Continuos Wavelet tranform analytic and nonanalytic

Hello there,

I'm here to ask a question about the meaning of the terms "analytic" and "nonanalytic" referred to wavelets. For example, when considering 'morl' (Morlet) MATLAB says that this wavelet is analytic, does it mean that is a complex-valued wavelet? On the other hand, 'mexh' (Mexican hat) wavelet is said to be nonanalytic, does it mean that it is real-valued?

Thanks in advance for your time and patience.

Lorenzo

Answer 1

[Prasanna Gude]

Analytic wavelets are Complex-valued wavelets which are useful in cases where you want to analyze phase as well as magnitude. Additionally, an Analytic wavelet supports frequency on half of the real line only i.e., its power spectra is zero at negative frequencies.

On the other hand, Non-Analytic wavelets are useful to analyze magnitude in time-frequency domain.

Refer to the following links to know more about ‘merl’(Morlet) and ‘mexh’(Mexican hat) Wavelet Transforms:

https://www.mathworks.com/help/wavelet/ug/wavelet-families-additional-discussion.html#f8-23897

https://www.mathworks.com/help/wavelet/ref/cwtft.html#buu64ih-2