A signal sample consistency test method based on instantaneous feature statistical distribution

Abstract

The application provides a signal sample consistency test method based on instantaneous characteristic statistical distribution, which comprises the following steps: S1: generating corresponding modulation simulation signals according to the modulation type of the real signal and the like, and the simulation signals do not consider the influence of a transmission channel; S2: calculating the instantaneous phase, the instantaneous frequency and the instantaneous amplitude of the AM simulation signal containing noise, and calculating the corresponding characteristic distribution; S3: calculating a correlation coefficient, performing sample consistency test, and verifying and judging the consistency between the AM simulation signal containing noise and the real signal. The confidence index of the simulation signal can directly judge the sample quality, and then guide the implementation of the simulation project.

Description

Technical Field

[0001] This invention belongs to the field of data engineering, and specifically relates to a signal sample consistency verification method based on instantaneous feature statistical distribution. Background Technology

[0002] Currently, big data models such as deep learning have been widely developed and applied. However, deep learning models typically require a large amount of training data to optimize their parameters when handling complex tasks, thereby ensuring high generalization ability and accuracy. However, in specific fields of practical application, especially in signal processing, it is often difficult to obtain enough high-quality real data. Since real data and simulation data share a common origin, simulation data can be used as training samples instead of real data. However, this leads to weaker robustness and generalization ability of the trained model. Therefore, the verification method of simulated signals is a very important and worthy direction for in-depth research in the field of data engineering. It is of great significance for ensuring the validity of simulation results, guiding model improvement, and supporting decision-making.

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

[0004] The earliest method used for static data consistency testing was hypothesis testing, including T-test and U-test. In 1969, Gafarian and Walsh et al. proposed applying nonparametric tests (including chi-square test, Smirnov test, etc.), analysis of variance, interval estimation, and other methods to static data consistency testing (Li Shu. Research on verification method of missile system simulation model [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 evaluation of quantitative methods, time-domain signal validation was the first area to be explored. As early as 1972, Wigan used simple regression to conduct preliminary validation work on time signals (Kheir NA, Holmes WM. On Validating Simulation Models of Missile Systems[J]. Simulation,1978,30(4):117-128.). Subsequently, in 1978, Kheir and Holmes introduced the Theil Inequality Coefficient (TIC) used in economic model forecasting into model validation work, applying it to the data validation of a flight simulation experiment. As a result, the TIC method began to be widely used in model validation work. In response to the shortcomings of the TIC method in verifying sparse signal data, Ronald optimized it (Murphy D C. Calculation of gini and theilinequality 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.). It defined the equivalence of two frequency spectra between simulation experimental data and actual experimental data, and verified the reliability of the queue simulation experiment in conjunction with corresponding verification steps. Later, Tytula proposed a scheme to verify stationary random signals 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 spectrograms of aircraft simulation and actual experimental data based on the classical Fourier transform, and constructed hypothesis tests by combining the characteristics of stochastic processes to 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 model testing 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 scheme for VV&A (Verification, Validation and Accretions) 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 the University of Glasgow proposed a model validation method based on reverse validation, introducing the method of deriving inputs from the same output in model building 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 models obtained from 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&ElectricalEngineering,2016.).

[0007] Despite the existence of numerous consistency testing and evaluation methods, there is currently no method directly applicable to detecting the consistency between simulated signals and real data. Typically, when simulated signals are used to replace real signals as training dataset samples for deep learning systems, the final inference results are needed as an indicator of the simulation signal's validity, lacking a direct basis for judgment. Summary of the Invention

[0008] To address the problems existing in the prior art, this 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 based on the modulation type used in the real signal, without considering the influence of the transmission channel.

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

[0011] S3: Calculate the correlation coefficient, perform a 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 actual signal;

[0014] The modulation type of the simulation signal is determined based on the modulation type of the real signal;

[0015] S12: Determine the actual relevant parameters of the modulation process based on the modulation type;

[0016] The range of actual relevant parameters in modulation engineering is determined by the corresponding modulation type; the specific values ​​of actual relevant parameters in modulation engineering 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 exactly the same as the time length of the real signal, which is denoted as T. The bandwidth of the real signal is directly obtained from the spectrum of the signal analysis software, and the power spectrum is obtained from the power spectrum of the signal analysis software.

