Signal sample consistency test method based on instantaneous characteristic statistical distribution

Abstract

The invention provides a signal sample consistency test method based on instantaneous characteristic statistical distribution, and the method comprises the following steps: S1, generating a corresponding modulation simulation signal according to a modulation type adopted by a real signal, and the simulation signal does not consider the influence of a transmission channel; s2, calculating an instantaneous phase, an instantaneous frequency and an instantaneous amplitude of the noise-containing AM simulation signal, and calculating corresponding feature distribution; and S3, calculating a correlation coefficient, performing sample consistency check, and verifying and judging the consistency between the noise-containing AM simulation signal and the real signal. According to the method, the confidence index of the simulation signal is given, so that the sample quality can be directly judged, and the implementation of a simulation project is guided.

Description

Technical Field

[0001] The present invention belongs to the field of data engineering, and in particular relates to a signal sample consistency verification method based on instantaneous characteristic statistical distribution. Background Art

[0002] At present, big data models such as deep learning have been widely developed and applied, but deep learning models usually require a large amount of training data to optimize their parameters when processing complex tasks, so as to ensure that the model has high generalization ability and accuracy. However, in specific fields of practical applications, especially in the field of signal processing, it is often difficult to obtain enough high-quality real data. Since real data and simulated data have the same source, simulated data can be used instead of real data as training set samples. At the same time, this will lead to weak robustness and generalization ability of the training model. Therefore, the verification method of simulated signals is a very important and worthy direction in the field of data engineering. It is of great significance to ensure the effectiveness of simulation results, guide model improvement, and support decision making.

[0003] As early as 1959, Conway proposed the problem of model verification in the simulation process (Conway RW, Johnson BM, Maxwell WL. Some Problems of Digital Systems Simulation [J]. Management Science, 1959, 6 (1): 92-110). The concept of simulation experiment verification and validation was first formally proposed in 1967 (Mckenny JL. Critique of "Verification of Computer Simulation Models" [J].); Shannon further pointed out in 1975 that the simulation model should be verified by comparing the simulation experiment output with the real experiment output when the simulation model input is equal to the real object input (Shannon R E. Tests for the verification and validation of computer simulation models [C] / / 1981: 573-577.).

[0004] The earliest methods used in static data consistency test were hypothesis test methods including T test, U test, etc. In 1969, Gafarian and Walsh et al. proposed to apply non-parametric test (including chi-square test, Smirnov test, etc.), variance analysis, interval estimation and other methods to static data consistency test (Li Shu. Research on Missile System Simulation Model Verification Method [D]. Changsha: Master's Thesis of National University of Defense Technology, 2013: 61-63.). In 1984, Balci and Sargent proposed the confidence interval method (Montgomery DC, Conard RG Comparison of Simulation and Flight-test Data for Missile Systems [J]. Simulation, 1980, 34 (2): 63-72.).

[0005] In the field of quantitative method evaluation, time domain signal verification was first started. As early as 1972, Wigan used a simple regression method to conduct preliminary verification of time signals (Kheir NA, Holmes WM. On Validating Simulation Models of Missile Systems [J]. Simulation, 1978, 30 (4): 117-128.). Later, in 1978, Kheir and Holmes introduced the TIC method results (Theil Inequality Coefficient) used in economic model forecasting, that is, Saybolt's coefficient, into the model verification work and used it in the data verification of a flight simulation experiment. Therefore, the TIC method began to be widely used in model verification work. In view of the shortcomings of the TIC method in verifying sparse signal data, Ronald optimized it (Murphy DC. Calculation of gini and the ilinequality coefficients for Irish household incomes in 1973 and 1980 [J]. Economic & Social Review, 1985, 16 (3): 225-249.).

