CN105467446A - Self-adaptive optimal kernel time-frequency analysis method based on radial Gaussian kernel - Google Patents

Abstract

The invention discloses a self-adaptive optimal kernel time-frequency analysis method based on a radial Gaussian kernel. The self-adaptive optimal kernel time-frequency analysis method comprises the steps that: one path of seismic data is input; a rectangular time window is added to a signal; limitation on volume of a kernel function is given; a fuzzy function of the signal in the rectangular time window is calculated; a local optimal kernel function is calculated within a window function, and the calculation of the optimal kernel function is realized by using two restricted conditions; and the kernel function is equivalent to weighting the fuzzy function, the kernel function and the fuzzy function are subjected to two-dimensional Fourier transform after being multiplied, a time-frequency spectrum for eliminating cross-term interference is obtained, and the rectangular time window is moved to obtain whole time-frequency spectra of the signal The self-adaptive optimal kernel time-frequency analysis method has the capability of depicting signal details, can effectively suppress cross terms in multi-component signal time-frequency distribution, has the resolution close to Wigner distribution, and is ideal time-frequency distribution when being applied to seismic signal analysis.

Description

Based on the adaptive optimal kernel Time-Frequency Analysis Method of radial Gaussian kernel

Technical field

The present invention relates to exploration geophysics information Processing Technology field, is the Time-Frequency Analysis Method based on adaptive optimal kernel, is the important tool of seismic data analysis and data process.

Background technology

Adaptive optimal kernel Time-Frequency Analysis Method grows up on the basis of radial Gaussian kernel Time-Frequency Analysis Method.At first, signal operate time and frequency Two Variables describe by Short Time Fourier Transform and Gabor transformation, open the gate of time frequency analysis.Then there is again the Linear Time-Frequency Analysis such as wavelet transformation, S-transformation method, in order to improve the time-frequency degree of focus of signal, having developed again the quadratic form time-frequency analysis method such as Wigner distribution, Cohen class.Cohen class Time-Frequency Analysis Method is a given kernel function in time frequency analysis process, comes Wigner distribution smoothing, reaches the object eliminating cross term interference.But Cohen class Time-Frequency Analysis Method, kernel function is single, does not have universality.

In order to improve the applicability of the method, there is radial Gaussian kernel Time-Frequency Analysis Method, it can use different kernel functions to different signals, but the design of the kernel function of this time-frequency distributions is relevant with whole signal, still shows deficiency for the time dependent signal of signal characteristic.Based on self-adaptive kernel Time-Frequency Analysis Method, the kernel function of the method not only can the dissimilar signal of self-adaptation, the more important thing is and can change with signal time variations, realize the self-adaptation to signal local feature, and its be also very suitable for signal real-time, process online, all there is adaptability to the signal of random length and any character, and any priori of undesired signal.

Non-linear Time-Frequency Analysis Method has good time-frequency focusing, Cohen is studied numerous time-frequency representation methods, finds that they are the different distortion of WVD distribution, unified form can be adopted to represent, be called Cohen class time-frequency distributions, its expression formula is:

$P(t,f)={\∫}_{-\∞}^{\∞}{\∫}_{-\∞}^{\∞}{\∫}_{-\∞}^{\∞}x(u+\frac{\mathrm{\τ}}{2})x^{*}(u-\frac{\mathrm{\τ}}{2})\mathrm{\φ}(\mathrm{\τ},v)e^{-i2\mathrm{\π}(\mathrm{tv}+\mathrm{\τf}-\mathrm{uv})}\mathrm{dudvd\τ}---\left(1\right)$

In formula, φ (τ, v) is kernel function.

In formula, note be referred to as ambiguity function, Cohen class time-frequency distributions is in fact with the two-dimension fourier transform of kernel function weighting as ambiguity function, so be also called generalized bilinear time-frequency distributions.

