CN112800862B - Non-stationary signal time-frequency matrix reconstruction method and system - Google Patents
Non-stationary signal time-frequency matrix reconstruction method and system Download PDFInfo
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Abstract
The invention relates to a non-stationary signal time-frequency matrix reconstruction method and a system, which firstly calculate Choi-Williams transformation when a sampling sequence selects different nuclear parameters to obtain a time-frequency matrix corresponding to each nuclear parameter, then respectively perform modulus extraction on each time-frequency matrix to obtain an amplitude matrix, and calculate the instantaneous normalization entropy of each column in each amplitude matrix to obtain an entropy matrix. Finally, selecting the minimum value of each row in the entropy value matrix, and recording the minimum value as R nk And then selecting the nth column in the amplitude matrix corresponding to the kth kernel parameter as the nth column of the reconstructed time-frequency matrix to obtain the reconstructed time-frequency matrix, wherein the column of each time point of the reconstructed time-frequency matrix is obtained by calculation under the optimal kernel parameter of the time point, so that each column is ensured to have the comprehensive optimal performance of time-frequency aggregation and cross item inhibition, and the overall optimization is realized through the optimization of each time point, thereby achieving the purpose of optimizing the overall performance of time-frequency analysis.
Description
Technical Field
The invention relates to the technical field of signal processing, in particular to a non-stationary signal time-frequency matrix reconstruction method and a non-stationary signal time-frequency matrix reconstruction system based on adaptive optimization.
Background
Communication signals are typical non-stationary signals, and the identification of the modulation mode of the communication signals has important research significance. Throughout the communication, the modulation identification is at the receiver location, specifically between the signal detector and the demodulator. The demodulator needs to demodulate the signal by using a corresponding demodulation method according to the currently identified signal modulation method, so the identification of the modulation method is particularly important. Modulation identification is of great significance in both military and civilian applications.
The main method of modulation recognition is a pattern recognition method based on feature extraction. The time-frequency characteristics of the signals are a common classification characteristic with wide application in the modulation identification technology, and therefore, a proper time-frequency analysis method needs to be adopted for the signals to extract the time-frequency characteristics of the signals. Currently, time-frequency analysis methods can be classified into two categories, linear time-frequency analysis methods and nonlinear time-frequency analysis methods. The linear time-frequency analysis method comprises short-time Fourier transform and continuous wavelet transform. However, the linear time-frequency analysis method is limited by the inaccurate measurement principle, so that high time-frequency aggregation cannot be obtained, and the application of the linear time-frequency analysis method is limited. Compared with a linear time-frequency analysis method, the nonlinear time-frequency analysis method has higher time-frequency aggregation, and comprises Wigner-Ville distribution, Cohen type distribution and the like. However, the nonlinear time-frequency distribution has the problem of cross term interference, which affects the analysis of useful signal terms, so the Cohen type distribution inhibits cross terms by designing different kernel functions. The Choi-Williams distribution is used as one of Cohen type distributions, has wider application, is a common method for extracting time-frequency characteristics in modulation identification, and effectively inhibits cross terms. But it reduces the time-frequency aggregation while suppressing cross terms. That is, the time-frequency aggregation property and cross term inhibition of Choi-Williams distribution are restricted, and cannot be achieved simultaneously, so that selection between the time-frequency aggregation property and the cross term inhibition is often needed, or compromise is selected.
Therefore, in practical application, especially in time-frequency feature extraction of modulation signal identification, how to make time-frequency aggregation and cross term inhibition achieve the best compromise effect and make the overall performance of the time-frequency aggregation and the cross term inhibition optimal is a problem which needs to be solved urgently.
Disclosure of Invention
The invention aims to provide a non-stationary signal time-frequency matrix reconstruction method and a non-stationary signal time-frequency matrix reconstruction system, which can solve the problem that the time-frequency aggregation and cross item inhibition cannot be simultaneously achieved in the existing time-frequency analysis method, can better extract time-frequency characteristics from received modulation signals, and lay a good foundation for modulation identification of the modulation signals.
