CN113553901A - Improved synchronous extraction time-frequency analysis method based on self-adaptive window length - Google Patents
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Abstract
The invention discloses an improved synchronous extraction time-frequency analysis method based on a self-adaptive window length, which comprises the following steps: performing short-time Fourier transform on an input signal; estimating the frequency change rate of each time frequency point according to a second-order local modulation operator; iteratively solving an optimization problem through a stripping algorithm, and extracting time-frequency ridge lines to obtain the frequency change rate of each component; designing an adaptive time window for the single-component signal; for multi-component signals, designing a self-adaptive time-frequency window according to the variation trend of different components; constructing self-adaptive short-time Fourier transform; constructing a new frequency redistribution operator based on the local peak value to obtain the instantaneous frequency estimation of the signal; and extracting the time-frequency coefficient by using an improved synchronous extraction operator, and reserving signal intensity information. The improved synchronous extraction transformation provided by the invention can adaptively change the window length in the time and frequency directions, can more finely depict different characteristics of multi-component signals, is suitable for various types of signals, and has higher time-frequency resolution.
Description
Technical Field
The invention belongs to a signal processing technology, and particularly relates to an improved synchronous extraction time-frequency analysis method based on a self-adaptive window length.
Background
A Time Frequency Analysis (TFA) method is an effective tool for describing time-varying characteristics of non-stationary signals, and is widely applied to the engineering fields of communication, radar, sonar and the like. Classical linear methods, such as short-time fourier transform (STFT) and Wavelet Transform (WT), can extend one-dimensional time series signals to a two-dimensional time-frequency (TF) plane, from which time-varying characteristics of the signal can be observed and decomposition of multi-component signals can be achieved. However, limited by the heisenberg uncertainty principle, the time-frequency representation produced by the conventional method is often ambiguous and cannot provide an accurate time-frequency description for the time-varying signal.
The disadvantages of the conventional TFA methods severely limit their application in practical data processing, and in order to solve this problem, many advanced post-processing methods such as a re-distribution method (RM), a synchronous compression transform (SST), and a Synchronous Extraction Transform (SET) have been developed in recent years. The RM firstly calculates the reassigned position of each time frequency point based on the time frequency phase information, and then reassigns the time frequency coefficient to the instantaneous track along the two-dimensional time frequency direction, thereby greatly improving the time frequency resolution, but the RM lacks the capability of reconstructing signals. SST pushes the time-frequency coefficients into the temporal traces only in the frequency direction, so that the signal can be reconstructed accurately while improving the performance of the classical TFA method. Compared with SST, the SET only retains the time-frequency coefficient most relevant to the time-varying characteristics of the signal, and has higher energy aggregation and noise robustness. The above post-processing methods are all based on the STFT of a fixed window length, and the analysis performance for emphasizing frequency signals and multi-component signals is difficult to be satisfactory.
Chinese patent publication No. CN 107576943a discloses a rayleigh entropy-based adaptive time-frequency synchronization compression method, which first measures the aggregation of local energy of signals by using rayleigh entropy, estimates an optimal window parameter sequence suitable for signal time-frequency analysis, improves aggregation by time-frequency synchronization compression, and realizes separation of multi-component signals. The method has higher time-frequency resolution, and the self-adaptive time window can also adapt to signals of more forms, but for multi-component signals with large frequency change difference, the method is difficult to adapt to the change of each component at the same time.
Chinese patent publication No. CN108694392A discloses a high-precision synchronous extraction generalized S-transform time-frequency analysis method, which combines three-parameter generalized S-transform and synchronous extraction, and can adjust the window length according to the signal frequency, so that the method has a high time-frequency resolution, but the performance of the method is greatly affected by the parameters, so that it is difficult to determine the optimal parameters, and is not suitable for strong frequency modulation signals, and the signal strength information is lost.
Disclosure of Invention
The invention aims to provide an improved synchronous extraction time-frequency analysis method based on a self-adaptive window length.