[0006] The frequency domain data consistency verification method was first proposed by Fishman and Kiviat in 1967 (Fishman GS, Kiviat P J. The Analysis of Simulation-Generated Time Series [J]. Management Science, 1967, 13 (7): 525-557.), which defined the equivalence of the two frequency spectra between the simulation experimental data and the actual experimental data, and combined the corresponding verification steps to verify the reliability of the queue simulation experiment. Later, Tytula proposed a scheme for verifying the stationary random signal by using the statistical probability distribution density (Tytula T PA method for validating missile system simulation models [J]. A Method for Validating Missile System Simulation Models, 1978, 78.). Montgomery estimated the frequency spectrum of aircraft simulation experiment and actual experimental data based on the classical Fourier transform, combined with the characteristics of random processes to construct hypothesis tests and complete the mathematical statistical verification of data consistency (Montgomery, Douglas C. Design and analysis of experiments / -2nd ed [M]. Wiley, 2000.). DJ Ewins, B Weekes, D Carri et al. used the model testing method to verify the structure of discrete nonlinear models (Ewins DJ, Weekes B, Carri A D. Modal testing for model validation of structures with discrete nonlinearities [J]. 2015, 373 (2051).). Ma YT proposed a specific VV&A (Verification, Validation and Accretions) plan for rocket engine model verification (Ma YT, Wang XR, Zha BL, et al. Research on VV&A Strategy of Modeling and Simulation for Rocket Motor[C] / / Asian Simulation Conference. Springer Singapore, 2016: 553-560.).Murray Smith of Glasgow University proposed a model validation method based on reverse validation, which introduced the method of reversely deriving inputs based on the same output in model establishment into model validation (Murray Smith DJ, Wong B O. Inverse simulation techniques applied to the external validation of nonlinear models [J]. 1997.). Cho IK used the model validation method to validate the model obtained by machine learning (Cho IK, Kasa K. Learning and Model Validation [J]. Review of Economic Studies, 2015, 82 (1): págs. 45-82.). In 2016, Zecheng Li et al. applied cloud computing to the validation of simulation models (Li Z, Liao L, Leung H, et al. Evaluating the credibility of cloud services [J]. Computers & Electrical Engineering, 2016.).

[0007] Although there are many consistency test evaluation methods, there is no method that can directly detect the consistency between simulated signals and actual data. Usually, when using simulated signals instead of real signals as training data set samples for deep learning systems, the final inference results are needed as the evaluation index of the qualification of the simulated signals, which lacks a direct basis for judgment. Summary of the invention

[0008] In view of the problems existing in the prior art, the present invention proposes a signal sample consistency verification method based on instantaneous feature statistical distribution, which specifically includes the following steps:

[0009] S1: Generate a corresponding modulation simulation signal according to the modulation type used by the real signal, and the simulation signal does not consider the influence of the transmission channel;

[0010] S2: Calculate the instantaneous phase, instantaneous frequency, instantaneous amplitude of the noisy AM simulation signal, and calculate the corresponding characteristic distribution;

[0011] S3: Calculate the correlation coefficient, perform sample consistency test, and verify the consistency between the noisy AM simulation signal and the real signal.

[0012] In one embodiment of the present invention, step S1 is specifically as follows:

[0013] S11: Determine the modulation type of the real signal;

[0014] Determine the corresponding simulation signal modulation type according to the modulation type of the real signal;

[0015] S12: Determine actual relevant parameters of the modulation project according to the modulation type;

[0016] The range of the actual relevant parameters of the modulation project is determined by the corresponding modulation type; the specific values ​​of the actual relevant parameters of the modulation project are determined by the corresponding international standards;

[0017] S13: Determine the time range of the real signal, observe and record the bandwidth and power spectrum parameters of the real signal;

[0018] The time range of the simulated signal is completely consistent with the time length of the real signal, and the time length of the real signal is recorded as T; the bandwidth of the real signal is directly obtained from the spectrum diagram results of the signal analysis software, and the power spectrum is obtained from the power spectrum diagram results of the signal analysis software;

[0019] S14: Generate a simulation signal according to the modulation type and parameters determined in S12 and S13;

[0020] Assume that the real signal s AM (t) has been identified as AM modulation in step S11, the time range of the modulation signal and the bandwidth and power spectrum parameters of the signal are obtained in step S13, and simulation is performed based on the above parameters in step S14;