The time-frequency distributions based on signal radial Gaussian kernel that Cohen class basis grows up is that the two-dimensional function being all Gauss type on any radial section is defined as kernel function to be asked, that is:

Wherein σ (Ψ) is called spread function, and for controlling the expansion of radially Gaussian kernel function in radial angle Ψ direction, Ψ is angle that is radial and horizontal direction, in general, radial Gaussian function represents more convenient in polar coordinates, order then

The radially Gaussian kernel function that One-Dimensional Extended function parameterization can be given expression to completely two dimension can being found out, therefore can obtain Φ (θ, τ) by solving σ (Ψ).Solve optimum kernel function, kernel function and signal are matched most, then can obtain good time-frequency distributions, solving optimum kernel function is then solve following optimization problem:

$\underset{\mathrm{\Φ}}{\max }{\∫}_0^{2\mathrm{\π}}{\∫}_0^{\∞}|A(r,\mathrm{\Ψ})\mathrm{\Φ}(r,\mathrm{\Ψ}){|}^2\mathrm{rdrd\Ψ}---\left(4\right)$

Constraint condition is

a. $\mathrm{\Φ}(r,\mathrm{\Ψ})=\exp (-\frac{r^2}{2{\mathrm{\σ}}^2\left(\mathrm{\Ψ}\right)})$

b. $\frac{1}{2\mathrm{\π}}{\∫}_0^{2\mathrm{\π}}{\∫}_0^{\∞}{\left|\mathrm{\Φ}(r,\mathrm{\Ψ})\right|}^2\mathrm{rdrd\Ψ}=\frac{1}{2\mathrm{\π}}{\∫}_0^{2\mathrm{\π}}{\mathrm{\σ}}^2\left(\mathrm{\Ψ}\right)\mathrm{d\Ψ}\≤\mathrm{\α},\mathrm{\α}\≥0$

In formula, A (r, Ψ) is the ambiguity function represented in polar coordinates, and the constraint condition a scope limited in optimization problem is radial Gaussian kernel class (lowpass function), and constraint condition b limits the volume of optimum core.Concerning multicomponent data processing, being generally distributed near initial point from component of its ambiguity function, mutual component is then away from initial point, and the effect of constraint condition makes to pass through from component, and mutual component is suppressed, and Here it is, and above-mentioned optimization problem is local cleverly.The effect of Max function is for the fixing kernel function of a certain volume, allows as much as possible from component energy by with the loss reduced from component.

Time-frequency distributions based on signal radial Gaussian kernel has excellent characteristic very much, its kernel function can make corresponding change along with the difference of signal, and then suppressing crossterms well, the time-frequency energy distribution of signal has good focusing, just can realize optimized algorithm by simple iteration, the time-frequency distributions calculated amount making the calculated amount of whole process almost fixing with kernel function is identical.But the weak point based on the time-frequency distributions of signal radial Gaussian kernel is only to devise an optimum kernel function to whole signal, it is a kind of total algorithm, show certain limitation when analyzing the signal that perdurability, longer or characteristic changed greatly in time, and be not suitable for the real-time process of signal.

Summary of the invention

The object of the invention is to for the deficiencies in the prior art, a kind of adaptive optimal kernel Time-Frequency Analysis Method based on radial Gaussian kernel is provided, with the cross term interference of the focusing and compacting time frequency analysis that improve the time-frequency spectrum of signal time frequency analysis.

Technology path of the present invention is on the basis of radial Gaussian kernel Time-Frequency Analysis Method, proposes the adaptive optimal kernel Time-Frequency Analysis Method based on radial Gaussian kernel.Adaptive optimal kernel time-frequency distributions adopts short-time ambiguity function and time dependent self-adaptive kernel function, can distinguish the detail section of multicomponent data processing in time-frequency distributions.Adaptive optimal kernel time-frequency distributions theory is a kind of modern signal processing method, and it is the Time-Frequency Analysis Method adopting nonlinear transformation process non-stationary signal.

Technical scheme of the present invention is:

1) one geological data first, is inputted;

2) in order to the local characteristics of outstanding signal, signal adds rectangular time window; Give restriction to the volume of kernel function simultaneously;

3) according to the size of rectangular time window, the ambiguity function of signal in rectangular time window is calculated;

4) in window function internal calculation local optimum kernel function, in computation process, asking for of optimum kernel function is realized with two restrictive conditions, two restrictive conditions one are the scopes of restriction optimization problem is radial Gauss's class (lowpass function), and another limits the volume of optimum kernel function;

5) kernel function is equivalent to carry out weighting to ambiguity function, and after the two product, do two-dimensional Fourier transform, the time-frequency spectrum of the cross term interference that is eliminated, mobile rectangular time window obtains the time-frequency spectrum of whole signal.

Such scheme also comprises: complete 1)-5) after step, for extracting a series of time-frequency attributes of seismic trace, analyzing and longitudinally above differentiating thin layer and prediction thickness of thin layer; And multiple tracks earthquake carries out cycle calculations according to overall flow.