The technical solution for realizing the purpose of the invention is as follows: an improved synchronous extraction time-frequency analysis method based on self-adaptive window length comprises the following steps:
step 6, constructing new short-time Fourier transform by using a self-adaptive window function to obtain a time-frequency coefficient with higher aggregation;
step 7, constructing a new frequency redistribution operator by detecting the local maximum value of the time-frequency coefficient in the frequency direction to obtain an estimated value of the instantaneous frequency of the signal;
and 8, extracting the time-frequency coefficient by using an improved synchronous extraction operator, removing fuzzy time-frequency energy and retaining signal intensity information.
An electronic device comprises a memory, a processor and a computer program stored on the memory and running on the processor, wherein the processor executes the program to realize the improved synchronization extraction time-frequency analysis method based on the adaptive window length.
A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, implements the above-mentioned improved synchronization extraction time-frequency analysis method based on an adaptive window length.
Compared with the prior art, the invention has the following remarkable advantages: 1) the invention has the self-adaptive time-frequency window, can self-adaptively change the window length according to the frequency modulation intensity of each component, so that each component has clear time-frequency representation and high time-frequency aggregation, and is suitable for signals of various forms; 2) the invention can better extract weak amplitude signals and keep the strength information of each component.
The present invention is described in further detail below with reference to the attached drawing figures.
Drawings
FIG. 1 is a flow chart of an improved synchronization extraction time-frequency analysis method based on adaptive window length according to the present invention.
FIG. 2 is a time-frequency analysis result diagram in embodiment 1 of the present invention.
Fig. 3 is a time-frequency analysis result diagram of the embodiment 1 of synchronous compression.
Fig. 4 is a graph of the instantaneous frequency estimate absolute error versus the synchronous compression embodiment 1 of the present invention.
FIG. 5 is a time-frequency analysis result diagram in embodiment 2 of the present invention.
Fig. 6 is a time-frequency analysis result diagram of the synchronous compression embodiment 2.
Detailed Description
Referring to fig. 1, the present invention is an improved synchronization extraction time-frequency analysis method based on adaptive window length, including the following steps:
wherein t is a time variable; ω is a frequency variable; τ is an integral variable; i is a complex unit; g (t) is a Gaussian window function, taken as
Where σ is the standard deviation of the Gaussian window, representing the Gaussian window length;
wherein,
short-time Fourier transform of window functions g ' (t), g ' (t), tg ' (t), respectively;
wherein, tnIs the nth time, N belongs to { 1., N }, and N is the total time; lkIs the kth time-frequency ridge line, K belongs to { 1., K }, and K is the total component number of the signal; lk(tn) Is that the k time-frequency ridge line is at tnA frequency point of a moment;
the short-time Fourier coefficient after k-1 ridge lines and the neighborhood thereof are stripped is represented, t is time, and omega is a frequency variable;
is that the k time-frequency ridge line is at tnTemporal short-time Fourier coefficients; λ is the amplification factor;
is a second order local modulation operator; gamma raynIs tnThe self-defined threshold value of the time can be set as
The method comprises the following specific steps:
step 3-1, at t1Time of day, search for global energy peaks in the frequency direction
Determining a threshold value gamma1；
Step 3-2, from t1To tNRepeating the step 3-1 at any moment to obtain the threshold value gamma of each momentn；
Step 3-3, at t1At the moment, local peaks are searched in the frequency direction, and the amplitude needs to be larger than a threshold value gamma1To obtain a frequency satisfying the conditionPoint (omega)1、ω2…)；
Step 3-4, determining the initial position (t) of the ridge line1，ω1) At t2Time and constrained frequency domain interval
Searching the place with the maximum energy and the amplitude is larger than the threshold value gamma2To obtain a time-frequency point (t) satisfying the condition2，ω2)；
Step 3-5, from t1To tN-1Repeating the steps 3-4 all the time to obtain the 1 st time-frequency ridge line l1；
Step 3-6, ridge line l1And its domain coefficients are removed from the initial short-time Fourier coefficients, recorded as
Step 3-7, repeating the step 3-3 to the step 3-6 to obtain K time-frequency ridge lines;