[0021] Assume m(t) is a simulated signal to be modulated, the signal length is consistent with the time range of the simulated signal in S13, and AM modulation is used to generate a simulated AM modulated signal s AM1 (t) is expressed as follows

[0022]

[0023] Where A represents the carrier amplitude; t is the signal duration, and the signal duration t of m(t) ranges from [0 to T]; f c is the modulated carrier frequency, is the initial phase of the carrier;

[0024] S15: applying noise to the simulated AM modulated signal;

[0025] s AM2 (t) = s AM1 (t)+n(t)

[0026] Among them, s AM2 (t) is a noisy AM simulation signal, the simulation noise n(t) is Gaussian white noise, the noise mean is 0, and the variance is set according to the simulation requirements.

[0027] In a specific embodiment of the present invention, in step S14, the initial phase is set to a random phase.

[0028] In another embodiment of the present invention, step S2 is specifically as follows:

[0029] S21: The real signal s AM (t) and the noisy AM simulation signal s AM2 (t) is expanded into the real part and the imaginary part respectively;

[0030] s AM (t)=I(t)+jQ(t)

[0031] s AM2 (t)=I2(t)+jQ2(t)

[0032] Among them, I(t)+jQ(t) is s AM (t) is expanded in the form of real and imaginary parts, I(t) is the real part, Q(t) is the imaginary part, and the same is true for I2(t)+jQ2(t);

[0033] S22: Calculate the real signal s AM (t) and the noisy AM simulation signal s AM2 The instantaneous phase of (t) is normalized to obtain the instantaneous phase distribution value;

[0034]

[0035]

[0036] in, and They represent the instantaneous phase of the real signal and the noisy AM simulation signal respectively. arctan() is the inverse tangent function. The instantaneous phase value is between; and They represent the instantaneous phase mean of the real signal and the noisy AM simulation signal, and They represent the instantaneous phase standard deviation of the real signal and the simulated signal with noise, and They represent the instantaneous phase normalized values ​​of the real signal and the noisy AM simulated signal respectively;

[0037] S23: Calculate the instantaneous frequency of the real signal and the noisy AM simulation signal, and normalize them;

[0038]

[0039] Where f(t) and f2(t) represent the instantaneous frequencies of the real signal and the noisy AM simulation signal, respectively, and π is the circumference of a circle. is a mathematical differential operator; μ f and Respectively represent the instantaneous frequency mean of the real signal and the noisy AM simulation signal, σ f and They represent the instantaneous frequency standard deviations of the real signal and the noisy AM simulated signal, respectively, and f′(t) and f2′(t) represent the instantaneous frequency normalized values ​​of the real signal and the noisy AM simulated signal, respectively;

[0040] S24: calculating the instantaneous envelopes of the real signal and the noisy AM simulation signal, and normalizing them;

[0041]

[0042] Where a(t) and a2(t) represent the instantaneous envelope of the real signal and the noisy AM simulated signal respectively; μ a and Respectively represent the instantaneous envelope mean of the real signal and the noisy AM simulation signal, σ a and They represent the instantaneous envelope standard deviations of the real signal and the noisy AM simulated signal respectively, and a′(t) and a2′(t) represent the normalized values ​​of the instantaneous envelopes of the real signal and the noisy AM simulated signal respectively.

[0043] In another embodiment of the present invention, step S3 is specifically as follows:

[0044] S31: Calculate the correlation coefficient of the instantaneous phase characteristics of the real signal and the noisy AM simulation signal, and obtain the consistency of the instantaneous phase characteristics of the sample;

[0045]

[0046] In the formula, Represents the correlation coefficient between the instantaneous frequency statistics of the real signal and the noisy AM simulation signal;

