CN102521210A - Order selection method of time-frequency distribution progression - Google Patents

Abstract

The invention discloses an order selection method of time-frequency distribution progression, which comprises the following steps of: solving a normalization entropy of each order of TFDS (Temporal Functional Dependencies); judging aggregation of each term and cross term conditions according to the normalization entropy of each order of TFDS, wherein the TDFS with maximum normalization entropy has good time frequency distribution aggregation and less cross terms, thus the order corresponding to the maximum value of the normalization entropy is selected as a value of an order D. According to the invention, the TFDS order with high aggregation is selected by using the normalization entropy as a TFDS aggregation measurement, thus the defect that the order of the TFDS is selected artificially and objectively without quantitative basis. According to the order selection method, better noise cancelling performance is obtained without being nearly influenced by noise in signals.

Description

A kind of exponent number system of selection of time-frequency distributions progression

Technical field

The invention belongs to the signal processing technology field, be specifically related to a kind of exponent number system of selection of time-frequency distributions progression.

Background technology

Wigner-Ville distribution (Wigner-Ville Distribution is called for short WVD) is a most basic a kind of bilinearity time-frequency representation form.This distribution is to be proposed in quantum mechanics by Wigner at first, by Ville it is referenced to signal analysis afterwards.The WVD of signal z (t) can be expressed as:

${\mathrm{WVD}}_z(t,f)={\&Integral;}_{-\&infin;}^{+\&infin;}z(t+\frac{1}{2}\mathrm{\&tau;})z^{*}(t-\frac{1}{2}\mathrm{\&tau;})e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="DEST\_PATH\_HDA0000131212030000012.png,DEST\_PATH\_HDA0000131212030000014.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;f\&tau;}}\mathrm{d\&tau;}---\left(1\right)$

Following formula claims also that from WVD τ is the time delay variable in the formula, and t is a time variable, and f is a frequency variable, z ^*(t) be the complex conjugate function of z (t).

WVD has a lot of important properties, like real-valued property, symmetry, local edge, time and frequency shifting characteristic, high time-frequency aggregation etc.Because these good properties, it is studied widely, and in actual engineering, has obtained extensive application.

Two signal z ₁(t) and z ₂Mutual WVD (t) (Cross WVD XWVD) is defined as:

${\mathrm{WVD}}_{z_1,z_2}(t,f)={\&Integral;}_{-\&infin;}^{+\&infin;}{{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="DEST\_PATH\_HDA0000131212030000013.png,DEST\_PATH\_HDA0000131212030000014.png"\; state="\{\{state\}\}">z</figure-callout>}}_1}^{*}(t-\frac{1}{2}\mathrm{\&tau;})z_2(t+\frac{1}{2}\mathrm{\&tau;})e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="DEST\_PATH\_HDA0000131212030000012.png,DEST\_PATH\_HDA0000131212030000014.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;f\&tau;}}\mathrm{d\&tau;}---\left(2\right)$

Two signals and WVD be:

${\mathrm{WVD}}_{z_1+z_2}={\mathrm{WVD}}_{z_1}+{\mathrm{WVD}}_{z_2}+2\mathrm{Re}\left[{\mathrm{WVD}}_{z_1,z_2}\right]---\left(3\right)$

is the interference that is caused by signal plus in the formula, is commonly referred to cross term or distracter.

Following formula shows that the WVD of two signal sums not only comprises the WVD of signal separately, also comprises their mutual WVD.Cross term can make time-frequency distributions thicken, sometimes also can with from overlaid, had a strong impact on physical interpretation to WVD.Under most situation, cross term is harmful to, and therefore, the existence of cross term has become the obstacle of WVD widespread use.But simultaneously also just the existence of these cross terms just guaranteed to that is to say a lot of good characteristics of WVD, between the good characteristic of WVD and cross term, have balance, can when guaranteeing good characteristic, have the existence of cross term again.

Time-frequency distributions progression (Time-Frequency Distribution Series; Be called for short TFDS) be early 1990s; A kind of new time-frequency distributions that people such as Qian utilize linear time-frequency representation (Gabor expansion) and bilinearity time-frequency distributions (WVD) to propose is through the cross term and the aggregation of exponent number D may command time-frequency distributions.Basic way is to utilize Gabor to launch signal decomposition is become the linear combination of basis function (time-frequency atom) earlier; Calculate the WVD that Gabor launches the back signal then; This WVD is made up of basis function interactional cross term between the linear superposition of WVD and each basis function, that is:

${\mathrm{WVD}}_s(t,f)=\underset{m,n}{\mathrm{\&Sigma;}}{\left|c_{m,n}\right|}^2{\mathrm{WVD}}_g(t,f)+\underset{m,n}{\mathrm{\&Sigma;}}\underset{m^{\&prime;}\&NotEqual;m,n^{\&prime;}\&NotEqual;n}{\mathrm{\&Sigma;}}{c}_{m,n}{c}_{m^{\&prime;}{n}^{\&prime;}}^{*}{\mathrm{WVD}}_{g,g^{\&prime;}}(t,f)---\left(4\right)$

In the formula, c _{M, n}Be the Gabor expansion coefficient, g, g ' are the Gabor basis function, WVD _gAnd WVD _{G, g '}Can regard time-frequency energy atom as.