In order to achieve the purpose, the invention provides the following scheme:
a non-stationary signal time-frequency matrix reconstruction method comprises the following steps:
performing time domain sampling on the modulated communication signal by using a signal detector to obtain a discrete sampling sequence x (n) of the communication signal; n is 1, 2.. No. N; n is the number of sampling points;
selecting K nuclear parameters in Choi-Williams transformation;
when the kth nuclear parameter is selected, calculating the Choi-Williams transformation of the sampling sequence x (n) to obtain a time-frequency matrix corresponding to the kth nuclear parameter; k1, 2.. K;
respectively performing modulus extraction on each time-frequency matrix to obtain K amplitude matrixes; each amplitude matrix is an M multiplied by N matrix; m is the number of frequency points;
calculating the instantaneous normalization entropy of each column in each amplitude matrix to obtain an entropy matrix; the entropy matrix is an NxK matrix;
selecting the minimum value of each row in the entropy value matrix, and recording the minimum value as R nk And selecting the nth column in the amplitude matrix corresponding to the kth kernel parameter as the nth column of the reconstructed time-frequency matrix to obtain the reconstructed time-frequency matrix.
A non-stationary signal time-frequency matrix reconstruction system, the reconstruction system comprising:
the sampling sequence acquisition module is used for carrying out time domain sampling on the modulated communication signals by using the signal detector to obtain discrete sampling sequences x (n) of the communication signals; n is 1, 2.. No. N; n is the number of sampling points;
the time-frequency matrix calculation module is used for selecting K nuclear parameters in Choi-Williams transformation; when the kth nuclear parameter is selected, calculating the Choi-Williams transformation of the sampling sequence x (n) to obtain a time-frequency matrix corresponding to the kth nuclear parameter; k1, 2.. K;
the amplitude matrix calculation module is used for respectively performing modulus extraction on each time-frequency matrix to obtain K amplitude matrixes; each amplitude matrix is an M multiplied by N matrix; m is the number of frequency points;
the entropy matrix calculation module is used for calculating the instantaneous normalization entropy of each column in each amplitude matrix to obtain an entropy matrix; the entropy matrix is an NxK matrix;
a reconstructed time-frequency matrix obtaining module for selecting the minimum value of each row in the entropy value matrix, and recording the minimum value as R nk And selecting the nth column in the amplitude matrix corresponding to the kth nuclear parameter as the nth column of the reconstructed time-frequency matrix to obtain the reconstructed time-frequency matrix.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention provides a method and a system for reconstructing a non-stationary signal time-frequency matrix, which are characterized in that a signal detector is used for carrying out time-domain sampling on a modulation communication signal to obtain a discrete sampling sequence of the communication signal, Choi-Williams transformation is carried out when the sampling sequence selects different nuclear parameters to obtain a time-frequency matrix corresponding to each nuclear parameter, then modulus is respectively taken for each time-frequency matrix to obtain an amplitude matrix, and then instantaneous normalization entropy of each column in each amplitude matrix is calculated to obtain an entropy matrix. Finally, selecting the minimum value of each row in the entropy value matrix, and recording the minimum value as R nk And selecting the nth column in the amplitude matrix corresponding to the kth kernel parameter as the nth column of the reconstructed time-frequency matrix to obtain the reconstructed time-frequency matrix. The invention takes the instantaneous normalization entropy as an index for measuring the complexity of the frequency domain at a single time point, and the index enables the comprehensive performance of time-frequency aggregation and cross item inhibition to be more visual, and the optimal kernel parameter obtained based on the instantaneous normalization entropy is dynamically changed along with the time self-adaption, each time point corresponds to an optimal kernel parameter, and then the invention reconstructs the time-frequency matrix, the column of each time point is calculated under the optimal kernel parameter of the time point, thereby ensuring that each column has the time-frequency aggregation and cross item inhibitionThe method improves the problem that the time-frequency aggregation performance and the cross term inhibition cannot be simultaneously obtained in the existing time-frequency analysis method, can better extract time-frequency characteristics from the received modulation signals, and lays a good foundation for the identification of the modulation signals.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without creative efforts.
Fig. 1 is a flowchart of a time-frequency matrix reconstruction method according to embodiment 1 of the present invention.
Fig. 2 is a time domain waveform diagram of a quadrature frequency shift keying signal added with white gaussian noise according to embodiment 1 of the present invention.
Fig. 3 is a time-frequency analysis diagram obtained by the method of the present invention in embodiment 1 of the present invention.
Fig. 4 is a time-frequency analysis diagram obtained without the method of the present invention in embodiment 1 of the present invention.