[0047] when When , it means there is no linear correlation, that is, the instantaneous phase characteristics of the samples are inconsistent; when When , it indicates weak correlation, that is, the instantaneous phase characteristics of the samples are less consistent; when When , it indicates moderate correlation, that is, the instantaneous phase characteristics of the samples have moderate consistency; when When , it indicates that the correlation is strong, that is, the instantaneous phase characteristics of the samples are highly consistent; when When , it indicates complete correlation, that is, the instantaneous phase characteristics of the samples are completely consistent;

[0048] S32: Calculate the correlation coefficient of the instantaneous frequency characteristics of the real signal and the AM simulation signal containing noise, and obtain the consistency of the instantaneous frequency characteristics of the sample;

[0049]

[0050] In the formula, r f Represents the correlation coefficient between the instantaneous frequency statistics of the real signal and the noisy AM simulation signal;

[0051] When | r f When |=0, it means there is no linear correlation, that is, the instantaneous frequency characteristics of the samples are inconsistent; when 0<|r f |<0.3, it indicates weak correlation, that is, the consistency of the instantaneous frequency characteristics of the samples is weak; when 0.3≤|r f |<0.7, it indicates moderate correlation, that is, the instantaneous frequency characteristics of the samples have moderate consistency; when 0.7≤|r f |<1, it indicates strong correlation, that is, the instantaneous frequency characteristics of the samples are highly consistent; when |r f When |=1, it indicates complete correlation, that is, the instantaneous frequency characteristics of the samples are completely consistent;

[0052] S33: Calculate the correlation coefficient of the instantaneous envelope characteristics of the real signal and the AM simulation signal containing noise, and obtain the consistency of the instantaneous envelope characteristics of the sample;

[0053]

[0054] In the formula, r a Represents the correlation coefficient between the instantaneous envelope statistics of the real signal and the noisy AM simulation signal;

[0055] When | r a When |=0, it means there is no linear correlation, that is, the instantaneous envelope characteristics of the samples are inconsistent; when 0<|r a |<0.3, it indicates weak correlation, that is, the instantaneous envelope feature consistency of the sample is weak; when 0.3<|r a |<0.7, it indicates moderate correlation, that is, the instantaneous envelope feature consistency of the sample is moderate; when 0.7≤|r a |<1, it indicates strong correlation, that is, the instantaneous envelope characteristics of the samples are highly consistent; when |r a When |=1, it indicates complete correlation, that is, the instantaneous envelope characteristics of the samples are completely consistent.

[0056] The present invention starts with the instantaneous characteristics of the signal (instantaneous phase, instantaneous frequency, instantaneous amplitude), and proposes to test the consistency of the simulated signal and the real signal through the correlation coefficient of the characteristic statistical distribution. The advantages of the present invention are: using the direct detection method of the correlation coefficient instead of data training to indirectly test the credibility of the simulated data, giving the qualification criterion of the simulated sample, and testing the simulated signal in the data set before deep learning training data, which greatly saves the time, manpower and material resources in deep learning. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is a flow chart of a signal sample consistency verification method based on instantaneous characteristic statistical distribution according to an embodiment of the present invention. DETAILED DESCRIPTION

[0058] Aiming at aviation communications in actual scenarios, the present invention models and simulates typical modulation signals, extracts their instantaneous characteristics, and verifies and evaluates the consistency of the statistical distribution of the instantaneous characteristics of the simulated signals and the real signals.

[0059] A signal sample consistency verification method based on instantaneous feature statistical distribution according to an embodiment of the present invention includes:

[0060] S1: Generate a corresponding modulation simulation signal according to the modulation type used by the real signal, etc. The simulation signal of the present invention does not consider the influence of the transmission channel for the time being;

[0061] The details are as follows:

[0062] S11: Determine the modulation type of the real signal;

[0063] The purpose of this step is to determine the corresponding simulation signal modulation type according to the modulation type of the real signal.

[0064] The modulation type of the real signal is realized by an automatic modulation recognition algorithm, such as modulation recognition based on cumulative amount, modulation recognition based on constellation diagram, etc. Such algorithms do not belong to the protection scope of the present invention. The specific method of determining the corresponding modulation type of the simulated signal according to the modulation type of the real signal is well known to those skilled in the art and will not be repeated.

