wvd

Generate a 1000-sample impulse and a 1000-sample tone with normalized frequency $\pi /2$. Compute the Wigner-Ville distribution of the sum of the two signals.

x = zeros(1001,1);
x(500) = 10;

y = sin(pi*(0:1000)/2)';

[d,f,t] = wvd(x+y);

Plot the Wigner-Ville distribution.

imagesc(t,f,d)
axis xy
colorbar

Reproduce the result by calling wvd with no output arguments.

wvd(x+y)

Generate a signal consisting of a 200 Hz sinusoid sampled at 1 kHz for 1.5 seconds.

fs = 1000;
t = (0:1/fs:1.5)';
x = cos(2*pi*t*200);

Compute the Wigner-Ville distribution of the signal.

wvd(x,fs)

Add to the signal a chirp whose frequency varies sinusoidally between 250 Hz and 450 Hz. Convert the signal to a MATLAB® timetable. Compute the Wigner-Ville distribution.

x = x + vco(cos(2*pi*t),[250 450],fs);
xt = timetable(seconds(t),x);

wvd(xt)

Set to zero the distribution elements with amplitude less than 0.

wvd(xt,MinThreshold=0)

Generate a signal sampled at 1 kHz for 1 second. One component of the signal is a chirp that increases in frequency quadratically from 100 Hz to 400 Hz during the measurement. The other component of the signal is a chirp that decreases in frequency linearly from 350 Hz to 50 Hz in the same lapse.

Store the signal in a timetable.

fs = 1000;
t = 0:1/fs:1;

x = chirp(t,100,1,400,"quadratic") + chirp(t,350,1,50);

Compute the Wigner-Ville distribution of the signal.

wvd(x,fs)

Compute the smoothed pseudo Wigner-Ville distribution of the signal. Specify 501 frequency points and 502 time points.

wvd(x,fs,"smoothedPseudo",NumFrequencyPoints=501,NumTimePoints=502)

Increase the number of time points so the quadratic chirp becomes visible.

wvd(x,fs,"smoothedPseudo",NumFrequencyPoints=501,NumTimePoints=522)

Increase the frequency points and time points to get a sharper image.

wvd(x,fs,"smoothedPseudo",NumFrequencyPoints=1000,NumTimePoints=1502)

Generate a two-component signal sampled at 3 kHz for 1 second. The first component is a quadratic chirp whose frequency increases from 300 Hz to 1300 Hz during the measurement. The second component is a chirp with sinusoidally varying frequency content. The signal is embedded in white Gaussian noise. Express the time between consecutive samples as a duration scalar.

fs = 3000;
t = 0:1/fs:1-1/fs;
dt = seconds(t(2)-t(1));

x1 = chirp(t,300,t(end),1300,"quadratic");
x2 = exp(2j*pi*100*cos(2*pi*2*t));

x = x1 + x2 + randn(size(t))/10;

Compute and plot the smoothed pseudo Wigner Ville of the signal. Window the distribution in time using a 601-sample Hamming window and in frequency using a 305-sample rectangular window. Use 600 frequency points for the display. Set to zero those components of the distribution with amplitude less than $-$50.

wvd(x,dt,"smoothedPseudo",hamming(601),rectwin(305), ...
    NumFrequencyPoints=600,MinThreshold=-50)

Generate a signal composed of four Gaussian atoms. Each atom consists of a sinusoid modulated by a Gaussian. The sinusoids have frequencies of 100 Hz and 400 Hz. The Gaussians are centered at 150 milliseconds and 350 milliseconds and have a variance of $0.{01}^2$. All atoms have unit amplitude. The signal is sampled at 1 kHz for half a second.

fs = 1000;
t = (0:1/fs:0.5)';

f1 = 100;
f2 = 400;

mu1 = 0.15;
mu2 = 0.35;

gaussFun = @(A,x,mu,f) exp(-(x-mu).^2/(2*0.01^2)).*sin(2*pi*f.*x)*A';

s = gaussFun([1 1 1 1],t,[mu1 mu1 mu2 mu2],[f1 f2 f1 f2]);

Compute and display the Wigner-Ville distribution of the signal. Interference terms, which can have negative values, appear halfway between each pair of auto-terms.

wvd(s,fs)

Compute and display the smoothed pseudo Wigner-Ville distribution of the signal. Smoothing in time and frequency attenuates the interference terms.

wvd(s,fs,"smoothedPseudo")