Some useful properties of the timely frequency division cloth of the energy of signal time-frequency distributions mainly be by each basis function WVD from and the cross term between the basis function of close proximity decision in time-frequency plane, and the cross term that the basis function of apart from each other produces is very little to the influence of the useful quality of time-frequency distributions.If only last of modus ponens (4), then obtains one and just distribute, but aggregation is very poor.The way of Qian is, in keeping first all from, the cross term that produces by the basis function of close proximity in keeping second, these cross terms can improve the aggregation of signal from item, the time-frequency distributions that this method obtains is TFDS:

${\mathrm{TFDS}}_D(t,\mathrm{\&omega;})=\underset{|m-m^{\&prime;}|+\left|n{-n}^{\&prime;}\right|}{\mathrm{\&Sigma;}}{c}_{m,n}{c}_{m^{\&prime;}{n}^{\&prime;}}^{*}{\mathrm{WVD}}_{g,g^{\&prime;}}(t,\mathrm{\&omega;})---\left(5\right)$

In the formula, | m-m ' |+| n-n ' | be atom g _{M, n}(t) and g _{M ' n '}(t) the Manhattan distance between, D is called exponent number.

Exponent number may command cross term and calculated amount, when D=0, the performance of TFDS is near short time discrete Fourier transform; When D increased, the resolution of TFDS and aggregation all can improve, and cross term increases, calculated amount increases but make; When D tended to infinite, TFDS converged on WVD.Usually, for taking into account resolution and cross term, the span of D is 2～4, and the time-frequency distributions of this moment has not only kept some useful attributes of WVD, has reduced the calculated amount when exponent number is higher again.At present, the system of selection of exponent number D be mostly according in using to the requirement of cross term and the character of time-frequency distributions, artificial subjective definite.

Document " based on the Gabor conversion window function width adaptive selection method of entropy " (" electronics and information journal "; 2008) proposed Shannon entropy is improved; Make its span [0; 1] between, the normalization entropy after the improvement can be used as a kind of performance metric of time-frequency distributions aggregation, defines as follows:

$H_1=1+\underset{m}{\mathrm{\&Sigma;}}\underset{n}{\mathrm{\&Sigma;}}{P}_s(m,n){\log }_{\mathrm{MN}}\left(P_s(m,n)\right)---\left(6\right)$

In the formula, N, M are respectively the time and the frequency of time-frequency distributions and count.

Can draw H by formula (6) ₁Span be closed interval [0,1], when the energy of signal time-frequency distributions evenly distributes in time-frequency plane, i.e. P _s(m, n)=1/MN, m=1, L, M; N=1, L, N, H ₁Obtain minimum value 0; When the energy of signal time-frequency distributions focuses in time-frequency plane when a bit, i.e. P _s(m, n)=δ (m-m ₀, n-n ₀), 1≤m ₀≤M, 1≤n ₀≤N, H ₁Obtain maximal value 1.The aggregation of time-frequency distributions is poor more or signal is more complicated, and the value of its normalization entropy just approaches minimum value 0 more; The aggregation of time-frequency distributions is good more or signal is simple more, and the value of its normalization entropy just approaches maximal value 1 more.

Summary of the invention

For solving the problems referred to above that prior art exists, the present invention will design a kind of automatically time-frequency distributions progression exponent number system of selection that selective aggregation property is good.

To achieve these goals, technical scheme of the present invention is following: a kind of exponent number system of selection of time-frequency distributions progression may further comprise the steps:

A, ask the normalization entropy of each rank TFDS $H_{}$ ${}_1=1+\underset{m}{\mathrm{\&Sigma;}}\underset{n}{\mathrm{\&Sigma;}}{P}_s(m,n){\mathrm{Log}}_{\mathrm{MN}}\left(P_s(m,n)\right)$

In order to say something, calculate TFDS and normalization entropy thereof below 8 rank;

B, obtain the corresponding exponent number of maximal value of normalization entropy

Cross term is more, the value of entropy is more little, and aggregation is good more, the value of entropy is big more, therefore can judge its aggregation and cross term situation from item through the normalization entropy of each rank TFDS; The TFDS that the normalization entropy is maximum, its time-frequency distributions aggregation is good, and cross term is few; So the exponent number of the maximal value correspondence of selection normalization entropy is as the value of divisor D.

Compared with prior art, the present invention has following beneficial effect:

1, the present invention adopts the normalization entropy as TFDS aggregation tolerance, and with the high TFDS exponent number of its selective aggregation property, having overcome does not have quantitative basis, the subjective artificially defective of selecting when the TFDS exponent number is selected.

