Matlab Wavelets discrepancy with Mexican hat and Gaussian ??

Question

Paul C 2015-4-1

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https://ww2.mathworks.cn/matlabcentral/answers/195682-matlab-wavelets-discrepancy-with-mexican-hat-and-gaussian

回答： SHAOHAN WANG 2020-12-20

Hi

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.