CN108009347A - Combine the Time-Frequency Analysis Method for improving generalized S-transform based on synchronous compression - Google Patents
Combine the Time-Frequency Analysis Method for improving generalized S-transform based on synchronous compression Download PDFInfo
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Abstract
The invention discloses a kind of Time-Frequency Analysis Method for combining improvement generalized S-transform based on synchronous compression, this method is on the basis of the improved generalized S-transform of window function, introduce synchronous compression conversion, in time-frequency plane along frequency direction by signal energy into rearrangement so that on energy accumulating to instantaneous frequency.Specific implementation comprises the following steps：Fast Fourier Transform (FFT) is carried out after signal sampling, the partial derivative of window function and window function to the time is determined according to gained frequency spectrum, generalized S-transform is improved to signal with window function and its partial derivative respectively afterwards, obtain signal transient frequency and time-frequency spectrum, it is last that energy rearrangement is carried out to time-frequency spectrum according to instantaneous frequency, obtain high-resolution time-frequency spectrum.This method not only remains the advantages of applicable wide, high resolution for improving generalized S-transform, but also contains the high-energy aggregation feature of synchronous compression, is a kind of high performance Time-Frequency Analysis Method.
Description
Technical field
It is particularly a kind of that improvement generalized S-transform is combined based on synchronous compression the invention belongs to signal processing technology field
Time-Frequency Analysis Method.
Background technology
Non-stationary signal is most common signal in Radar Signal Processing, and time frequency analysis be analyze such signal it is important
Instrument.For the local characteristics of accurate signal Analysis, one-dimensional time-domain signal is mapped to two-dimentional time-frequency plane by time frequency analysis, so that
Obtain the time-frequency distributions of signal.At present, common Time-Frequency Analysis Method mainly includes Short Time Fourier Transform (STFT), small echo becomes
Change (WT), S-transformation (ST) etc..
Dennis Gabor propose Short Time Fourier Transform in nineteen forty-six, its basic thought is to realize signal by adding window
Piecewise Fourier conversion, so as to obtain the time-varying characteristics of signal.But window function is fixed used in STFT, with time and frequency without
Close, be a kind of analysis method of single resolution ratio.It is a kind of window and the thought source of wavelet transformation is in flexible and shift method
Area is fixed but the changeable Time-Frequency Localization analysis method of shape, can adaptively adjust time-frequency according to low-and high-frequency signal characteristic
Window.But wavelet kernel difficulty is larger, there is the constraint of admissibility condition, while there are time frequency resolution deficiency, scale frequency
The defects of conversion is complicated.In order to make up the deficiency of Short Time Fourier Transform and wavelet transformation, Stockwell proposes S-transformation, draws
Entered variable Gauss function, and when window width be inversely proportional with frequency derivative.The time-frequency spectrum that this method obtains is in low frequency part frequency
Rate high resolution, i.e. resolution changable low in high frequency section frequency resolution.But this inverse relation causes window function in office
There is the problem of window length is wide and narrow in portion, causes timi requirement at low frequency to fail, the positioning failure of high frequency treatment frequency.
Number of patent application is CN201610946585.5, a kind of entitled " earthquake based on deconvolution generalized S-transform
The Chinese patent of spectral imaging method ", is obtained by the way that original signal wigner-ville distribution respective with Gaussian window is carried out two-dimentional convolution
To time-frequency spectrum.This method can suppress the generation of the cross term of Wigner-Ville distribution, while obtain generalized S-transform spectrum
Higher time-frequency locality, but it is limited in that the lack of resolution problem of low frequency and high frequency treatment cannot solve.
And although a kind of long Time-Frequency Analysis Method of limited window of the improvement S-transformation proposed before realizes the variable feelings of window function
Window length control under condition, has preferable time frequency resolution, but still limited by Heisenberg uncertainty principles, the time point
Resolution and frequency resolution are unable to reach optimal.