2, the present invention is through selecting the TFDS exponent number to different signal-noise ratio signals (signal to noise ratio (S/N ratio) is respectively-5dB, 0dB, 5dB); Fig. 7-9 is the relation between the exponent number of entropy and TFDS of TFDS; Can draw this method have simultaneously good noise proofness can, this method receives the The noise that exists in the signal hardly.

Description of drawings

9 in the total accompanying drawing of the present invention, wherein:

Fig. 1 is the gaussian envelope oscillator signal;

Fig. 2 is the WVD of Fig. 1 gaussian envelope oscillator signal;

Fig. 3 is 0 rank TFDS of Fig. 1 gaussian envelope oscillator signal;

Fig. 4 is 1 rank TFDS of Fig. 1 gaussian envelope oscillator signal;

Fig. 5 is 2 rank TFDS of Fig. 1 gaussian envelope oscillator signal;

Fig. 6 is 5 rank TFDS of Fig. 1 gaussian envelope oscillator signal;

Fig. 7 is the relation between the exponent number of the entropy of the TFDS that obtains behind Fig. 1 gaussian envelope oscillator signal interpolation-5db white Gaussian noise and TFDS;

Fig. 8 adds the relation between the exponent number of entropy and TFDS of the TFDS that obtains behind the 0db white Gaussian noise for Fig. 1 gaussian envelope oscillator signal;

Fig. 9 adds the relation between the exponent number of entropy and TFDS of the TFDS that obtains behind the 5db white Gaussian noise for Fig. 1 gaussian envelope oscillator signal.

The energy value of representing time-frequency distributions among the figure with gray scale, black represent energy maximum, and white energy is minimum.

Embodiment

Below in conjunction with accompanying drawing and specific embodiment the present invention is further described:

In conjunction with Fig. 1, signal length is 256 points among the figure, and SF is 10MHz; The waveform that comprises 3 gaussian envelope altogether; And preceding two adjacent waveforms exist overlapping, and each waveform is respectively 5 μ s, 6 μ s, 21 μ s time of arrival, and centre frequency is respectively 3MHz, 2MHz, 2.5MHz.This signal is used for verifying the aggregation and the time frequency resolution of time-frequency distributions among the present invention.

Fig. 2-6 is the WVD of signal shown in Figure 1 and the TFDS of different rank.When calculating TFDS, the window width of Gabor conversion confirms that by the window width system of selection in the patent of invention " the Gabor translating self-adapting window width system of selection (CN200710072627.8) that ultrasonic signal is represented " it is 32 that time-sampling is counted, and over-sampling rate is 4.Fig. 2 is the WVD of signal shown in Figure 1, by finding out the time-frequency position at each gaussian envelope waveform among the figure, very high aggregation and time frequency resolution is arranged all, yet the existence meeting of cross term causes interference to the explanation of flaw echo.Fig. 3 is 0 rank TFDS of signal shown in Figure 1 because exponent number is 0 o'clock, TFDS be each basis function from WVD with, therefore, do not have cross term in the time-frequency distributions, though the time-frequency position that can tell each Gaussian waveform this moment, the aggregation of time-frequency distributions is relatively poor.Fig. 4 is 1 rank TFDS of signal shown in Figure 1, compares with 0 rank TFDS, some cross terms occurred, but aggregation is better; Compare with WVD, each component aggregation extent is poor slightly, but cross term significantly reduces; Fig. 5 is 2 rank TFDS of signal shown in Figure 1, and aggregation is better than 1 rank TFDS.Fig. 6 is 5 rank TFDS of signal shown in Figure 1, and cross term increases.The normalization entropy of four time-frequency distributions shown in Fig. 2-6 is respectively: 0.2745,0.2185,0.2755,0.2900,0.2246, and entropy shows that also the aggregation of 3 rank TFDS is best, and is identical with the result through the time-frequency distributions map analysis.

Claims (1)

1. the exponent number system of selection of a time-frequency distributions progression is characterized in that: may further comprise the steps:

A, ask the normalization entropy of each rank TFDS $H_1=1+\underset{m}{\mathrm{\&Sigma;}}\underset{n}{\mathrm{\&Sigma;}}{P}_s(m,n){\mathrm{Log}}_{\mathrm{MN}}\left(P_s(m,n)\right)$

In order to say something, calculate TFDS and normalization entropy thereof below 8 rank;

B, obtain the corresponding exponent number of maximal value of normalization entropy

Cross term is more, the value of entropy is more little, and aggregation is good more, the value of entropy is big more, therefore can judge its aggregation and cross term situation from item through the normalizing entropy of each rank TFDS; The TFDS that the normalization entropy is maximum, its time-frequency distributions aggregation is good, and cross term is few; So the exponent number of the maximal value correspondence of selection normalization entropy is as the value of divisor D.

Images