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

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

[0021] Let m(t) be a simulated signal to be modulated, with a signal length consistent with the time range of the simulated signal in S13. AM modulation is used to generate the simulated AM modulated signal s. AM1 (t) represents the following

[0022]

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

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

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

[0026] Among them, s AM2 (t) is the AM simulation signal containing noise, and the simulation noise n(t) is Gaussian white noise with a mean of 0. 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: Transfer the real signal s AM (t) and the noisy AM simulation signal s AM2 (t) can be expanded into real and imaginary parts respectively;

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

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

[0032] Where I(t) + jQ(t) is s AM The expansion of (t) in the form of real and imaginary parts, where I(t) is the real part and Q(t) is the imaginary part, and I2(t)+jQ2(t) is similar;

[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 Represent the instantaneous phases of the real signal and the noisy AM simulation signal, respectively. arctan() is the arctangent function, and the instantaneous phase value is in... between; and These represent the instantaneous phase mean values ​​of the real signal and the noisy AM simulation signal, respectively. and These represent the instantaneous phase standard deviations of the real signal and the noisy simulated signal, respectively. and These represent the instantaneous phase normalization values ​​of the real signal and the noisy AM simulation signal, respectively.

[0037] S23: Calculate the instantaneous frequencies 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 mathematical constant pi. For mathematical differentiation operators; μ f and σ represents the instantaneous frequency mean of the real signal and the noisy AM simulation signal, respectively. f and denoted as the instantaneous frequency standard deviations of the real signal and the noisy AM simulation signal, respectively; f′(t) and f2′(t) represent the instantaneous frequency normalized values ​​of the real signal and the noisy AM simulation signal, respectively.

[0040] S24: Calculate the instantaneous envelope of the real signal and the noisy AM simulation signal, and normalize them;

[0041]

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

[0043] In yet 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 AM simulation signal with noise, and obtain the consistency of the instantaneous phase characteristics of the samples accordingly;

[0045]

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

[0047] when When , it indicates no linear correlation, meaning the instantaneous phase characteristics of the samples are inconsistent; when When, it indicates a weak correlation, meaning the consistency of the instantaneous phase characteristics of the samples is relatively weak; when When, it indicates moderate correlation, meaning the consistency of the instantaneous phase characteristics of the samples is moderate; when When the correlation is high, it indicates a strong correlation, meaning the instantaneous phase characteristics of the samples are highly consistent; when When the time interval is 1, it indicates that the samples are completely correlated, meaning that 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 with noise, and thereby determine the consistency of the instantaneous frequency characteristics of the samples;

[0049]

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

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

[0052] S33: Calculate the correlation coefficient of the instantaneous envelope features of the real signal and the noisy AM simulation signal, and obtain the consistency of the instantaneous envelope features of the samples accordingly;

[0053]

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

[0055] When |r a When | = 0, it indicates no linear correlation, meaning the instantaneous envelope features of the samples are inconsistent; when 0 < |r a When |r < 0.3, it indicates a weak correlation, meaning the consistency of the instantaneous envelope features of the samples is relatively weak; when 0.3 < |r a When | < 0.7, it indicates moderate correlation, meaning the consistency of the instantaneous envelope features of the samples is moderate; when 0.7 ≤ |r a When | < 1, it indicates a strong correlation, meaning the instantaneous envelope features of the samples have high consistency; when | r a When |=1, it indicates complete correlation, meaning that the instantaneous envelope features of the samples are completely consistent.

[0056] This invention starts with the instantaneous characteristics of signals (instantaneous phase, instantaneous frequency, and instantaneous amplitude) and proposes to use the correlation coefficient of the statistical distribution of these characteristics to verify the consistency between simulated and real signals. The advantages of this invention are: it replaces the indirect verification of simulation data through data training with a direct detection method of the correlation coefficient, providing a criterion for the qualification of simulation samples. This allows for the verification of simulated signals in the dataset before deep learning training data is generated, significantly saving time, manpower, and material resources in deep learning. Attached Figure Description

[0057] Figure 1 This is a flowchart of a signal sample consistency verification method based on instantaneous feature statistical distribution according to an embodiment of the present invention. Detailed Implementation

[0058] This invention focuses on aviation communication in real-world scenarios. It models and simulates typical modulation signals, extracts their instantaneous features, and verifies the consistency between the statistical distribution of the instantaneous features of the simulated signals and the real signals.