and 4, designing a self-adaptive time window for the single-component signal according to the instantaneous frequency change rate of the signal, wherein the specific steps are as follows:
step 4-1, constructing time-varying window length sigma (t)
Wherein l (t) is the time-frequency ridge of the signal;
is a second order local modulation operator; θ is a window length adjustment factor;
step 4-2, substituting sigma (t) into a Gaussian window function to construct an adaptive window function gσ(t) is:
and 5, for the multi-component signals, dividing the time-frequency domain into different regions according to the extracted ridge lines, and designing a self-adaptive time-frequency window according to the variation trend of different components, wherein the specific steps are as follows:
step 5-1, constructing the window length sigma changing along with time and frequencyk(t，ω)
Wherein,
is a second order local modulation operator; θ is a window length adjustment factor; frequency interval [ B ] of each component in the vicinity of its ridge pointk，Bk+1]The length of the inner window is fixed, |k(t) is the K-th ridge extracted, K ∈ {1, …, K }, K is the total number of signal components, assuming l1(t)≤l2(t)≤…lK(t), then, it is preferable
Wherein M is the total frequency point number;
step 5-2, mixing sigmakSubstituting (t, omega) into Gaussian window function to construct adaptive window function gσ(t, ω) is:
step 6, constructing new short-time Fourier transform by using a self-adaptive window function to obtain a time-frequency coefficient F with stronger aggregationA(t, ω), specifically:
wherein t is a time variable; ω is a frequency variable; τ is an integral variable; i is a complex unit, gσ(t, ω) is an adaptive window function;
step 7, constructing a new frequency redistribution operator by detecting the local maximum value of the time-frequency coefficient in the frequency direction to obtain the estimated value of the signal instantaneous frequency
Specifically, the method comprises the following steps of;
wherein, FA(t, ω) is the adaptive time-frequency coefficient, Δ is the defined spectral interval;
step 8, extracting an accurate time-frequency coefficient by using an improved synchronous extraction operator ASEO, removing fuzzy time-frequency energy, and retaining signal intensity information, wherein the specific steps are as follows:
step 8-1, calculating and improving a synchronous extraction operator according to the obtained instantaneous frequency estimation
Where η is a frequency variable;
is an estimate of the instantaneous frequency of the signal; fA(t, ω) is the adaptive time-frequency coefficient; m is the mean of the time-frequency coefficients.
Step 8-2, and self-adaptive short-time Fourier coefficient FAThe (t, ω) cascade results in an adaptive improved synchronous extraction transform:
wherein t is a time variable; η is a frequency variable; ω is an integral variable;
is the signal instantaneous frequency estimated value; fA(t, ω) is the adaptive time-frequency coefficient.
The invention also provides an electronic device, which comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the processor executes the program to realize the improved synchronous extraction time-frequency analysis method based on the adaptive window length.
And a computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements the above-described improved synchronization extraction time-frequency analysis method based on an adaptive window length.
The invention is described in further detail below with reference to two examples.
Example 1
The simulation signal is two non-linear frequency-modulated signals x1(t)、x2(t) is superposed, and the analytic formula is as follows:
x1(t)＝(1-0.6e-0.3t)sin(2π(38t+3sin(1.5t)))
x2(t)＝e-0.4tsin(2π(15t+2sin(4.5t)))
the sampling frequency was 100 Hz. Fig. 2 is a time-frequency spectrum obtained by adopting improved synchronous extraction transformation with adaptive window length, and it can be seen that the invention can clearly depict the frequency changes of two components at the same time and can reflect the intensity changes of signals. Fig. 3 is an analysis result of the original synchronous compression transform, and it can be seen from comparing fig. 2 and fig. 3 that the synchronous compression transform has a clearer time-frequency representation for the weak frequency modulation component, but for the emphasized frequency component, the energy of the time-frequency spectrum at the position of the frequency fast transform is dispersed, and the time-frequency result aggregation of the invention is stronger. Fig. 4 is an absolute error curve of the instantaneous frequency of the emphasized frequency component of the present invention and the synchronous compression transform estimation, and it can be seen that the instantaneous frequency estimation error of the present invention is smaller and more accurate.
