Determining periods using Continuous Wavelet Transform

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Richard 2012-1-27

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https://ww2.mathworks.cn/matlabcentral/answers/27266-determining-periods-using-continuous-wavelet-transform

Hi, I have a signal which contains some quasi-periodic patterns which I would like to determine.

As its spectral content changes with time, I think that Wavelet analysis is the method which best fits to my purpose. So that, I was wondering if there exists a canonical way to detect reasonable periods in this signal by looking to CWT coefficients.

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Answer 1

Wayne King 2012-1-28

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Hi Richard, you can use the approximate relationship between scale and frequency to do this.

Create a signal to illustrate this:

Fs = 1000;
t = 0:1/Fs:1-1/Fs;
x = zeros(size(t));
x([625,750]) = 2.5;
x = x+ cos(2*pi*100*t).*(t<0.25)+cos(2*pi*50*t).*(t>=0.5)+0.15*randn(size(t));
plot(t,x);

Set up the scale vector and spacing:

ds = 0.15;
J = fix((1/ds)*log2(length(x)/8));
dt = 1/Fs;
scales = 2*dt*2.^((0:J).*ds);

Obtain the CWT and plot the response:

    cwtstruct = cwtft({x,0.001},'Scales',scales,'Wavelet','morl');
    periods = cwtstruct.scales.*(4*pi)/(6+sqrt(38));
    freq  = 1./periods;
    cfs = cwtstruct.cfs;
    contour(t,freq,abs(cfs));
    set(gca,'xtick',[0 0.25 0.4 0.5 0.6 0.75 1]); grid on;
    xlabel('Time (seconds)'); ylabel('Hz');