[0059] An embodiment of the present invention provides a signal sample consistency verification method based on instantaneous feature statistical distribution, comprising:

[0060] S1: Based on the modulation type used in the real signal, a corresponding modulation simulation signal is generated. The simulation signal of this invention does not consider the influence of the transmission channel.

[0061] Specifically as follows:

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

[0063] The purpose of this step is to determine the corresponding modulation type of the simulated signal based on the modulation type of the real signal.

[0064] The modulation type of the real signal is determined by an automatic modulation identification algorithm, such as modulation identification based on cumulative quantities or modulation identification based on constellation diagrams. These algorithms are not within the scope of this invention. The specific methods for determining the corresponding modulation type of the simulated signal based on the modulation type of the real signal are well known to those skilled in the art and will not be elaborated upon further.

[0065] S12: Determine the actual relevant parameters of the modulation process based on the modulation type;

[0066] The range of actual relevant parameters in modulation engineering is determined by the corresponding modulation type, such as AM modulation depth for AM modulation and symbol rate for FSK. The specific values ​​of the actual relevant parameters in modulation engineering are determined by the corresponding international standards, and the measurement methods for these parameters are not within the scope of this 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 exactly the same as the time length of the real signal, denoted as T. The bandwidth of the real signal can be directly obtained from the spectrum graph results of the signal analysis software, and the power spectrum can be obtained from the power spectrum graph results of the signal analysis software. Signal analysis software includes, but is not limited to, Matlab, etc., and the code and commands involved in the analysis software are not within the scope of this invention.

[0069] S14: Generate a simulation signal based on 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. The code and commands involved in the simulation software are not within the scope of this invention and are considered to be known.

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

[0072] Let m(t) be a simulated signal to be modulated (such as any signal sequence like a voice signal), with a signal length consistent with the time range of the simulated signal in S13. AM modulation is used to generate the simulated AM modulated signal s. AM1 (t) represents the following

[0073]

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

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

[0076] Taking AM modulation in S14 above as an example

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

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

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

[0080] Specifically as follows:

[0081] S21: Transfer the real signal s AM (t) and the noisy AM simulation signal s AM2 (t) can be expanded into real and imaginary parts respectively;

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

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

[0084] Where I(t) + jQ(t) is s AM The expansion of (t) in the form of real and imaginary parts uses the series expansion and Euler's formula in mathematics. I(t) is the real part and Q(t) is the imaginary part. Similarly, I2(t)+jQ2(t) is expanded.

[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 These represent the instantaneous phases of the real signal and the noisy AM simulation signal, respectively. The square root operator is used in mathematics. `arctan()` is the arctangent function, where the instantaneous phase value is... between. and These represent the instantaneous phase mean values ​​of the real signal and the noisy AM simulation signal, respectively. and These represent the instantaneous phase standard deviations of the real signal and the noisy simulated signal, respectively. and These represent the instantaneous phase normalization values ​​of the real signal and the noisy AM simulation signal, respectively.

[0088] S23: Calculate the instantaneous frequencies 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 mathematical constant pi. μ is the mathematical differential operator. f and σ represents the instantaneous frequency mean of the real signal and the noisy AM simulation signal, respectively. f and denoted as f'(t) and f2'(t), respectively, represent the instantaneous frequency standard deviations of the real signal and the noisy AM simulation signal, respectively.

[0091] S24: Calculate the instantaneous envelope of the real signal and the noisy AM simulation signal, and normalize them;

[0092]

[0093] Where a(t) and a2(t) represent the instantaneous envelopes of the real signal and the noisy AM simulation signal, respectively. μ a and Let σ represent the instantaneous envelope mean of the real signal and the noisy AM simulation signal, respectively. a and denoted as the instantaneous envelope standard deviations of the real signal and the noisy AM simulation signal, respectively, and a′(t) and a2′(t) represent the instantaneous envelope normalized values ​​of the real signal and the noisy AM simulation signal, respectively.