From the foregoing, it will be observed that existing Time-Frequency Analysis Method also Shortcomings, need to further improve to realize high-precision time-frequency
Analysis.
The content of the invention
Technical problem solved by the invention is to provide a kind of time-frequency based on synchronous compression combined and improve generalized S-transform
Analysis method.
The technical solution for realizing the object of the invention is：It is a kind of based on synchronous compression combine improve generalized S-transform when
Frequency analysis method, comprises the following steps：
Step 1, carry out Fast Fourier Transform (FFT) to input signal, obtains signal spectrum；
Step 2, the value according to controlling elements a, b, c in signal spectrum and the definite improvement generalized S-transform of analysis requirement, obtain
Window function expression formula；
Step 3, be improved generalized S-transform to signal, obtains time-frequency distributions MGST (t, f)；
Step 4, to window function derivation, obtain the corresponding partial derivative of each Frequency point；
Step 5, using window function partial derivative as new window function carry out generalized S-transform to signal, and combines threshold calculations
Instantaneous frequency vMGST(t,f)；
Step 6, synchronize compression to time-frequency plane signal, obtains high-resolution time-frequency distributions；
Compared with prior art, the present invention its remarkable advantage is：1) for the present invention comprising generalized S-transform is improved, window function can
Adaptively to be adjusted according to frequency, and by arctan function limit window grow excursion, solve low-and high-frequency area
The defects of domain lack of resolution；2) present invention is for different types of signal, can be realized by adjusting controlling elements value
High-resolution time frequency analysis, has very strong flexibility；3) present invention carries out energy rearrangement by synchronous compression to time frequency signal,
Energy accumulating is improved, overcomes the limitation of Heisenberg uncertainty principles.
The present invention is described in further detail below in conjunction with the accompanying drawings.
Brief description of the drawings
Fig. 1, which is that the present invention is a kind of, combines the Time-Frequency Analysis Method flow chart for improving generalized S-transform based on synchronous compression.
Fig. 2 is the time frequency analysis result figure that 1 signal of the embodiment of the present invention improves generalized S-transform.
Fig. 3 is the time frequency analysis result figure that 1 signal synchronous compression of embodiment of the present invention joint improves generalized S-transform.
Fig. 4 is the time frequency analysis result figure that 2 signal of the embodiment of the present invention improves generalized S-transform.
Fig. 5 is the time frequency analysis result figure that 2 signal synchronous compression of embodiment of the present invention joint improves generalized S-transform.
Fig. 6 is the time frequency analysis result figure that 3 signal of the embodiment of the present invention improves generalized S-transform.
Fig. 7 is the time frequency analysis result figure that 3 signal synchronous compression of embodiment of the present invention joint improves generalized S-transform.
Embodiment
With reference to Fig. 1, a kind of Time-Frequency Analysis Method for combining improvement generalized S-transform based on synchronous compression of the invention, including
Following steps：
Step 1, carry out Fast Fourier Transform (FFT) to input signal, obtains signal spectrum；
Step 2, according to signal spectrum determine improve generalized S-transform in controlling elements a, b, c value, obtain window function expression
Formula；Concretely comprise the following steps：
Step 2-1, according to true timing window value range [the Δ t of signal spectrummin,Δtmax], wherein Δ tminFor minimum when window
Length, Δ tmaxFor maximum time window length, the value range of a and c are determined by following inequality：
Step 2-2, the value of a and c is determined in value range, and is takenWhereinfsFor sample frequency,
And the value of a, b, c are substituted into the long control function of window：
Wherein f is the frequency variable in time frequency analysis；
Step 2-3, the long control function of window is brought into window function, obtains improved window function expression formula：
Wherein t is the time variable in time frequency analysis, and f is frequency variable.
Step 3, be improved generalized S-transform to signal, obtains time-frequency distributions MGST (t, f), and formula is：
Wherein τ is integration variable.