Fig. 5 is a relation scatter diagram between different kernel parameters and entropy values provided in embodiment 1 of the present invention.
Fig. 6 is a block diagram of a time-frequency matrix reconstruction system provided in embodiment 2 of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a non-stationary signal time-frequency matrix reconstruction method and a non-stationary signal time-frequency matrix reconstruction system, which can solve the problem that the existing time-frequency analysis method cannot simultaneously achieve time-frequency aggregation and cross item inhibition, can better extract time-frequency characteristics from received modulation signals, and lay a good foundation for modulation identification of the modulation signals.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Example 1:
the present embodiment is configured to provide a non-stationary signal time-frequency matrix reconstruction method, as shown in fig. 1, where the reconstruction method includes the following steps:
step 101: performing time domain sampling on the modulated communication signal by using a signal detector to obtain a discrete sampling sequence x (n) of the communication signal; n is 1, 2.. No. N; n is the number of sampling points;
the sampling object of this embodiment is a modulated communication signal, and the reconstruction method of this embodiment is used to obtain a reconstructed time-frequency matrix of the modulated communication signal to better extract time-frequency characteristics, so that a modulation mode used by the modulated communication signal can be conveniently identified, and the demodulator demodulates the modulated communication signal according to the identified modulation mode.
Step 102: selecting K nuclear parameters in Choi-Williams transformation; k kernel parameter composition sets
The values of the K kernel parameters are different.
Step 103: when the kth nuclear parameter is selected, calculating the Choi-Williams transformation of the sampling sequence x (n) to obtain a time-frequency matrix corresponding to the kth nuclear parameter; k1, 2.. K;
due to the fact that
Contains K different kernel parameters, so obtaining K time-frequency matrixes TFR 1 、TFR 2 、......TFR K Forming a time-frequency matrix set S, wherein the kth time-frequency matrix TFR in the set S k And collections
The kth kernel parameter in (1) corresponds;
the expression of the Choi-Williams transformation is as follows:
in formula 1, CWD (t, ω) is a Choi-Williams transformation of the signal x (t); t is a time variable; omega is a frequency variable; sigma is a nuclear parameter; τ is the time delay; u is an integral variable; x is the number of * Is the conjugate of x.
Step 104: respectively performing modulus extraction on each time-frequency matrix to obtain K amplitude matrixes; each amplitude matrix is an M multiplied by N matrix; m is the number of frequency points;
the kth amplitude matrix
Wherein, w mn Not less than 0; m ═ 1, 2,... M; n is 1, 2.. No.. N; each row of the amplitude matrix represents the change of the amplitude along with the time at a certain frequency; each column of the amplitude matrix represents the variation of the amplitude with the frequency at a certain time;
step 105: calculating the instantaneous normalization entropy of each column in each amplitude matrix to obtain an entropy matrix; the entropy matrix is an NxK matrix;
the instantaneous normalized entropy of each column in the amplitude matrix is calculated, that is, the normalized entropy at each time point in the amplitude matrix is calculated. When the signal energy is concentrated on a few frequencies, the entropy value is small; when the signal frequency components are complex, the entropy value is large. Entropy is minimal, especially when the signal energy is concentrated at a single frequency; when the signals are uniformly distributed on different frequencies, the entropy value is maximum. Therefore, the instantaneous normalized entropy can be used as an index for measuring the complexity of the frequency domain at a single time point. In addition, the time-frequency aggregation and cross term inhibition effects are considered simultaneously, and the comprehensive performance of the time-frequency aggregation and the cross term inhibition effects is reflected on the numerical value: the lower the time-frequency aggregation, the poorer the cross term inhibition effect, and the larger the entropy value; conversely, the smaller the entropy value. The index enables the comprehensive performance of time-frequency aggregation and cross item inhibition to be more intuitive.
The calculation formula of the instantaneous normalization entropy is as follows:
wherein, R (n) is the instantaneous normalization entropy value of the nth column in the amplitude matrix; alpha is the order, and alpha is more than or equal to 2; m ═ 1, 2,... M; w (m, n) is the value of the element in the m-th row and n-th column of the amplitude matrix.
To simplify the calculation, α in the present embodiment is an integer.
The resulting matrix of entropy values is:
element R in the matrix of entropy values nk When the nuclear parameter is sigma k And calculating the instantaneous normalization entropy value of the nth column of the obtained amplitude matrix.