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

[0095] Specifically as follows:

[0096] S31: Calculate the correlation coefficient of the instantaneous phase characteristics of the real signal and the AM simulation signal with noise, and obtain the consistency of the instantaneous phase characteristics of the samples accordingly;

[0097]

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

[0099] when When , it indicates no linear correlation, meaning the instantaneous phase characteristics of the samples are inconsistent; when When, it indicates a weak correlation, meaning the consistency of the instantaneous phase characteristics of the samples is relatively weak; when When, it indicates moderate correlation, meaning the consistency of the instantaneous phase characteristics of the samples is moderate; when When the correlation is high, it indicates a strong correlation, meaning the instantaneous phase characteristics of the samples are highly consistent; when When the time is equal to 0, it indicates that the samples are completely correlated, meaning that 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 with noise, and thereby determine the consistency of the instantaneous frequency characteristics of the samples;

[0101]

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

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

[0104] S33: Calculate the correlation coefficient of the instantaneous envelope features of the real signal and the noisy AM simulation signal, and obtain the consistency of the instantaneous envelope features of the samples accordingly;

[0105]

[0106] In the formula, r a This 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 indicates no linear correlation, meaning the instantaneous envelope features of the samples are inconsistent; when 0 < |r a When | < 0.3, it indicates a weak correlation, meaning the consistency of the instantaneous envelope features of the samples is relatively weak; when 0.3 ≤ |r a When | < 0.7, it indicates moderate correlation, meaning the consistency of the instantaneous envelope features of the samples is moderate; when 0.7 ≤ |r a When | < 1, it indicates a strong correlation, meaning the instantaneous envelope features of the samples have high consistency; when | r a When |=1, it indicates complete correlation, meaning that the instantaneous envelope features of the samples are completely consistent.