Step 4, to window function derivation, obtain the corresponding partial derivative of each Frequency point, formula is：
Step 5, using window function partial derivative as new window function carry out generalized S-transform to signal, and combines threshold calculations
Instantaneous frequency vMGST(t,f)；
Step 5-1, using window function partial derivative as new window function, generalized S-transform is carried out to signal, is obtained：
Step 5-2, reference threshold γ is set, according to criterion calculation instantaneous frequency vMGST(t, f), instantaneous frequency calculation formula
For：
Step 6, synchronize compression to time-frequency plane signal, obtains high-resolution time-frequency distributions.
Step 6-1, for l-th of Frequency point on instantaneous frequency axis, Δ v is calculatedl, Δ vl=vl-vl-1, wherein l ∈ [1,
N], N always counts for signal sampling, determines to reset section [vl-Δvl,vl+Δvl]；
Step 6-2, energy rearrangement is carried out, obtains SSTMGST(t,vl), calculation formula is：
Wherein, vlFor the frequency after synchronous compression, fkTo improve the discretization Frequency point in generalized S-transform spectrum, Δ fk=
fk-fk-1, k ∈ [1, N]；
Step 6-3, repeat step 6-1, step 6-2, until all instantaneous frequency points are completed to calculate, obtain time-frequency result.
One aspect of the present invention, which includes, improves generalized S-transform, can realize high-resolution by adjusting controlling elements values
Time frequency analysis, has very strong flexibility；On the other hand, add synchronous compression conversion, by time-frequency plane to signal
Carry out energy rearrangement and realize high-resolution time-frequency result.
The present invention is described in further detail with reference to embodiment.
Embodiment 1
Superposition of the signal for two sinusoidal signals is emulated, signal frequency is respectively 100Hz and 400Hz, and analytic expression is：
H (t)=sin (200 π t)+sin (800 π t) t ∈ [0,1]
Signal sampling frequencies fs=1024Hz, Fig. 2 are to improve generalized S-transform as a result, Fig. 3 is that synchronous compression joint improvement is wide
The simulation result of adopted S-transformation, wherein threshold gamma=0.001.In Fig. 2, frequency component is in zonal distribution, and combine synchronous compression it
Frequency component is thin linear pattern afterwards, and time frequency resolution is higher, and the edge divergence problem of script has also obtained larger improvement.And compare
According to color bar in figure, it can clearly be seen that the amplitude by the frequency component in the time frequency analysis result of synchronous compression is not much larger than
Through overcompression, therefore it is concluded that：By synchronous compression, signal energy aggregation is obviously improved, time-frequency distributions
Readability greatly improve.
Embodiment 2
Emulation signal is the linear FM signal that chirp rate is k=400, and analytic expression is：
Signal sampling frequencies fs=1024Hz, Fig. 4 are to improve generalized S-transform as a result, Fig. 5 is that synchronous compression joint improvement is wide
The simulation result of adopted S-transformation, wherein threshold gamma=0.001.It can be seen that, the when frequency division of window function is based purely on from analysis result
Analysis limit be subject to Heisenberg uncertainty principles all the time, though adjustment controlling elements to optimal, continuous improvement window function performance,
Still it cannot solve the problems, such as that signal energy dissipates, the frequency curve in time-frequency distributions has certain bandwidth all the time.And combine
The time frequency analysis of synchronous compression solves the deficiency of the time frequency analysis based on window function well, by the energy of certain frequency scope
Amount effectively focuses on instantaneous frequency, and also solves the problem of signal edge obscures in S-transformation.