[0065] S12: Determine actual relevant parameters of the modulation project according to the modulation type;

[0066] The range of the actual relevant parameters of the modulation project is determined by the corresponding modulation type, such as AM modulation depth, FSK symbol rate, etc. The specific values ​​of the actual relevant parameters of the modulation project are determined by the corresponding international standards, and the measurement method of the parameters does not belong to the protection scope of the present invention.

[0067] S13: Determine the time range of the real signal, observe and record the bandwidth and power spectrum parameters of the real signal;

[0068] The time range of the simulated signal is completely consistent with the time length of the real signal, and the time length of the real signal is recorded as T. The bandwidth of the real signal can be directly obtained from the spectrum result of the signal analysis software, and the power spectrum can be obtained from the power spectrum result of the signal analysis software. The signal analysis software includes but is not limited to Matlab, etc., and the codes and commands involved in the analysis software do not belong to the scope of the present invention.

[0069] S14: Generate a simulation signal according to the modulation type and parameters determined in S12 and S13;

[0070] The generation of simulation signals can be performed in software including but not limited to Matlab, and the codes and commands involved in the simulation software do not belong to the scope of the present invention and are considered to be known.

[0071] In one embodiment of the present invention, it is assumed that the real signal (denoted as s AM (t)) has been identified as AM modulation in step S11, and the time range of the modulated signal and the bandwidth (modulation frequency) and power spectrum parameters (carrier amplitude) of the signal are obtained in S13. Step S14 will perform simulation based on the above parameters.

[0072] Assume m(t) is a simulated signal to be modulated (such as a voice signal or any other signal sequence), the signal length is consistent with the simulated signal time range in S13, and AM modulation is used to generate a simulated AM modulated signal s AM1 (t) is expressed as follows

[0073]

[0074] Wherein, A represents the carrier amplitude; t is the signal duration, and the signal duration t of m(t) ranges from [0 to T]. The actual signal to be modulated, in this embodiment, is a voice signal or an arbitrary signal sequence, and its length is consistent with the simulation signal time range in S13; f c is the modulated carrier frequency, is the initial phase of the carrier. The initial phase is generally random and its result does not affect subsequent steps.

[0075] S15: applying noise to the simulated AM modulated signal;

[0076] Take the AM modulation in S14 above as an example

[0077] s AM2 (t) = s AM1 (t)+n(t)

[0078] Among them, s AM2(t) is a noisy AM simulation signal, the simulation noise n(t) is Gaussian white noise, the noise mean is 0, and the variance is set according to the simulation requirements and is generally not fixed.

[0079] S2: Calculate the instantaneous phase, instantaneous frequency, instantaneous amplitude of the noisy AM simulation signal, and calculate the corresponding characteristic distribution;

[0080] The details are as follows:

[0081] S21: The real signal s AM (t) and the noisy AM simulation signal s AM2 (t) is expanded into the real part and the imaginary part respectively;

[0082] s AM (t)=I(t)+jQ(t)

[0083] s AM2 (t)=I2(t)+jQ2(t)

[0084] Among them, I(t)+jQ(t) is s AM (t) is expanded in the form of real and imaginary parts using the series expansion and Euler's formula in mathematics, where I(t) is the real part and Q(t) is the imaginary part, and the same goes for I2(t)+jQ2(t).

[0085] S22: Calculate the real signal s AM (t) and the noisy AM simulation signal s AM2 The instantaneous phase of (t) is normalized to obtain the instantaneous phase distribution value;

[0086]

[0087] in, and They represent the instantaneous phase of the real signal and the noisy AM simulated signal, is the mathematical square root operator, arctan() is the inverse tangent function, and the instantaneous phase value is between. and They represent the instantaneous phase mean of the real signal and the noisy AM simulation signal, and They represent the instantaneous phase standard deviation of the real signal and the simulated signal with noise, and They represent the instantaneous phase normalized values ​​of the real signal and the noisy AM simulated signal respectively.

