectrum is f s / 2, and extract the amplitudes of n main frequencies from the spectrum.

[0027] Preferably, sub-step S42 includes the following sub-steps:

[0028] Sub-step S421: Decompose the one-dimensional pseudo-random signal time series x(n) into p groups, and there is N = p·q,

[0029] Sub-step S422: Calculate through the following formula

[0030]

[0031] In the above formula, r = 0, 1,..., q - 1,

[0032]

[0033] where W is the weight of the mixed-radix fast Fourier transform, and its definition is

[0034] The beneficial effects of the method for quickly generating and analyzing the semi-period matrix of the pseudo-random signal of the present invention are as follows:

[0035] 1. The present invention uses matrix operations to replace algebraic operations, with a simple mathematical form and is easy to design a fast algorithm for generating pseudo-random signals; matrix operations satisfy the self-closed ternary number addition group and are easy to apply pseudo-random signals in actual production.

[0036] 2. The present invention uses matrix operations to generate a one-dimensional pseudo-random signal time series, improving the speed and accuracy of generating pseudo-random signals.

[0037] 3. According to the sampling rate and sampling time, the present invention can improve the convergence speed of the spectrum of the pseudo-random signal and obtain more accurate power information.

[0038] 4. The present invention uses the mixed-radix fast Fourier transform to improve the efficiency of the fast algorithm for generating pseudo-random signals, and can effectively avoid spectrum leakage and ensure the accuracy of spectrum calculation and analysis. Description of the Drawings

[0039] To more clearly elaborate the purpose, design concept, and innovation of the multi-source remote sensing cross-domain classification method based on the hierarchical mask adversarial network proposed by the present invention, the present invention will be described in detail below in conjunction with the accompanying drawings and tables.

[0040] Figure 1 The 9-frequency pseudo-random signal generated by the half-cycle - matrix pseudo-random signal generation method of the present invention and its spectrum.

[0041] Figure 2 The 15-frequency pseudo-random signal generated by the half-cycle - matrix pseudo-random signal generation method of the present invention and its spectrum.

[0042] Figure 3 The computational flowchart of the present invention. Specific Embodiments

[0043] The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0044] The following describes the specific embodiments of the present invention to facilitate those skilled in the art of the present technology to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art of the present technology, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concept of the present invention are within the scope of protection.

[0045] A method for fast generation and analysis of a half-cycle matrix of pseudo-random signals, comprising the following steps:

[0046] Step S1: Use multiple frequencies with an adjacent frequency ratio of 2, with the lowest frequency as the fundamental frequency of the 2n-sequence pseudo-random signal, and generate the number of columns of the matrix and the number of frequencies used to generate the number of rows of the matrix within the bandwidth range of 2 -7 ~2 14 Hz by the multiple of the lowest and highest frequencies to form a two-dimensional matrix composed of elements.

[0047] Step S2: Use the three-element self-closed addition principle to sum the matrix by column and perform amplitude correction, self-closed in the ternary number addition group to generate an equally spaced one-dimensional pseudo-random signal time series.

[0048] Step S3: Sample the one-dimensional time series by the sampling rate and sampling time to achieve analog-to-digital conversion and form a time-domain discrete pseudo-random signal.

[0049] Step S4: Generate a spectrum through a mixed-radix fast Fourier transform to analyze the power characteristics of the pseudo-random signal.

[0050] Step S1 of this implementation scheme includes the following sub-steps:

[0051] Sub-step S11: Select n adjacent frequencies with a frequency ratio of 2, and use the lowest frequency among them as the fundamental frequency of the sequence pseudo-random signal; n Sequence pseudo-random signal fundamental frequency;

[0052] Sub-step S12: Assign values to each frequency component from high to low to obtain each row of the matrix, and obtain a generation matrix of a one-dimensional pseudo-random signal time series with n rows and 2 columns n Column one-dimensional pseudo-random signal time series generation matrix Among them, the number of signal cycle repetitions in each row is the ratio of its frequency to the lowest frequency.

[0053] The one-dimensional pseudo-random signal time series of step S2 of this implementation scheme is:

[0054]

[0055] The specific content of the three-element self-closed addition principle of step S2 of this implementation scheme is:

[0056]

[0057] Sum the semi-period matrix by column and perform amplitude correction through the following formula;

[0058]

[0059] In the formula, n is the frequency of the selected signal, e n Is an n-row all-1 vector, Is the generation matrix of the one-dimensional pseudo-random signal time series;

[0060]

[0061] Step S3 of this implementation scheme includes the following sub-steps:

[0062] Sub-step S31: Sample the one-dimensional pseudo-random signal time series by the sampling rate f s And the sampling time t s Sample the one-dimensional pseudo-random signal time series;

[0063] Sub-step S32: Repeat each element in the one-dimensional pseudo-random signal time series f s / 2 n Times, and repeat the new sequence after repetition t s Times to achieve analog-to-digital conversion and form a time-domain discrete pseudo-random signal.

[0064] Step S4 of this implementation scheme includes the following sub-steps:

[0065] Sub-step S41: According to the sampling rate f s And the sampling time t sMix the discrete pseudo-random signal in the time domain obtained by analog-to-digital conversion;

[0066] Sub-step S42: Obtain the spectrum according to the mixed-radix fast Fourier transform. The highest frequency of the spectrum is f s / 2, and extract the amplitudes of n main frequencies from the spectrum.

