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:
