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XWVD.

Cross Wigner-Ville distribution and cross smoothed pseudo Wigner-Ville distribution

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Syntax

d = xwvd(x,y)
d = xwvd(x,y,fs)
d = xwvd(x,y,ts)
d = xwvd(___,'smoothedPseudo')
d = xwvd(___,'smoothedPseudo',twin,fwin)
d = xwvd(___,'smoothedPseudo','NumFrequencyPoints',nf)
d = xwvd(___，'minthreshold'，thresh)
[d,f,t] = xwvd(___)
XWVD.(___)

Description

example

d= XWVD（x,y)returns the cross Wigner-Ville distribution ofx和y。

example

d= XWVD（x,y,fs)返回十字架Wigner-Ville分销x和yare sampled at a ratefs。

d= XWVD（x,y,TS.)返回十字架Wigner-Ville分销x和yare sampled with a time intervalTS.between samples.

d= XWVD（___,'smoothedPseudo')returns the cross smoothed pseudo Wigner-Ville distribution ofx和y。该功能使用输入信号的长度来选择用于时间和频率平滑的窗口的长度。此语法可以包括来自先前语法的任何输入参数的组合。

d= XWVD（___,'smoothedPseudo',双胞胎,FWIN.)指定时间窗口，双胞胎, and the frequency window,FWIN., used for smoothing. To use the default window for either time or frequency smoothing, specify the corresponding argument as empty,[]。

d= XWVD（___,'smoothedPseudo','NumFrequencyPoints',NF.)计算交叉平滑的伪Wigner-Ville分销NF.frequency points. You can specify双胞胎和FWIN.in this syntax, or you can omit them.

d= XWVD（___，'minthreshold'，thresh)sets to zero those elements ofd谁的幅度小于thresh。This syntax applies to both the cross Wigner-Ville distribution and the cross smoothed pseudo Wigner-Ville distribution.

[d,f,t] = xwvd(___)还返回频率的向量，f, and a vector of times,t，在那里dis computed.

example

XWVD.(___)with no output arguments plots the real part of the cross Wigner-Ville or cross smoothed pseudo Wigner-Ville distribution in the current figure.

Examples

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打开直播脚本

Generate two signals sampled at 1 kHz for 1 second and embedded in white noise. One signal is a sinusoid of frequency 150 Hz. The other signal is a chirp whose frequency varies sinusoidally between 200 Hz and 400 Hz. The noise has a variance of 0 。 1 2 。

fs = 1000; t = (0:1/fs:1)'; x = cos(2*pi*t*150) + 0.1*randn(size(t)); y = vco(cos(3*pi*t),[200 400],fs) + 0.1*randn(size(t));

计算信号之和的Wigner-Ville分布。

wvd(x+y,fs)

图包含轴对象。具有标题Wigner-Ville分布的轴对象包含类型图像的对象。

计算并绘制信号的交叉Wigner-Ville分布。交叉分布对应于Wigner-Ville分布的横向术。

XWVD（X，Y，FS）

图包含轴对象。The axes object with title Cross Wigner-Ville Distribution contains an object of type image.

打开直播脚本

生成由两个啁啾组成的双通道信号。信号在3 kHz上采样一秒钟。第一啁啾具有400 Hz的初始频率，在采样结束时达到800 Hz。第二个啁啾从500 Hz开始，最后达到1000赫兹。第二啁啾具有第一啁啾幅度的两倍。

fs = 3000; t = (0:1/fs:1-1/fs)'; x1 = chirp(t,1400,t(end),800); x2 = 2*chirp(t,200,t(end),1000);

将信号存储为时间表。计算并绘制两个通道的十字Wigner-Ville分布。

xt = timetable(seconds(t),x1,x2); xwvd(xt(:,1),xt(:,2))

图包含轴对象。The axes object with title Cross Wigner-Ville Distribution contains an object of type image.

打开直播脚本

Compute the instantaneous frequency of a signal by using a known reference signal and the cross Wigner-Ville distribution.

创建由在1 kHz的高斯原子采样1秒的高斯原子组成的参考信号。高斯原子是由高斯调制的正弦问题。规定了50 Hz的正弦频率。高斯以64毫秒为中心，并具有差异 0 。 01. 2 。

FS = 1E3;t =（0：1 / fs：1-1 / fs）';mu = 0.064;sigma = 0.01;fsin = 50;XR = exp（ - （t-mu）。^ 2 /（2 * sigma ^ 2））。* sin（2 * pi * fsin * t）;

Create the "unknown" signal to analyze, consisting of a chirp. The signal starts suddenly at 0.4 second and ends suddenly half a second later. In that lapse, the frequency of the chirp decreases linearly from 400 Hz to 100 Hz.

f0 = 400; f1 = 100; xa = zeros(size(t)); xa(t>0.4 & t<=0.9) = chirp((0:1/fs:0.5-1/fs)',f0,0.5,f1);

Create a two-component signal consisting of the sum of the unknown and reference signals. The smoothed pseudo Wigner-Ville distribution of the result provides an "ideal" time-frequency representation.

Compute and display the smoothed pseudo Wigner-Ville distribution.

w = wvd(xa+xr,fs,'smoothedpseudo'）;WVD（XA + XR，FS，'smoothedpseudo')

图包含轴对象。The axes object with title Smoothed Pseudo Wigner-Ville Distribution contains an object of type image.