[0088] S23: Calculate the instantaneous frequency of the real signal and the noisy AM simulation signal, and normalize them;

[0089]

[0090] Where f(t) and f2(t) represent the instantaneous frequencies of the real signal and the noisy AM simulation signal, respectively, and π is the circumference of a circle. Is the mathematical differential operator. f and Respectively represent the instantaneous frequency mean of the real signal and the noisy AM simulation signal, σ f and They represent the instantaneous frequency standard deviations of the real signal and the noisy AM simulated signal respectively, and f′(t) and f2′(t) represent the instantaneous frequency normalized values ​​of the real signal and the noisy AM simulated signal respectively.

[0091] S24: calculating the instantaneous envelopes of the real signal and the noisy AM simulation signal, and normalizing them;

[0092]

[0093] Where a(t) and a2(t) represent the instantaneous envelope of the real signal and the noisy AM simulated signal, respectively. a and Respectively represent the instantaneous envelope mean of the real signal and the noisy AM simulation signal, σ a and They represent the instantaneous envelope standard deviations of the real signal and the noisy AM simulated signal respectively, and a′(t) and a2′(t) represent the instantaneous envelope normalized values ​​of the real signal and the noisy AM simulated signal respectively.

[0094] S3: Calculate the correlation coefficient and perform sample consistency test to verify the consistency between the noisy AM simulation signal and the real signal;

[0095] The details are as follows:

[0096] S31: Calculate the correlation coefficient of the instantaneous phase characteristics of the real signal and the noisy AM simulation signal, and obtain the consistency of the instantaneous phase characteristics of the sample;

[0097]

[0098] In the formula, Represents the correlation coefficient between the instantaneous frequency statistics of the real signal and the noisy AM simulated signal.

[0099] when When , it means there is no linear correlation, that is, the instantaneous phase characteristics of the samples are inconsistent; when When , it indicates weak correlation, that is, the instantaneous phase characteristics of the samples are less consistent; when When , it indicates moderate correlation, that is, the instantaneous phase characteristics of the samples have moderate consistency; when When , it indicates that the correlation is strong, that is, the instantaneous phase characteristics of the samples are highly consistent; when , it indicates complete correlation, that is, the instantaneous phase characteristics of the samples are completely consistent.

[0100] S32: Calculate the correlation coefficient of the instantaneous frequency characteristics of the real signal and the AM simulation signal containing noise, and obtain the consistency of the instantaneous frequency characteristics of the sample;

[0101]

[0102] In the formula, r f Represents the correlation coefficient between the instantaneous frequency statistics of the real signal and the noisy AM simulated signal.

[0103] When | r f When |=0, it means there is no linear correlation, that is, the instantaneous frequency characteristics of the samples are inconsistent; when 0<|r f |<0.3, it indicates weak correlation, that is, the consistency of the instantaneous frequency characteristics of the samples is weak; when 0.3≤|r f |<0.7, it indicates moderate correlation, that is, the instantaneous frequency characteristics of the samples have moderate consistency; when 0.7≤|r f |<1, it indicates strong correlation, that is, the instantaneous frequency characteristics of the samples are highly consistent; when |r f When |=1, it indicates complete correlation, that is, the instantaneous frequency characteristics of the samples are completely consistent.

[0104] S33: Calculate the correlation coefficient of the instantaneous envelope characteristics of the real signal and the AM simulation signal containing noise, and obtain the consistency of the instantaneous envelope characteristics of the sample;

[0105]

[0106] In the formula, r a It represents the correlation coefficient between the instantaneous envelope statistics of the real signal and the noisy AM simulation signal. a When |=0, it means there is no linear correlation, that is, the instantaneous envelope characteristics of the samples are inconsistent; when 0<|r a |<0.3, it indicates weak correlation, that is, the instantaneous envelope feature consistency of the sample is weak; when 0.3≤|r a |<0.7, it indicates moderate correlation, that is, the instantaneous envelope feature consistency of the sample is moderate; when 0.7≤|r a |<1, it indicates strong correlation, that is, the instantaneous envelope characteristics of the samples are highly consistent; when |r a When |=1, it indicates complete correlation, that is, the instantaneous envelope characteristics of the samples are completely consistent.

