Continuous Wavelet Analysis

This example shows how to perform time-frequency analysis using the continuous wavelet transform (CWT). Continuous wavelet analysis provides a time-scale/time-frequency analysis of signals and images. The Wavelet Toolbox™ software has both command line and interactive functionality to support continuous wavelet analysis of 1-D signals.

Construct a signal consisting of two sinusoids with frequencies of 100 and 50 Hz, and white noise. The support of the two sinusoids is disjoint. The 100-Hz sine wave begins at t = 0 and has a duration of 1 second. The 100-Hz sinusoid has an amplitude of 2. The 50-Hz sinusoid begins at three seconds and has a duration of two seconds. The 50-Hz sinusoid has an amplitude of 1. The sampling frequency is 1 kHz. The signal length is 5000 samples.

Fs = 1000;
t = linspace(0,5,5e3);
x = 2*cos(2*pi*100*t).*(t<1)+cos(2*pi*50*t).*(3<t)+0.3*randn(size(t));

Plot the signal.

plot(t,x)
xlabel('Time (s)')
ylabel('Amplitude')

Use cwt to obtain the CWT of the signal and plot its scalogram. The magnitudes of the sinusoid components in the colorbar are essentially their amplitudes even though they are at different scales.

cwt(x,Fs)