计算未知和参考信号的十字Wigner-Ville分布。取出分布的绝对值并设置为零的幅度小于10的元素。交叉Wigner-Ville分布等于双组分信号的横向级。

Plot the real part of the cross Wigner-Ville distribution.

[C，FC，TC] = XWVD（XA，XR，FS）;c = abs（c）;C（C <10）= 0;XWVD（XA，XR，FS）

图包含轴对象。The axes object with title Cross Wigner-Ville Distribution contains an object of type image.

Enhance the Wigner-Ville cross-terms by adding the ideal time-frequency representation to the cross Wigner-Ville distribution. The cross-terms of the Wigner-Ville distribution occur halfway between the reference signal and the unknown signal.

d = w + c;d = abs(真正的(d));显示亮度图像(tc、fc、d)轴XYcolorbar

图包含轴对象。The axes object contains an object of type image.

Identify and plot the high-energy ridge corresponding to the cross-terms. To isolate the ridge, find the time values where the cross-distribution has nonzero energy.

ff = tfridge（c，fc）;电视=总和（c）> 0;ff = ff（电视）;tc = tc（电视）;抓住在绘图（TC，FF，'r--','linewidth',2) hold离开

图包含轴对象。The axes object contains 2 objects of type image, line.

Reconstruct the instantaneous frequency of the unknown signal by using the ridge and the reference function. Plot the instantaneous frequency as a function of time.

tEst = 2*tc - mu; fEst = 2*ff - fsin; plot(tEst,fEst)

图包含轴对象。The axes object contains an object of type line.

Input Arguments

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输入信号, specified as vectors or MATLAB®时刻表each containing a single vector variable.x和y必须既是向量或两者都是时间表，必须具有相同的长度。

如果输入信号具有奇数长度，则该函数附加零以使长度均匀。

Example:因为(π/ 8 * (0:159))' + randn (160 1) / 10specifies a sinusoid embedded in white noise.

Example:timetable(seconds(0:5)',rand(6,1))指定以1 Hz采样4秒的随机变量。

数据类型：单身的|双倍的
Complex Number Support:是的

Sample rate, specified as a positive numeric scalar.

采样时间, specified as aduration标量。

Time and frequency windows used for smoothing, specified as vectors of odd length. By default,XWVD.uses Kaiser windows with shape factorβ= 20。

  • 默认长度双胞胎is the smallest odd integer greater than or equal toround(length(x)/10)。

  • 默认长度FWIN.is the smallest odd integer greater than or equal toNF./ 4.。

Each window must have a length smaller than or equal to2 *ceil(length(x）/ 2）。

Example:凯泽斯（65,0.5）specifies a 65-sample Kaiser window with a shape factor of 0.5.

频率点数，指定为整数。此参数控制频率过采样程度。频率点的数量必须至少是(length(FWIN.）+1）/ 2和cannot be greater than the default.

最小非零值，指定为真正的标量。该功能设置为零的这些元素dwhose amplitudes are less thanthresh。

输出参数

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交叉Wigner-Ville分布，作为矩阵返回。跨越列的时间增加d, and frequency increases down the rows. The matrix is of sizeNf×Nt， 在哪里Nfis the length off和Ntis the length oft。

频率，作为向量返回。

  • 如果输入有时间信息，那么f包含Hz中表达的频率。

  • 如果输入没有时间信息，那么f包含Rad / Sample中表达的归一化频率。

时间瞬间，作为向量返回。

  • 如果输入有时间信息，那么tcontains time values expressed in seconds.

  • 如果输入没有时间信息，那么t包含样品号。

The number of time points is fixed as4 *ceil(length(x）/ 2）。

More About

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Cross Wigner-Ville Distribution

For continuous signalsx(t)和y(t),交叉Wigner-Ville分销被定义为

XWVD. x , y ( t , f ) = ∫ - ∞ ∞ x ( t + τ 2 ) y * ( t - τ 2 ) e - j 2 π f τ d τ 。

用于离散信号N样品，分配变为

XWVD. x , y ( n , k ) = σ. m = - N N x ( n + m / 2 ) y * ( n - m / 2 ) e - j 2 π k m / N 。

对于奇数值m,definition requires evaluation of the signal at half-integer sample values. It therefore requires interpolation, which makes it necessary to zero-pad the discrete Fourier transform to avoid aliasing.

The cross Wigner-Ville distribution contains interference terms that often complicate its interpretation. To sharpen the distribution, one can filter the definition with lowpass windows. The cross smoothed pseudo Wigner-Ville distribution uses independent windows to smooth in time and frequency:

XSPWVD. x , y g , H ( t , f ) = ∫ - ∞ ∞ g ( t ) H ( f ) x ( t + τ 2 ) y * ( t - τ 2 ) e - j 2 π f τ d τ 。

References

[1] Cohen, Leon.时频分析：理论与应用。Englewood Cliffs，NJ：1995年Prentice-Hall。

[2] Mallat，Stéphane。信号处理的小波巡回赛。Second Edition. San Diego, CA: Academic Press, 1999.

[3] Malnar, Damir, Victor Sucic, and Boualem Boashash. "A cross-terms geometry based method for components instantaneous frequency estimation using the cross Wigner-Ville distribution." In11th International Conference on Information Sciences, Signal Processing and their Applications (ISSPA), pp. 1217–1222. Montréal: IEEE®, 2012.

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Introduced in R2018b

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Functions

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