Can I "turn off" the CWT normalization, to directly compare the CWTs of different signals?

I am looking to compare the CWT of different signals in time, and I would like there to be an equivalence on different CWT plots. I.e., a magnitude of 0.5 on one CWT plot is the same as a magnitude of 0.5 on another CWT plot, and they both show up at the same colour.

I see in the documentation that the CWT uses the L1 normalization, here is my attempt to "undo" that such that I can compare across different observations. I essentially multiply each row of the wavelet transform output by its corresponding frequency.

[wt,f,coi] = cwt(Q,'amor',VoicesPerOctave = 48); % Q is the timetable of my signal
f = f';
T = conj(wt).*wt;

% attempt to unscale the L1 normalization of the CWT
N_f = length(f);
T_scaled = T;
f_flip = flip(f); % frequency vector is backwards so need to flip

for i=1:1:N_f % multiply each row of T by its corresponding frequency
    T_scaled(i,:)=f_flip(i)*T(i,:);
end

T = T_scaled;

Am I on the right track, or what would be a better method of doing this to compare CWTs of different signals? Is unscaling the normalization the right way to go?

Answer 1

[Ashutosh Thakur]

Hi AG,

I understand that you are trying to unscale the L1 Normalization in a CWT signals.

Their is not any option present in the "cwt" function to turn off the L1 Normalization as it is designed in a such a way to ensure that each wavelet have the same energy. Their could be possible reasons for the code provided above to mark two CWT plots with the same signale:

• The scaling factor which you are applying may not be completedly correct to get exact inverse of the L1 Normalization used by the "cwt" functions. More trial and error work would be required to find the correct Normalization.
• I suggest to use "clim" to set the limit of the axes of these plots. These will help you in ensuring the same color represents only the same magnitude wavelet accross different plots.

Please refer to the following documentation links for reference:

• https://www.mathworks.com/help/wavelet/ref/cwt.html
• https://www.mathworks.com/help/matlab/ref/clim.html

I hope this helps!