zero average condition

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Pavan Kumar B

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Apr 12, 2016, 11:59:37 PM4/12/16

to Discussion forum for Foundations of Wavelets & Multirate DSP

Sir ,

zero average condition is necessary for a wavelet ,but why mexican hat and morlet wavelts does not satisfy zero average condition ?

NOC16 March - May

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Apr 14, 2016, 9:06:54 AM4/14/16

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Hi,

you are absolutely correct. Zero average condition is necessary for a wavelet as it means to have a zero at the w=0. In that sense Morelt and maxican wavelets can't be called as a wavelets. They are called wavelets in an approximate sense. e.g Morlet wavelet is used in practice with f_0 >>0 with minimal error. you can find some of the details in the book "The Illustrated Wavelet Transform Handbook By Paul S Addison" Page :35