Morlet wavelet: what is the difference between 'morl' and 'amor' wavelets?

Dear wavelet fan,

My question as in the title: what is the difference between 'morl' and 'amor' wavelets?

is it all the same, just different name used in the old and new 'cwt' function?

Thank you for the answer in advance!

Best, Maja

Answer 1

[SungJun Cho]

Hi Maja,

It seems quite late to answer your question, but to simply put, the difference between 'morl' and 'amor' wavelets lies in whether they are complex valued in the time domain or not. The 'morl' wavelets are real-valed Morlet wavelets that are not complex valued in the time domain (c.f., here), whereas the 'amor' wavelets are analytic Morlet wavelets that are complex valued in the time domain (c.f., wikipedia and here).

If you refer to the links above or use waveinfo('morl') command, you can see the equations and mathematical details about these wavelets.

Hope this helps.

Best,

SungJun

[Elias Odelstad]

The waveinfo function does not recognize 'amor' as a wavelet family short name, but there is a 'cmor' family, comprising compex Morlet wavelets. Is this identical to the "analytic" Morlet wavelet called 'amor' in the cwt function?

[SungJun Cho]

No not quite. 'amor' and 'cmor' are defined by different equations. For 'cmor', the equation can be found on the MATLAB document. For 'amor', the equations can be found from the link below:

https://www.mathworks.com/matlabcentral/answers/824015-understanding-cwt-morlet-time-and-frequency-resolution?s_tid=srchtitle