[0067] Sub-step S42 of this implementation scheme includes the following sub-steps:

[0068] Sub-step S421: Decompose the one-dimensional pseudo-random signal time series x(n) into p groups, and N = p·q,

[0069] Sub-step S422: Calculate through the following formula

[0070]

[0071] In the above formula, r = 0, 1,..., q - 1,

[0072]

[0073] Among them, W is the weight of the mixed-radix fast Fourier transform, and its definition is

[0074] When this implementation scheme is implemented,

[0075] The specific steps of the present invention are as follows:

[0076] 1. Generation of semi-period matrix

[0077] (1) Determine the number of rows and columns of the matrix according to the frequency n;

[0078] (2) Recursively generate the matrix of the one-dimensional pseudo-random signal time series through the following formula:

[0079]

[0080] ...

[0082] 2. Calculation and amplitude correction of one-dimensional pseudo-random signal time series

[0083] Based on the following calculation rules of the self-closed ternary number addition group:

[0084]

[0085] Sum the columns of the generation matrix of the one-dimensional pseudo-random signal time series and perform amplitude correction through the following formula:

[0086]

[0087] where, e n is an n-row all-1 vector. The pseudo-random signal is generated recursively through the following formula:

[0088] ...

[0090] 3. Sampling and analog-to-digital conversion

[0091] (1) Repeat each element in the one-dimensional pseudo-random signal time series f s / 2 n times;

[0092] (2) Repeat the new sequence after repetition t s times to achieve analog-to-digital conversion and form a discrete pseudo-random signal in the time domain.

[0093] 4. Calculation of frequency-power spectrum

[0094] (1) Calculate the mixed-radix Fourier transform through the following formula

[0095]

[0096] In the above formula

[0097] r = 0, 1, …, q - 1

[0098]

[0099] where, k = 1, 2,..., N - 1.

[0100] (2) Take the modulus |x(e 2πfj )| of the obtained frequency-domain signal X(e 2πfj ) to obtain the spectrum.

Claims

1. A method for quickly generating and analyzing a semi - period matrix of a pseudo - random signal, characterized in that, Including the following steps: Step S1: Use multiple frequencies with a frequency ratio of 2 between adjacent ones, and take the lowest frequency as 2 n as the fundamental frequency of the sequence pseudo-random signal. Within the bandwidth of 2 -7 to 2 14 Hz, generate the number of columns of the matrix through the multiple of the lowest and highest frequencies, and generate the number of rows of the matrix of the used frequencies, forming a two-dimensional matrix composed of elements; Step S2: Sum the matrix column by column and perform amplitude correction using the three-element self-closed addition principle, which is self-closed in the ternary number addition group Generate a one-dimensional pseudo-random signal time series with equal time intervals; Step S3: Sampling the one-dimensional time series by the sampling rate and sampling time to achieve analog-to-digital conversion, forming a discrete pseudo-random signal in the time domain; Step S4: Generating a spectrum through a mixed-radix fast Fourier transform to analyze the power characteristics of the pseudo-random signal.

2. The method for fast generation and analysis of the semi-period matrix of the pseudo-random signal according to claim 1, characterized in that The said step S1 includes the following sub-steps: Sub-step S11: Select n adjacent frequencies with a frequency ratio of 2, and use the lowest frequency among them as the fundamental frequency of the sequence pseudo-random signal; n ​ Sub-step S12: Each frequency component is assigned values from high to low to obtain each row of the matrix, resulting in a generation matrix of a one-dimensional pseudo-random signal time series with n rows and 2 n columns Among them, the number of signal cycle repetitions for each row is the ratio of its frequency to the lowest frequency.

3. The method for fast generation and analysis of the half - period matrix of the pseudo - random signal according to claim 1, wherein The one-dimensional pseudo-random signal time series of the said step S2 is:

4. The method for fast generation and analysis of the half-period matrix of the pseudo-random signal according to claim 1, wherein The specific of the three-element self-closed addition principle of the said step S2 is: Summating the semi-period matrix column by column and performing amplitude correction through the following formula: where n is the frequency of the selected signal, and e n is an all-ones vector of n rows, is the generation matrix of the one-dimensional pseudo-random signal time series; 5. The method for quickly generating and analyzing the half-period matrix of a pseudo-random signal according to claim 1, wherein The said step S3 includes the following sub-steps: Sub-step S31: Sampling the one-dimensional pseudo-random signal time series with a sampling rate f s and a sampling time t s ; Sub-step S32: Repeat each element in the one-dimensional pseudo-random signal time series f s / 2 n times, and repeat the new sequence after repetition t s times to achieve analog-to-digital conversion and form a discrete pseudo-random signal in the time domain.

6. The method for fast generation and analysis of the half-period matrix of the pseudo-random signal according to claim 1, characterized in that The said step S4 includes the following sub-steps: Sub-step S41: Mix the discrete pseudo-random signal in the time domain obtained by analog-to-digital conversion according to the sampling rate f s and the sampling time t s ​ Sub-step S42: Obtain the spectrum according to the mixed-radix fast Fourier transform. The highest frequency of the spectrum is f s / 2, and extract the amplitudes of n main frequencies from the spectrum.

7. The method for fast generation and analysis of the half-period matrix of a pseudo-random signal according to claim 6, characterized in that The said sub-step S42 includes the following sub-steps: Sub-step S421: Decomposing the one-dimensional pseudo-random signal time series x(n) into p groups, and N = p·q, Sub-step S422: Calculating through the following formula In the above formula, r = 0, 1, …, q - 1, Among them, W is the weight of the mixed-radix fast Fourier transform, and its definition is

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