In the new version of cwt(), what is the bandwidth of the default Morlet wavelet?

Hi,

In the old version of cwt() (before 2016b), we could specify the bandwidth parameter, f_b, as part of the wname. See the below link:

https://www.mathworks.com/help/wavelet/ug/wavelet-families-additional-discussion.html#f8-40178

I would often use 'cmor2-1' which corresponds to a complex morelet wavelet with bandwidth of 2 and center frequency of 1. Increasing teh bandwidth parameter increased the number of wiggles before the wavelet decayed.

In the new version of cwt() we can use the 'amor' wavelet, but I can't figure out what the default bandwidth parameter is. Or, how do I completely specify the parameters of the wavelet. We are trying to publish a paper where I used the new version of cwt() and 'amor', but we'd like to more fully characterize the wavelet that I used.

A relate question is: if I used cwt() with 'amor' how can I visualize the mother wavelet? For the old version I would use cmorwavf(), but what would work for the new version?

Thanks so much in advance. I really appreciate all of the folks who help answer questions here.

Tom

Answer 1

[Balavignesh]

Hello Tom,

It is my understanding that you would like to characterize the wavelet you used, and visualize the mother wavelet.

I recommend utilizing the 'scales' function to extract the mother wavelet from the filter banks. The sample code provided below could assist you in achieving this task:

% This is an example dataset. 
load mtlb.mat;
figure
cwt(mtlb, "amor" , 7400); % returns the wavelet for a specified frequency of 7400 Hz.

% Getting the mother wavelet of a filterbank
sigLen = 4096;
fb60 = cwtfilterbank(SignalLength=sigLen);
[psi60,t] = wavelets(fb60);
sca60 = scales(fb60);
[~,idx60] = min(abs(sca60-1));
m60 = psi60(idx60,:);

% Plotting the mother wavelet 
figure
plot(t,abs(m60))
grid on
hold on
plot(t,real(m60))
plot(t,imag(m60))
hold off
xlim([-30 30])
legend("abs(m60)","real(m60)","imag(m60)")
title("Mother wavelet")

Kindly refer to the following documentation links to have more information on:

• 'cwt' function: https://www.mathworks.com/help/wavelet/ref/cwt.html#d126e10622
• 'scales' function: https://in.mathworks.com/help/wavelet/ref/cwt.html#namevaluepairarguments:~:text=Use%20the%20scales%20function%20to%20find%20the%20mother%20wavelet%20for%20each

Hope this helps!

Balavignesh