Step 106: selecting the minimum value of each row in the entropy value matrix, and recording the minimum value as R nk And selecting the nth column in the amplitude matrix corresponding to the kth kernel parameter as the nth column of the reconstructed time-frequency matrix to obtain the reconstructed time-frequency matrix.
Minimum value R of each row nk Corresponding kernel parameter is sigma k ，σ k That is, the optimal kernel parameter corresponding to the nth time point in the sampling sequence x (n) is selected as the kth kernel parameter sigma k Corresponding widthValue matrix | TFR k And (4) taking the nth column in the | as the nth column of the reconstructed time-frequency matrix, traversing all rows of the entropy matrix, namely traversing all time points, and reconstructing all columns of the time-frequency matrix to obtain the reconstructed time-frequency matrix. Furthermore, the time-varying optimal kernel parameter obtained based on the instantaneous normalized entropy is dynamically changed along with time adaptation, each time point corresponds to an optimal kernel parameter, and based on the reconstructed time-frequency matrix, the column of each time point is obtained by calculation under the optimal kernel parameter of the time point, so that each column is ensured to have the comprehensive optimal performance of time-frequency aggregation and cross term inhibition, the overall optimization of the time-frequency matrix is realized through the optimization of each time point, the purpose of optimizing the overall performance of time-frequency analysis is achieved, the problem that the time-frequency aggregation and cross term inhibition cannot be simultaneously obtained in the existing time-frequency analysis method is solved, the time-frequency characteristics can be better extracted, and a good foundation is laid for modulation signal identification.
After obtaining the reconstruction time-frequency matrix, the reconstruction method further comprises: and according to the reconstructed time-frequency matrix, a time-frequency analysis graph of the sampling sequence x (n) is drawn by using matlab, so that the time-frequency characteristics of the signals are more accurately reflected on the time-frequency analysis graph.
In order to make those skilled in the art better understand the reconstruction method described in the present embodiment, the reconstruction method is described below with reference to a specific example.
Selecting the simulation signal as a quaternary frequency shift keying (4fsk) signal in the modulation signal, wherein the sampling frequency is 600KHz, and the carrier signal frequency is f 1 ＝100KHZ，f 2 ＝60KHZ，f 3 ＝80KHZ，f 4 The sampling point number N is 256 at 40KHZ, and the signal amplitude is 1. Gaussian white noise is added, and the signal-to-noise ratio is 0 dB. As shown in fig. 2, it is a time domain waveform diagram of a 4fsk signal with gaussian white noise added.
Sampling the simulation signal, wherein the sampling frequency is 600KHz, and the number of sampling points is 256, so as to obtain a sampling sequence x (n); n 1, 2.. 256;
selecting 10 nuclear parameters in Choi-Williams transformation, and forming a set by the 10 nuclear parameters
When the kth nuclear parameter is selected, calculating the Choi-Williams transformation of a sampling sequence x (n) to obtain a time-frequency matrix corresponding to the kth nuclear parameter; 1, 2.. 10; due to the fact that
The method comprises 10 different kernel parameters, so that 10 time frequency matrixes are obtained.
And taking a modulus for each time-frequency matrix to obtain an amplitude matrix.
Amplitude matrix
Wherein, w mn ≥0；m＝1，2，......512；n＝1，2，......256；
And calculating the instantaneous normalization entropy of the column where the nth time point is located, namely the nth column in each amplitude matrix, and traversing all the time points to obtain an entropy value matrix.
The resulting matrix of entropy values is:
selecting the minimum value of each row in the entropy value matrix, and selecting the minimum value R of each row nk Corresponding kernel parameter is sigma k ，σ k That is, the optimal kernel parameter corresponding to the nth time point in the sampling sequence x (n) is selected as the kth kernel parameter sigma k Corresponding magnitude matrix | TFR k And (4) taking the nth column in the | as the nth column of the reconstructed time-frequency matrix, traversing all rows of the entropy matrix, namely traversing all time points, and reconstructing all columns of the time-frequency matrix to obtain the reconstructed time-frequency matrix.
And drawing a time-frequency analysis graph of the sampling sequence x (n) by using matlab according to the reconstructed time-frequency matrix, wherein the obtained time-frequency analysis graph is shown in FIG. 3. Fig. 4 is a Choi-Williams transform time-frequency diagram of a simulation signal when the reconstruction method of the embodiment is not used, and it is obvious that the reconstruction method of the embodiment improves cross term suppression and time-frequency aggregation effect, and makes time-frequency characteristics of a modulation signal clearer, compared with fig. 3.