Such scheme comprises further:

In step 2) in, the length of time window is the Nth power of 2, and the size of kernel function generally between 1 ~ 5, and sets the volume upper limit of kernel function according to actual needs.

In step 3) in, calculate the ambiguity function of signal in rectangular time window, signal s (t), definition instantaneous correlation function is

$R(t,\mathrm{\τ})=s^{*}(t-\frac{\mathrm{\τ}}{2})s(t+\frac{\mathrm{\τ}}{2})---\left(1\right)$

Wherein t is instantaneous time, and τ is a time delay of signal s (t), and s (t) is signal function to be analyzed, s ^*t () is the conjugate function of s (t), R (t, τ) is the instantaneous correlation function of s (t), so short-time ambiguity function expression formula

$A=(t:\mathrm{\θ},\mathrm{\τ})=\∫R(u,\mathrm{\τ})w^{*}(u-t-\frac{\mathrm{\τ}}{2})w(u-t+\frac{\mathrm{\τ}}{2})e^{\mathrm{j\θu}}\mathrm{du}=\∫s^{*}(u-\frac{\mathrm{\τ}}{2})w^{*}(u-t-\frac{\mathrm{\τ}}{2})s(u+\frac{\mathrm{\τ}}{2})w(u-t+\frac{\mathrm{\τ}}{2})e^{\mathrm{j\θu}}\mathrm{du}---\left(2\right)$

Wherein, t is instantaneous time, τ is a time delay of signal s (t) is also signal ambiguity domain variable simultaneously, and θ is signal ambiguity domain variable, A (t: θ, τ) short-time ambiguity function, u is the time variable of instantaneous correlation function, and R (u, τ) is the instantaneous correlation function of s (t), w (u) is rectangular window function, s ^*t () is the conjugate function of s (t).

In step 3) in, in the process of short-time ambiguity function calculating signal in rectangular window, according to relational expression A (t: θ, τ)=A ^*(t:-θ ,-τ), utilizes calculated short-time ambiguity function to ask other short-time ambiguity function, and need not double counting.

In step 4) in, calculate the optimum kernel function in window function:

$\underset{\mathrm{\Φ}}{\max }{\∫}_0^{2\mathrm{\π}}{\∫}_0^{\∞}|A(t:r,\mathrm{\Ψ})\mathrm{\Φ}(t:r,\mathrm{\Ψ}){|}^2\mathrm{rdrd\Ψ}---\left(3\right)$

Restrictive condition is

a. $\mathrm{\Φ}(t:r,\mathrm{\Ψ})=\exp (-\frac{r^2}{2{\mathrm{\σ}}^2(t:\mathrm{\Ψ})})$

b. $\frac{1}{2\mathrm{\π}}{\∫}_0^{2\mathrm{\π}}{\∫}_0^{\∞}{\left|\mathrm{\Φ}(t:r,\mathrm{\Ψ})\right|}^2\mathrm{rdrd\Ψ}=\frac{1}{2\mathrm{\π}}{\∫}_0^{2\mathrm{\π}}{\mathrm{\σ}}^2(t:\mathrm{\Ψ})\mathrm{d\Ψ}\≤\mathrm{\α},\mathrm{\α}\≥0$

Wherein, t is instantaneous time, r and Ψ is signal ambiguity domain of function polar coordinates variablees, and r is the radius variable under polar coordinates, A (t:r, Ψ) with Φ (t:r, be Ψ) short-time ambiguity function under polar coordinates and kernel function respectively, wherein σ (Ψ) is called spread function, for controlling the expansion of radially Gaussian kernel function in radial angle Ψ direction, Ψ is angle that is radial and horizontal direction α is step 2) in the volume of kernel function, A (t:r, Ψ) with Φ (t:r, Ψ) be short-time ambiguity function under polar coordinates and kernel function respectively, the constraint condition a scope limited in optimization problem is radial Gaussian kernel class lowpass function, and constraint condition b limits the volume of optimum core.