Claims

1. A method of signal sample consistency test based on instantaneous feature statistical distribution, characterized in that, Specifically comprising the following steps: S1: According to the modulation type of the real signal, etc., the corresponding modulation simulation signal is generated, and the simulation signal does not consider the influence of the transmission channel; Specifically as follows: S11: Determine the modulation type of the real signal; According to the modulation type of the real signal, determine the corresponding simulation signal modulation type; S12: According to the modulation type, determine the modulation engineering actual related parameters; The range of modulation engineering actual related parameters is determined by the corresponding modulation type; The specific value of the modulation engineering actual related parameters is determined by the corresponding international standard; 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 simulation 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 result of the signal analysis software, and the power spectrum is obtained from the power spectrum diagram result of the signal analysis software; S14: According to the modulation type and parameters determined in S12 and S13, generate a simulation signal; Assuming the real signal s AM (t) has been identified as AM modulation in step S11, the time range of the modulated signal and the bandwidth, power spectrum parameters of the signal are acquired in S13, and simulation is performed in step S14 based on the above parameters. Let m(t) be a certain to-be-modulated simulation signal, the signal length is consistent with the simulation signal time range in S13, AM modulation is adopted, and the generated simulation AM modulated signal s AM1 (t) is represented as follows Wherein, A represents the carrier amplitude; t is the signal length, the signal length t of m(t) is in the range of [0, T]; f c is the modulation carrier frequency, is the initial phase of the carrier; S15: Apply noise to the simulation AM modulated signal; s AM2 (t) = s AM1 (t) + n(t) where s AM2 (t) is the AM signal with noise, the simulation noise n(t) is Gaussian white noise, the noise mean is 0, and the variance is set according to the requirement of the simulation; S2: Calculate the instantaneous phase, instantaneous frequency and instantaneous amplitude of the noise-containing AM simulation signal, and calculate the corresponding feature distribution; Specifically as follows: S21 : the real signal s AM (t) and the noisy AM simulation signal s AM2 (t) are respectively expanded into the form of real and imaginary parts; s AM (t) = I(t) + jQ(t) s AM2 (t) = I2(t) + jQ2(t) where I(t) + jQ(t) is s AM (t) in real and imaginary parts, I(t) being the real part and Q(t) being the imaginary part, and I2(t) + jQ2(t) by analogy; S22: Calculate the real signal s AM (t) and the noisy AM simulation signal s AM2 (t) and normalize it to get the instantaneous phase distribution value in, and Represent the instantaneous phases of the real signal and the noisy AM simulation signal, respectively. arctan() is the arctangent function, and the instantaneous phase value is in... between; and These represent the instantaneous phase mean values ​​of the real signal and the noisy AM simulation signal, respectively. and These represent the instantaneous phase standard deviations of the real signal and the noisy simulated signal, respectively. and These represent the instantaneous phase normalization values ​​of the real signal and the noisy AM simulation signal, respectively. S23: Calculate the instantaneous frequency of the real signal and the noise-containing AM simulation signal, and normalize it; where f(t) and f2(t) are the instantaneous frequency of the real signal and the noisy AM simulated signal respectively, and π is the circular constant, is the mathematical differential operator; μ f is the real signal and are the instantaneous frequency mean of the real signal and the noisy AM simulated signal respectively, and σ f is the real signal and are the instantaneous frequency standard deviation of the real signal and the noisy AM simulated signal respectively, and f'(t) and f2'(t) are the normalized instantaneous frequency of the real signal and the noisy AM simulated signal respectively; S24: Calculate the instantaneous envelope of the real signal and the noise-containing AM simulation signal, and normalize it; where a(t) and a2(t) represent the instantaneous envelope of the real signal and the noisy AM simulated signal, respectively; μ a and represent the mean of the instantaneous envelope of the real signal and the noisy AM simulated signal, respectively, σ a and represent the standard deviation of the instantaneous envelope of the real signal and the noisy AM simulated signal, respectively, a'(t) and a2'(t) represent the normalized value of the instantaneous envelope of the real signal and the noisy AM simulated signal, respectively; S3: Calculate the correlation coefficient, perform sample consistency test, and verify the consistency between the noise-containing AM simulation signal and the real signal; Specifically as follows: S31: Calculate the correlation coefficient of the instantaneous phase feature of the real signal and the noise-containing AM simulation signal, and obtain the sample instantaneous phase feature consistency accordingly; wherein represents the correlation coefficient of the instantaneous frequency statistics of the real signal and the noisy AM simulation signal. When , it means no linear correlation, i.e. the sample instantaneous phase features are inconsistent; when , it means weak correlation, i.e. the consistency of the sample instantaneous phase features is weak; when , it means moderate correlation, i.e. the consistency of the sample instantaneous phase features is moderate; when , it means relatively strong correlation, i.e. the consistency of the sample instantaneous phase features is relatively high; and when , it means complete correlation, i.e. the sample instantaneous phase features are completely consistent. S32: Calculate the correlation coefficient of the instantaneous frequency feature of the real signal and the noise-containing AM simulation signal, and obtain the sample instantaneous frequency feature consistency accordingly; where r f represents the correlation coefficient of the instantaneous frequency statistics of the real signal and the noisy AM simulation signal. When |r f When | = 0, it indicates no linear correlation, meaning the instantaneous frequency characteristics of the samples are inconsistent; when 0 < |r f When | < 0.3, it indicates a weak correlation, meaning the consistency of the instantaneous frequency characteristics of the samples is relatively weak; when 0.3 ≤ |r f When | < 0.7, it indicates moderate correlation, meaning the consistency of instantaneous frequency characteristics of the samples is moderate; when 0.7 ≤ |r f When | < 1, it indicates a strong correlation, meaning the instantaneous frequency characteristics of the samples are highly consistent; when | r f When |=1, it indicates perfect correlation, meaning that the instantaneous frequency characteristics of the samples are completely consistent; S33: Calculate the correlation coefficient of the instantaneous envelope feature of the real signal and the noise-containing AM simulation signal, and obtain the sample instantaneous envelope feature consistency accordingly; where r a represents the correlation coefficient of the real signal and the statistical envelope of the noisy AM simulation signal When |r a When | = 0, it indicates no linear correlation, meaning the instantaneous envelope features of the samples are inconsistent; when 0 < |r a When | < 0.3, it indicates a weak correlation, meaning the consistency of the instantaneous envelope features of the samples is relatively weak; when 0.3 ≤ |r a When | < 0.7, it indicates moderate correlation, meaning the consistency of the instantaneous envelope features of the samples is moderate; when 0.7 ≤ |r a When | < 1, it indicates a strong correlation, meaning the instantaneous envelope features of the samples have high consistency; when | r a When |=1, it indicates complete correlation, meaning that the instantaneous envelope features of the samples are completely consistent.

2. The method for signal sample consistency check based on instantaneous feature statistical distribution according to claim 1, characterized in that, In step S14, the initial phase is set as a random phase.

Images