Claims

1. A signal sample consistency test method based on instantaneous characteristic statistical distribution, characterized in that: The specific steps include: S1: Generate a corresponding modulation simulation signal according to the modulation type used by the real signal, and the simulation signal does not consider the influence of the transmission channel; S2: Calculate the instantaneous phase, instantaneous frequency, instantaneous amplitude of the noisy AM simulation signal, and calculate the corresponding characteristic distribution; S3: Calculate the correlation coefficient, perform sample consistency test, and verify the consistency between the noisy AM simulation signal and the real signal.

2. The signal sample consistency verification method based on instantaneous characteristic statistical distribution according to claim 1, characterized in that: Step S1 is specifically as follows: S11: Determine the modulation type of the real signal; Determine the corresponding simulation signal modulation type according to the modulation type of the real signal; S12: Determine actual relevant parameters of the modulation project according to the modulation type; The range of the actual relevant parameters of the modulation project is determined by the corresponding modulation type; The specific values ​​of the actual relevant parameters of the modulation project are determined by the corresponding international standards; S13: Determine the time range of the real signal, observe and record the bandwidth and power spectrum parameters of the real signal; The time range of the simulated signal is completely consistent with the time length of the real signal, and the time length of the real signal is recorded as T; the bandwidth of the real signal is directly obtained from the spectrum diagram results of the signal analysis software, and the power spectrum is obtained from the power spectrum diagram results of the signal analysis software; S14: Generate a simulation signal according to the modulation type and parameters determined in S12 and S13; Assume that the real signal s AM (t) has been identified as AM modulation in step S11, the time range of the modulation signal and the bandwidth and power spectrum parameters of the signal are obtained in step S13, and simulation is performed based on the above parameters in step S14; Assume m(t) is a simulated signal to be modulated, the signal length is consistent with the time range of the simulated signal in S13, and AM modulation is used to generate a simulated AM modulated signal s AM1 (t) is expressed as follows Where A represents the carrier amplitude; t is the signal duration, and the signal duration t of m(t) ranges from [0 to T]; f c is the modulated carrier frequency, is the initial phase of the carrier; S15: applying noise to the simulated AM modulated signal; s AM2 (t)=s AM1 ((t)+n(t) Among them, s AM2 (t) is a noisy AM simulation signal, the simulation noise n(t) is Gaussian white noise, the noise mean is 0, and the variance is set according to the simulation requirements.

3. The signal sample consistency verification method based on instantaneous characteristic statistical distribution according to claim 2, characterized in that: In step S14, the initial phase is set to a random phase.

