MATLAB: How to create a daughter wavelet with scale ‘a’ and position ‘b’ for a known Mother Wavelet function in MATLAB

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Using the Morlet Function as the Mother Wavelet, how do I create a continuous Daughter Wavelet with different scale and position?

Best Answer

Multiresolution analysis on a function is simply performed in the continuous-time domain using the built-in Wavelet Toolbox function CWT and in the discrete-time domain using the DWT function.
A Daughter Wavelet with different scale and position from the Mother Wavelet can be created using scaling and shifting operations in MATLAB. The Daughter Wavelet is created changing the time index input of the variable from 't' to '(t-b)/a' in the wavelet function. The following example illustrates creating a daughter wavelet based on the Morlet function with scale a=0.5 and position b=3s.
a=0.5;
b=3;
t = linspace(-4,4,200);        % Wavelet support for t=[-4:4] with 200 sample points
s = exp(-(((t-b)/a).^2)/2) .* cos(5*(((t-b)/a)));
The center frequency of the daughter wavelet is only related to the scale factor (a) and is not related to the position (b) or the support bounds, which are -4 and +4 in this example.
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