In step 5) in, obtain the time-frequency spectrum expression formula of whole signal

$P_{\mathrm{AOK}}(t,\mathrm{\ω})=\frac{1}{4{\mathrm{\π}}^2}\∫\∫A(t:r,\mathrm{\Ψ}){\mathrm{\Φ}}_{o\mathrm{pt}}(t:r,\mathrm{\Ψ})e^{-\mathrm{jrt}-\mathrm{j\Ψ\ω}}\mathrm{drd\Ψ}---\left(4\right)$

Wherein, t is instantaneous time, and ω is the frequency variable of the time-frequency spectrum function of signal, P _aOK(t, ω) is the time-frequency spectrum of signal, r and Ψ is signal ambiguity domain of function polar coordinates variablees, and A (t:r, Ψ) is the short-time ambiguity function of signal, Φ _opt(t:r, Ψ) is the kernel function of the optimum calculated.

On the basis of such scheme, by carrying out adaptive optimal kernel time frequency analysis to single-channel seismic data, obtaining the time-frequency spectrum of single track signal, the analysis of thin interbed and sedimentary cycle can be carried out; The attribute section that time frequency analysis can obtain whole seismic section is carried out to per pass geological data.

Method of the present invention is the development to radial Gaussian kernel Time-Frequency Analysis Method, time-frequency attribute can be applied to the explanation that seismic section is carried out in Wheeler territory, and well solve the local of the Linear Time-Frequency Analysis methods such as Short Time Fourier Transform, wavelet transformation and S-transformation to signal and to portray not accurately and the non-linear Time-Frequency Analysis Method such as Cohen class is carrying out the problem of cross term interference of the existence in time frequency analysis process.Improve the precision of portraying non-stationary signal local on the one hand, be embodied in the restriction of Linear Time-Frequency Analysis method by window function, its time frequency resolution is subject to the constraint of the uncertain principle of Heisenberg, and temporal resolution and frequency resolution restrict mutually.Adaptive optimal kernel time-frequency distributions adopts short-time ambiguity function and time dependent self-adaptive kernel function, can distinguish the detail section of multicomponent data processing in time-frequency distributions.On the other hand, improve the compacting of non-linear time frequency analysis cross term interference.In the process solving optimum kernel function, the kind proposing restriction optimization problem Kernel Function is volume two constraint conditions of radial Gaussian kernel class and the optimum kernel function of restriction.By constraint condition, make to pass through from component, mutual component is suppressed, can well suppressing crossterms interference.

Accompanying drawing explanation

The process flow diagram of Fig. 1 an embodiment of the present invention.

The design sketch of several Time-Frequency Analysis Method of Fig. 2, wherein (a) reflection coefficient sequence; (b) theogram; C () Wigenr-Ville distributes; (d) Gabor transformation; (e) S-transformation; (f) Gauss Wavelet Transform; (g) time-frequency spectrum of the present invention.

The sedimentary cycle rule figure of the single track time-frequency spectrum that Fig. 3 utilizes adaptive optimal kernel to obtain, wherein (a) time frequency analysis result; (b) reflection coefficient sequence; (c) theogram.

The instantaneous attribute sectional view that Fig. 4 utilizes the inventive method to obtain.

Embodiment

For making above and other object of the present invention, feature and advantage can become apparent, cited below particularly go out preferred embodiment, and coordinate accompanying drawing, be described in detail below.

Fig. 1 illustrates the process flow diagram of a kind of specific embodiment of the present invention.

Adaptive optimal kernel Time-Frequency Analysis Method based on radial Gaussian kernel comprises:

First, input one geological data, then carry out as follows.

Step 101, in order to the local characteristics of outstanding signal, signal adds rectangular time window, and the length of rectangular time window should be the Nth power of 2, the realization that fast and easy calculates.And the size of kernel function is generally between 1 ~ 5, according to actual conditions, select different kernel function volumes.

Step 102, according to the size of rectangular time window, calculates the ambiguity function of signal in rectangular time window, signal s (t), and definition instantaneous correlation function is

$R(t,\mathrm{\τ})s^{*}(t-\frac{\mathrm{\τ}}{2})s(t+\frac{\mathrm{\τ}}{2})---\left(1\right)$

Wherein t is instantaneous time, and τ is a time delay of signal s (t), and s (t) is signal function to be analyzed, s ^*t () is the conjugate function of s (t), R (t, τ) is the instantaneous correlation function of s (t), so short-time ambiguity function expression formula