Example 2
The simulation signal is three non-linear frequency-modulated signals x with obviously different amplitudes1(t)、x2(t)、x3(t) is superposed, and the analytic formula is as follows:
x1(t)＝sin(2π(38t+3sin(1.5t)))
x2(t)＝0.1sin(2π(25t+3sin(1.5t)))
x3(t)＝0.01sin(2π(13t+3sin(1.5t)))
the sampling frequency was 100 Hz. Fig. 5 is a time-frequency spectrum obtained by using an improved synchronization extraction transform with an adaptive window length, and it can be seen that the present invention can clearly represent weak component signals. Fig. 6 is an analysis result of the original synchronous compression transformation, and comparing fig. 5 and fig. 6, it can be seen that the synchronous compression transformation is hardly observed for the weak frequency modulation component, but the time-varying trajectory of each component can be clearly characterized by the present invention, the time-frequency aggregation is high, and the intensity of each component can be reflected.
The invention can adapt to the frequency modulation intensity of different component signals, can adjust the window length in the time and frequency directions in a self-adaptive manner, can clearly represent the weak signal component, can reflect the signal intensity, is suitable for various signal forms, has fine time-varying characteristic depiction and high time-frequency resolution.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and improvements can be made without departing from the principle of the present invention, and these modifications and improvements should also be considered as the protection scope of the present invention.
Claims (10)
1. An improved synchronous extraction time-frequency analysis method based on self-adaptive window length is characterized by comprising the following steps:
step 1, performing short-time Fourier transform on an input signal;
step 2, estimating the frequency change rate of each time frequency point according to a second-order local modulation operator;
step 3, solving the optimization problem through a stripping algorithm iteration, searching a local energy peak value, extracting a time-frequency ridge line, and estimating the number of signal components to obtain the instantaneous frequency change rate of each component;
step 4, for the single component signal, designing a self-adaptive time window according to the instantaneous frequency change rate of the signal;
step 5, for multi-component signals, dividing a time-frequency domain into different regions according to the extracted ridge lines, and designing a self-adaptive time-frequency window according to the variation trend of different components;
step 6, constructing new short-time Fourier transform by using a self-adaptive window function to obtain a time-frequency coefficient with higher aggregation;
step 7, constructing a new frequency redistribution operator by detecting the local maximum value of the time-frequency coefficient in the frequency direction to obtain an estimated value of the instantaneous frequency of the signal;
and 8, extracting the time-frequency coefficient by using an improved synchronous extraction operator, removing fuzzy time-frequency energy and retaining signal intensity information.
2. The improved synchronous extraction time-frequency analysis method based on the self-adaptive window length as claimed in claim 1, wherein step 1 performs a preliminary short-time Fourier transform on the input signal x (t) to obtain short-time Fourier coefficients
The method specifically comprises the following steps:
wherein t is a time variable; ω is a frequency variable; τ is an integral variable; i is a complex unit; g (t) is a Gaussian window function, taken as
Where σ is the standard deviation of the gaussian window, representing the length of the gaussian window.
3. The improved synchronous extraction based on adaptive window length as claimed in claim 1The time-frequency analysis method is characterized in that the step 2 is based on a second-order local modulation operator
Estimating the frequency change rate of each time frequency point, specifically:
wherein,
the short-time Fourier transforms of the window functions g ' (t), g ' (t), tg ' (t), respectively, are represented.