Embodiment 3
NLFM signal is the signal that frequency is in sinusoidal variations, and analytic expression is：
H (t)=ej2π[6cos(10πt)+260t]t∈[0,1]
Signal sampling frequencies fs=1024Hz, Fig. 6 are to improve generalized S-transform as a result, Fig. 7 is that synchronous compression joint improvement is wide
The simulation result of adopted S-transformation, wherein threshold gamma=0.02.It is equal in the various pieces of frequency change for NLFM signal
There is higher resolution ratio, original frequency changes the problem of violent position signal energy diverging is serious and also obtained preferable solution
Certainly.Therefore, synchronous compression joint improves the Time-Frequency Analysis Method of generalized S-transform to either linear FM signal, also right and wrong
When linear FM signal is analyzed, all with greater advantage.
Claims (6)
1. a kind of combine the Time-Frequency Analysis Method for improving generalized S-transform based on synchronous compression, it is characterised in that including following step
Suddenly：
Step 1, carry out Fast Fourier Transform (FFT) to input signal x (t), obtains signal spectrum；
Step 2, according to signal spectrum determine improve generalized S-transform in controlling elements a, b, c value, obtain window function expression formula；
Step 3, be improved generalized S-transform to signal, obtains time-frequency distributions MGST (t, f)；
Step 4, to window function derivation, obtain the corresponding partial derivative g ' (t, f) of each Frequency point；
Step 5, using window function partial derivative as new window function to signal carry out generalized S-transform, and combine threshold calculations it is instantaneous
Frequency vMGST(t,f)；
Step 6, synchronize compression to time-frequency plane signal, obtains high-resolution time-frequency distributions.
2. according to claim 1 combine the Time-Frequency Analysis Method for improving generalized S-transform based on synchronous compression, its feature exists
In, the value of controlling elements a, b, c in improvement generalized S-transform are determined in step 2 according to signal spectrum, obtains window function expression formula,
Concretely comprise the following steps：
Step 2-1, according to true timing window value range [the Δ t of signal spectrummin,Δtmax], wherein Δ tminFor minimum when window grow
Degree, Δ tmaxFor maximum time window length, the value range of a and c are determined by following inequality：
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3. according to claim 1 combine the Time-Frequency Analysis Method for improving generalized S-transform based on synchronous compression, its feature exists
In being improved generalized S-transform to signal in step 3, obtain time-frequency distributions MGST (t, f), formula used is：
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4. according to claim 1 combine the Time-Frequency Analysis Method for improving generalized S-transform based on synchronous compression, its feature exists
In to window function derivation in step 4, obtaining the corresponding partial derivative g ' (t, f) of each Frequency point, formula used is：
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5. according to claim 1 combine the Time-Frequency Analysis Method for improving generalized S-transform based on synchronous compression, its feature exists
In using window function partial derivative as new window function to signal progress generalized S-transform in step 5, and it is instantaneous to combine threshold calculations
Frequency vMGST(t, f), concretely comprises the following steps：
Step 5-1, using window function partial derivative as new window function, generalized S-transform is carried out to signal, is obtained：
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6. according to claim 1 combine the Time-Frequency Analysis Method for improving generalized S-transform based on synchronous compression, its feature exists
In synchronizing compression to time-frequency plane signal in step 6, obtain high-resolution time-frequency distributions, concretely comprise the following steps：
Step 6-1, for l-th of Frequency point on instantaneous frequency axis, Δ v is calculatedl, Δ vl=vl-vl-1, wherein l ∈ [1, N], N be
Signal sampling is always counted, and determines to reset section [vl-Δvl,vl+Δvl]；
Step 6-2, energy rearrangement is carried out, obtains SSTMGST(t,vl), calculation formula is：
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Wherein, vlFor the frequency after synchronous compression, fkTo improve the discretization Frequency point in generalized S-transform spectrum, Δ fk=fk-fk-1,
k∈[1,N]；
Step 6-3, repeat step 6-1, step 6-2, until all instantaneous frequency points are completed to calculate, obtain time-frequency result.
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| CN111504640B (en) * | 2020-04-30 | 2021-08-06 | 电子科技大学 | Weighted sliding window second-order synchronous compression S transformation bearing fault diagnosis method |
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