As shown in FIG. 5, Williams entropy values of the Choi-Williams transform time-frequency matrix for the 4fsk signal, which is a normalized form of Renyi entropy, can be measured from the time-frequency analysis plot as a whole for the effects of time-frequency aggregation and cross term suppression, when the kernel parameters are taken at 0.01, 0.03, 0.05, 0.1, 0.15, 0.2, 0.3, and 1, respectively. As can be seen from fig. 5, the modulation signal time-frequency analysis method after time-frequency matrix reconstruction enables the time-frequency analysis diagram to have the minimum Williams entropy value. Therefore, the method of the embodiment enables the comprehensive performance of the time-frequency aggregation and cross term inhibition of the time-frequency analysis graph to be optimal.
Wherein, the calculation expression of Williams entropy is as follows:
in formula 3, P (n, k) is an element in the reconstructed time-frequency matrix, and α is 3.
Example 2:
this embodiment is configured to provide a non-stationary signal time-frequency matrix reconstruction system, as shown in fig. 6, where the reconstruction system includes:
a sampling sequence obtaining module M1, configured to perform time-domain sampling on the modulated communication signal by using the signal detector, so as to obtain a discrete sampling sequence x (n) of the communication signal; n is 1, 2.. No. N; n is the number of sampling points;
the time-frequency matrix calculation module M2 is used for selecting K nuclear parameters in Choi-Williams transformation; when the kth nuclear parameter is selected, calculating the Choi-Williams transformation of the sampling sequence x (n) to obtain a time-frequency matrix corresponding to the kth nuclear parameter; k1, 2.. K;
the expression of the Choi-Williams transformation is as follows:
wherein CWD (t, ω) is a Choi-Williams transformation of the signal x (t); t is a time variable; omega is a frequency variable; sigma is a nuclear parameter; τ is a time delay; u is an integral variable; x is the number of * Is the conjugate of x.
The amplitude matrix calculation module M3 is used for respectively performing modulus extraction on each time-frequency matrix to obtain K amplitude matrices; each amplitude matrix is an M multiplied by N matrix; m is the number of frequency points;
an entropy matrix calculation module M4, configured to calculate an instantaneous normalized entropy of each column in each amplitude matrix to obtain an entropy matrix; the entropy matrix is an NxK matrix;
the calculation formula of the instantaneous normalization entropy is as follows:
wherein, R (n) is the instantaneous normalization entropy value of the nth column in the amplitude matrix; alpha is the order, and alpha is more than or equal to 2; m ═ 1, 2,... M; w (m, n) is the value of the element in the m-th row and n-th column of the amplitude matrix. Alpha is an integer.
A reconstructed time-frequency matrix obtaining module M5, configured to select a minimum value of each row in the entropy matrix, and record the minimum value as R nk And selecting the nth column in the amplitude matrix corresponding to the kth kernel parameter as the nth column of the reconstructed time-frequency matrix to obtain the reconstructed time-frequency matrix.
As an optional implementation manner, the reconstruction system further includes a time-frequency analysis graph drawing module M6, configured to draw the time-frequency analysis graph of the sampling sequence x (n) by using matlab according to the reconstructed time-frequency matrix.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (10)
1. A non-stationary signal time-frequency matrix reconstruction method is characterized by comprising the following steps:
performing time domain sampling on the modulated communication signal by using a signal detector to obtain a discrete sampling sequence x (n) of the communication signal; n is 1, 2.. No. N; n is the number of sampling points;
selecting K nuclear parameters in Choi-Williams transformation;
when the kth nuclear parameter is selected, calculating the Choi-Williams transformation of the sampling sequence x (n) to obtain a time-frequency matrix corresponding to the kth nuclear parameter; k1, 2.. K;
respectively performing modulus extraction on each time-frequency matrix to obtain K amplitude matrixes; each amplitude matrix is an M multiplied by N matrix; m is the number of frequency points;
calculating the instantaneous normalization entropy of each column in each amplitude matrix to obtain an entropy matrix; the entropy matrix is an NxK matrix;
selecting the minimum value of each row in the entropy value matrix, and recording the minimum value as R nk And selecting the nth column in the amplitude matrix corresponding to the kth kernel parameter as the nth column of the reconstructed time-frequency matrix to obtain the reconstructed time-frequency matrix.