4. The improved synchronous extraction time-frequency analysis method based on the self-adaptive window length as claimed in claim 1, wherein step 3 iteratively solves the following optimization problem by a stripping algorithm, searches local energy peak values, and extracts K time-frequency ridge lines of the signals:
wherein, tnIs the nth time, N belongs to { 1., N }, and N is the total time; lkIs the kth time-frequency ridge line, K belongs to { 1., K }, and K is the total component number of the signal; lk(tn) Is that the k time-frequency ridge line is at tnA frequency point of a moment;
the short-time Fourier coefficient after k-1 ridge lines and the neighborhood thereof are stripped is represented, t is time, and omega is a frequency variable;
is that the k time-frequency ridge line is at tnTemporal short-time Fourier coefficients; λ is the amplification factor;
is a second order local modulation operator; gamma raynIs tnThe self-defined threshold value of the time can be set as
The method comprises the following specific steps:
step 3-1, at t1Time of day, search for global energy peaks in the frequency direction
Determining a threshold value gamma1；
Step 3-2, from t1To tNRepeating the step 3-1 at any moment to obtain the threshold value gamma of each momentn；
Step 3-3, at t1At the moment, local peaks are searched in the frequency direction, and the amplitude needs to be larger than a threshold value gamma1To obtain the frequency point (omega) satisfying the condition1、ω2…)；
Step 3-4, determining the initial position (t) of the ridge line1，ω1) At t2Time and constrained frequency domain interval
Searching the place with the maximum energy and the amplitude is larger than the threshold value gamma2To obtain a time-frequency point (t) satisfying the condition2，ω2)；
Step 3-5, from t1To tN-1Repeating the steps 3-4 all the time to obtain the 1 st time-frequency ridge line l1；
Step 3-6, ridge line l1And its domain coefficients are removed from the initial short-time Fourier coefficients, recorded as
And 3-7, repeating the steps 3-3 to 3-6 to obtain K time-frequency ridge lines.
5. The improved synchronization extraction time-frequency analysis method based on the adaptive window length as claimed in claim 1, wherein step 4 is to design an adaptive time window for the single component signal according to the instantaneous frequency change rate of the signal, and the specific steps are as follows:
step 4-1, constructing time-varying window length sigma (t)
Wherein l (t) is the time-frequency ridge of the signal;
is a second order local modulation operator; θ is a window length adjustment factor;
step 4-2, substituting sigma (t) into a Gaussian window function to construct an adaptive window function gσ(t) is:
6. the improved synchronous extraction time-frequency analysis method based on the adaptive window length as claimed in claim 1, wherein step 5 divides the time-frequency domain into different regions, designs the adaptive time-frequency window according to the frequency variation trend of different signal components, and comprises the following specific steps:
step 5-1, constructing the window length sigma changing along with time and frequencyk(t，ω)
Wherein,
is a second order local modulation operator; θ is a window length adjustment factor; frequency interval [ B ] of each component in the vicinity of its ridge pointk，Bk+1]The length of the inner window is fixed, |k(t) is the K-th ridge line extracted, K belongs to { 1., K }, K is the total component number of the signal, assuming that l1(t)≤l2(t)≤…lK(t), then, it is preferable
Wherein M is the total frequency point number;
step 5-2, mixing sigmakSubstituting (t, omega) into Gaussian window function to construct adaptive window function gσ(t, ω) is:
7. the improved synchronous extraction time-frequency analysis method based on the adaptive window length as claimed in claim 1, wherein step 7 constructs a new frequency re-allocation operator through the local maximum of energy to obtain an accurate estimation of the instantaneous frequency of the signal, specifically:
wherein,
is an estimate of the instantaneous frequency of the signal; fA(t, ω) is the adaptive time-frequency coefficient and Δ is the defined spectral interval.
8. The improved synchronization extraction time-frequency analysis method based on the adaptive window length as claimed in claim 1, wherein step 8 uses an improved synchronization extraction operator to extract time-frequency coefficients and retain signal strength information, and comprises the following specific steps:
step 8-1, calculating and improving a synchronous extraction operator according to the obtained instantaneous frequency estimation
Where η is a frequency variable;
is an estimate of the instantaneous frequency of the signal; fA(t, ω) is the adaptive time-frequency coefficient; m is the mean value of the time-frequency coefficients;
step 8-2, and self-adaptive short-time Fourier coefficient FAThe (t, ω) cascade results in an adaptive improved synchronous extraction transform:
wherein t is a time variable; η is a frequency variable; ω is an integral variable.
9. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the method for improved synchronization extraction time-frequency analysis based on adaptive window length according to any of claims 1-8 when executing the program.
10. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out a method for improved synchronization extraction time-frequency analysis based on adaptive window length according to any one of claims 1 to 8.
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