Re: Vanishing Moments

>     Can someone please explain what 'vanishing moments' are? Is it 
> something to do with the length of the wavelet filter banks?

There are lots of different ways to describe what vanishing moments are, 
but perhaps the most useful is the following characterization:

A filter has k vanishing moments if all polynomials of degree less than 
k can be expressed as a linear combination of integer-shifted copies of 
the scaling function (the low-pass filter of the filter bank).

This means that if your input looks like a polynomial of degree less 
than k, your high-pass coefficients will all be zero (vanish).

Now, in order to approximate higher degree polynomials, you will have to 
use more integer-shifted copies of the filter in order to get enough 
degrees of freedom. This means that your filter sizes must increase. So 
in general higher degrees of regularity require longer filters. You can 
still cheat computationally by making some of the interior filter 
coefficients zero.

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