2. The method for reconstructing a non-stationary signal time-frequency matrix according to claim 1, wherein the expression of the Choi-Williams transformation is:
wherein CWD (t, ω) is a Choi-Williams transformation of the signal x (t); t is a time variable; omega is a frequency variable; sigma is a nuclear parameter; τ is a time delay; u is an integral variable; x is the number of * Is the conjugate of x.
3. The method for reconstructing a non-stationary signal time-frequency matrix according to claim 1, wherein the instantaneous normalized entropy is calculated as:
wherein, R (n) is the instantaneous normalization entropy value of the nth column in the amplitude matrix; alpha is the order, and alpha is more than or equal to 2; m ═ 1, 2,... M; w (m, n) is the value of the element in the m-th row and n-th column of the amplitude matrix.
4. The method for reconstructing a non-stationary signal time-frequency matrix as claimed in claim 3, wherein α is an integer.
5. The method for reconstructing a non-stationary signal time-frequency matrix according to claim 1, wherein after obtaining the reconstructed time-frequency matrix, the method further comprises:
and drawing a time-frequency analysis graph of the sampling sequence x (n) by adopting matlab according to the reconstructed time-frequency matrix.
6. A non-stationary signal time-frequency matrix reconstruction system, the reconstruction system comprising:
the sampling sequence acquisition module is used for carrying out time domain sampling on the modulated communication signals by using the signal detector to obtain discrete sampling sequences x (n) of the communication signals; n is 1, 2.. No. N; n is the number of sampling points;
the time-frequency matrix calculation module is used for selecting K nuclear parameters in Choi-Williams transformation; when the kth nuclear parameter is selected, calculating the Choi-Williams transformation of the sampling sequence x (n) to obtain a time-frequency matrix corresponding to the kth nuclear parameter; k1, 2.. K;
the amplitude matrix calculation module is used for respectively performing modulus extraction on each time-frequency matrix to obtain K amplitude matrixes; each amplitude matrix is an M multiplied by N matrix; m is the number of frequency points;
the entropy matrix calculation module is used for calculating the instantaneous normalization entropy of each column in each amplitude matrix to obtain an entropy matrix; the entropy matrix is an NxK matrix;
a reconstructed time-frequency matrix obtaining module for selecting the minimum value of each row in the entropy value matrix, and recording the minimum value as R nk And selecting the nth column in the amplitude matrix corresponding to the kth kernel parameter as the nth column of the reconstructed time-frequency matrix to obtain the reconstructed time-frequency matrix.
7. The system for reconstructing a non-stationary signal time-frequency matrix as claimed in claim 6, wherein said Choi-Williams transform is expressed as:
wherein CWD (t, ω) is a Choi-Williams transformation of the signal x (t); t is a time variable; omega is a frequency variable; sigma is a nuclear parameter; τ is a time delay; u is an integral variable; x is the number of * Is the conjugate of x.
8. The system for reconstructing a non-stationary signal time-frequency matrix as claimed in claim 6, wherein said instantaneous normalized entropy is calculated by the formula:
wherein, R (n) is the instantaneous normalization entropy value of the nth column in the amplitude matrix; alpha is the order, and alpha is more than or equal to 2; m ═ 1, 2,... M; w (m, n) is the value of the element in the m-th row and n-th column of the amplitude matrix.
9. The system for reconstructing a non-stationary signal time-frequency matrix as claimed in claim 8, wherein α is an integer.
10. The system for reconstructing a non-stationary signal time-frequency matrix as claimed in claim 6, wherein said reconstruction system further comprises:
and the time-frequency analysis graph drawing module is used for drawing the time-frequency analysis graph of the sampling sequence x (n) by adopting matlab according to the reconstructed time-frequency matrix.
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| On the Use of Instantaneous Entropy to Measure the Momentary Predictability of Human Mobility;Paul Baumann等;《2013 IEEE 14th Workshop on Signal Processing Advances in Wireless Communications (SPAWC)》;20130926;第535-539页 * |
| 基于Choi—Williams时频分布的阵列声波测井信号时频分析;王祝文等;《地球物理学进展》;20071015;第22卷(第5期);第1481-1486页 * |
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