I'm having a problem with the wavelets implemented in matlab, more precisely the Mexican Hat and the Gaussian order 2.
These two wavelets are supposed to be almost the same: The Mexh wavelet writes exp(-x^2/2)*(1-x^2) The Gaussian order 2 writes -exp(-x^2)*(1-2x^2).
Now, performing CWT with MEXH and GAUS2 on a given function yields very different results.
On the contrary, if I create a 'manual' 2nd derivative of the Mexican hat (I basically copy the mexh file, and add y=gradient(gradient(y)) at the end of it), it will give very close results to GAUS2.
I can't understand this when looking at the wavelet expressions. GAUS2 is supposed to be similar to MEXH, not 2d derivative of MEXH (which reads exp(-x^2)*(x^4-6x^2+3)). Is there an additional step in Matlab calculations that I am not aware of??
Thank you for your answers.