$A=(t:\mathrm{\θ},\mathrm{\τ})=\∫R(u,\mathrm{\τ})w^{*}(u-t-\frac{\mathrm{\τ}}{2})w(u-t+\frac{\mathrm{\τ}}{2})e^{\mathrm{j\θu}}\mathrm{du}=\∫s^{*}(u-\frac{\mathrm{\τ}}{2})w^{*}(u-t-\frac{\mathrm{\τ}}{2})s(u+\frac{\mathrm{\τ}}{2})w(u-t+\frac{\mathrm{\τ}}{2})e^{\mathrm{j\θu}}\mathrm{du}---\left(2\right)$

Wherein, t is instantaneous time, τ is a time delay of signal s (t) is also signal ambiguity domain variable simultaneously, and θ is signal ambiguity domain variable, A (t: θ, τ) short-time ambiguity function, u is the time variable of instantaneous correlation function, and R (u, τ) is the instantaneous correlation function of s (t), w (u) is rectangular window function, s ^*t () is the conjugate function of s (t).In the process of short-time ambiguity function calculating signal in rectangular window, directly press above formula and calculate very time-consuming, utilize relational expression A (t: θ, τ)=A ^*(t:-θ ,-τ), can utilize calculated short-time ambiguity function to ask other short-time ambiguity function, and need not double counting.

Step 103, at window function internal calculation local optimum core.In computation process, realize asking for of optimum core with two restrictive conditions.Calculate the optimum kernel function in window function.Solving optimum kernel function is then solve following optimization problem:

$\underset{\mathrm{\Φ}}{\max }{\∫}_0^{2\mathrm{\π}}{\∫}_0^{\∞}|A(t:r,\mathrm{\Ψ})\mathrm{\Φ}(t:r,\mathrm{\Ψ}){|}^2\mathrm{rdrd\Ψ}---\left(3\right)$

Constraint condition is

a. $\mathrm{\Φ}(t:r,\mathrm{\Ψ})=\exp (-\frac{r^2}{2{\mathrm{\σ}}^2(t:\mathrm{\Ψ})})$

b. $\frac{1}{2\mathrm{\π}}{\∫}_0^{2\mathrm{\π}}{\∫}_0^{\∞}{\left|\mathrm{\Φ}(t:r,\mathrm{\Ψ})\right|}^2\mathrm{rdrd\Ψ}=\frac{1}{2\mathrm{\π}}{\∫}_0^{2\mathrm{\π}}{\mathrm{\σ}}^2(t:\mathrm{\Ψ})\mathrm{d\Ψ}\≤\mathrm{\α},\mathrm{\α}\≥0$

Wherein, t is instantaneous time, r and Ψ is signal ambiguity domain of function polar coordinates variablees, and r is polar radius variable, and Ψ is angle that is radial and horizontal direction, a (t:r, Ψ) and Φ (t:r, Ψ) is short-time ambiguity function under polar coordinates and kernel function respectively, and wherein σ (Ψ) is called spread function.α is the volume of the kernel function in step 101.A (t:r, Ψ) and Φ (t:r, Ψ) is short-time ambiguity function under polar coordinates and kernel function respectively.The constraint condition a scope limited in optimization problem is radial Gaussian kernel class (lowpass function), and constraint condition b limits the volume of optimum core.Concerning multicomponent data processing, being generally distributed near initial point from component of its ambiguity function, mutual component is then away from initial point, and the effect of constraint condition makes to pass through from component, and mutual component is suppressed, and Here it is, and above-mentioned optimization problem is local cleverly.The effect of Max function is for the fixing kernel function of a certain volume, allows as much as possible from component energy by with the loss reduced from component.

Step 104, kernel function is equivalent to carry out weighting to ambiguity function, after the two product, does two-dimensional Fourier transform, the time-frequency spectrum of the cross term interference that is eliminated.Mobile rectangular time window obtains the time-frequency spectrum of whole signal.

$P_{\mathrm{AOK}}(t,\mathrm{\ω})=\frac{1}{4{\mathrm{\π}}^2}\∫\∫A(t:r,\mathrm{\Ψ}){\mathrm{\Φ}}_{o\mathrm{pt}}(t:r,\mathrm{\Ψ})e^{-\mathrm{jrt}-\mathrm{j\Ψ\ω}}\mathrm{drd\Ψ}---\left(4\right)$

Wherein, t is instantaneous time, and ω is the frequency variable of the time-frequency spectrum function of signal, r and Ψ is signal ambiguity domain of function polar coordinates variablees, and r is polar radius variable, and Ψ is angle that is radial and horizontal direction, p _aOK(t, ω) is the time-frequency spectrum of signal, and A (t:r, Ψ) is the short-time ambiguity function of signal, Φ _opt(t:r, Ψ) is the kernel function of the optimum calculated.

Complete in steps after, can be used for extracting a series of time-frequency attributes of seismic trace, can analyze and longitudinally above differentiate thin layer and prediction thickness of thin layer.Multiple tracks earthquake carries out cycle calculations according to overall flow.

As Fig. 2, utilize WVD, Gabor transformation, Gauss Wavelet Transform, S-transformation and method of the present invention respectively, thin interbed theogram is carried out to the time-frequency spectrum of the composite traces that time frequency analysis obtains.Can find, the time-frequency precision of time-frequency spectrum of the present invention is the highest, and cross term interference is very little.

As Fig. 3, to the sedimentary cycle rule of this position, road that single-channel seismic data analysis obtains.The cycle rule on stratum can well be obtained by time frequency analysis.This model is gone up exactly and is just being descended derotation to return, and the main energy group of time-frequency spectrum first reduces to increase afterwards from top to bottom.

As Fig. 4, utilize Time-Frequency Analysis Method of the present invention to analyze real data, the instantaneous amplitude section of the real data obtained, utilize this result to carry out the reser-voir prediction and description work such as attributive analysis.

Claims (7)

1., based on the adaptive optimal kernel Time-Frequency Analysis Method of radial Gaussian kernel, it is characterized in that:

1) one geological data first, is inputted;

2) in order to the local characteristics of outstanding signal, signal adds rectangular time window; Give restriction to the volume of kernel function simultaneously;

3) according to the size of rectangular time window, the ambiguity function of signal in rectangular time window is calculated;

4) in window function internal calculation local optimum kernel function, in computation process, realize asking for of optimum kernel function with two restrictive conditions, two restrictive conditions one are the scopes of restriction optimization problem is radial Gauss's class, and another limits the volume of optimum kernel function;

5) kernel function is equivalent to carry out weighting to ambiguity function, and after the two product, do two-dimensional Fourier transform, the time-frequency spectrum of the cross term interference that is eliminated, mobile rectangular time window obtains the time-frequency spectrum of whole signal.

2. the adaptive optimal kernel Time-Frequency Analysis Method based on radial Gaussian kernel according to claim 1, is characterized in that: complete 1)-5) after step, extract a series of time-frequency attributes of seismic trace, analyze and longitudinally above differentiate thin layer and prediction thickness of thin layer; And multiple tracks earthquake carries out cycle calculations according to overall flow.

3. the adaptive optimal kernel Time-Frequency Analysis Method based on radial Gaussian kernel according to claim 1 and 2, is characterized in that: described step 2) in, the length of time window is the Nth power of 2, and the size of kernel function is generally between 1 ~ 5.

4. the adaptive optimal kernel Time-Frequency Analysis Method based on radial Gaussian kernel according to claim 3, is characterized in that: in step 3) in, calculate the ambiguity function of signal in rectangular window, signal s (t), definition instantaneous correlation function is

Wherein s ^*t () is the conjugate function of s (t), so short-time ambiguity function expression formula

Wherein, w (u) is rectangular time window function.

5. the adaptive optimal kernel Time-Frequency Analysis Method based on radial Gaussian kernel according to claim 4, it is characterized in that: in step 3) in, in the process of short-time ambiguity function calculating signal in rectangular window, according to relational expression A (t: θ, τ)=A ^*(t:-θ ,-τ), utilizes calculated short-time ambiguity function to ask other short-time ambiguity function, and need not double counting.

6. the adaptive optimal kernel Time-Frequency Analysis Method based on radial Gaussian kernel according to claim 5, is characterized in that: in step 4) in, calculate the optimum kernel function expression formula in window function

Restrictive condition is

a.

b.

α is step 2) in the volume of kernel function, A (t:r, Ψ) with Φ (t:r, Ψ) be short-time ambiguity function under polar coordinates and kernel function respectively, the constraint condition a scope limited in optimization problem is radial Gaussian kernel class, and constraint condition b limits the volume of optimum core.

7. the adaptive optimal kernel Time-Frequency Analysis Method based on radial Gaussian kernel according to claim 6, is characterized in that: in step 5) in, obtain the time-frequency spectrum expression formula of whole signal

。