4. The signal sample consistency verification method based on instantaneous characteristic statistical distribution according to claim 2, characterized in that: Step S2 is specifically as follows: S21: The real signal s AM (t) and the noisy AM simulation signal s AM2 (t) is expanded into the real part and the imaginary part respectively; s AM (t)=I(t)+jQ(t) s AM2 (t)=I2(t)+jQ2(t) Among them, I(t)+jQ(t) is s AM (t) is expanded in the form of real and imaginary parts, I(t) is the real part, Q(t) is the imaginary part, and the same is true for I2(t)+jQ2(t); S22: Calculate the real signal s AM (t) and the noisy AM simulation signal s AM2 The instantaneous phase of (t) is normalized to obtain the instantaneous phase distribution value; in, and They represent the instantaneous phase of the real signal and the noisy AM simulated signal respectively. arctan() is the inverse tangent function. The instantaneous phase value is between; and They represent the instantaneous phase mean of the real signal and the noisy AM simulation signal, and They represent the instantaneous phase standard deviation of the real signal and the simulated signal with noise, and They represent the instantaneous phase normalized values ​​of the real signal and the noisy AM simulated signal respectively; S23: Calculate the instantaneous frequency of the real signal and the noisy AM simulation signal, and normalize them; Where f(t) and f2(t) represent the instantaneous frequencies of the real signal and the noisy AM simulation signal, respectively, and π is the circumference of a circle. is a mathematical differential operator; μ f and Respectively represent the instantaneous frequency mean of the real signal and the noisy AM simulation signal, σ f and They represent the instantaneous frequency standard deviations of the real signal and the noisy AM simulated signal, respectively, and f′(t) and f2′(t) represent the instantaneous frequency normalized values ​​of the real signal and the noisy AM simulated signal, respectively; S24: calculating the instantaneous envelopes of the real signal and the noisy AM simulation signal, and normalizing them; Where a(t) and a2(t) represent the instantaneous envelope of the real signal and the noisy AM simulated signal respectively; μ a and Respectively represent the instantaneous envelope mean of the real signal and the noisy AM simulation signal, σ a and They represent the instantaneous envelope standard deviations of the real signal and the noisy AM simulated signal respectively, and a′(t) and a2′(t) represent the instantaneous envelope normalized values ​​of the real signal and the noisy AM simulated signal respectively.

5. The signal sample consistency verification method based on instantaneous characteristic statistical distribution according to claim 4, characterized in that: Step S3 is as follows: S31: Calculate the correlation coefficient of the instantaneous phase characteristics of the real signal and the noisy AM simulation signal, and obtain the consistency of the instantaneous phase characteristics of the sample; In the formula, Represents the correlation coefficient between the instantaneous frequency statistics of the real signal and the noisy AM simulation signal; when When , it means there is no linear correlation, that is, the instantaneous phase characteristics of the samples are inconsistent; when When , it indicates weak correlation, that is, the instantaneous phase characteristics of the samples are less consistent; when When , it indicates moderate correlation, that is, the instantaneous phase characteristics of the samples have moderate consistency; when When , it indicates that the correlation is strong, that is, the instantaneous phase characteristics of the samples are highly consistent; when When , it indicates complete correlation, that is, the instantaneous phase characteristics of the samples are completely consistent; S32: Calculate the correlation coefficient of the instantaneous frequency characteristics of the real signal and the AM simulation signal containing noise, and obtain the consistency of the instantaneous frequency characteristics of the sample; In the formula, r f Represents the correlation coefficient between the instantaneous frequency statistics of the real signal and the noisy AM simulation signal; When | r f When |=0, it means there is no linear correlation, that is, the instantaneous frequency characteristics of the samples are inconsistent; when 0<|r f |<0.3, it indicates weak correlation, that is, the consistency of the instantaneous frequency characteristics of the samples is weak; when 0.3≤|r f |<0.7, it indicates moderate correlation, that is, the instantaneous frequency characteristics of the samples have moderate consistency; when 0.7≤|r f |<1, it indicates strong correlation, that is, the instantaneous frequency characteristics of the samples are highly consistent; when |r f When |=1, it indicates complete correlation, that is, the instantaneous frequency characteristics of the samples are completely consistent; S33: Calculate the correlation coefficient of the instantaneous envelope characteristics of the real signal and the AM simulation signal containing noise, and obtain the consistency of the instantaneous envelope characteristics of the sample; In the formula, r a Represents the correlation coefficient between the instantaneous envelope statistics of the real signal and the noisy AM simulation signal; When | r a When |=0, it means there is no linear correlation, that is, the instantaneous envelope characteristics of the samples are inconsistent; when 0<|r a |<0.3, it indicates weak correlation, that is, the instantaneous envelope feature consistency of the sample is weak; when 0.3≤|r a |<0.7, it indicates moderate correlation, that is, the instantaneous envelope feature consistency of the sample is moderate; when 0.7≤|r a |<1, it indicates strong correlation, that is, the instantaneous envelope characteristics of the samples are highly consistent; when |r a When |=1, it indicates complete correlation, that is, the instantaneous envelope characteristics of the samples are completely consistent.

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