Creating and comparing wavelets

Abstract

This paper emphasizes two points about the design and application of filters and filter banks and wavelets:

• The algebra behind wavelet design is now quite simple.

• The comparison of two competing wavelets is still experimental and empirical.

As example we consider two particular 9/7 constructions (nine coefficients in analysis and seven in synthesis). Both are symmetric, so neither is orthogonal. Both have important advantages. We are unable to say which construction is better. The paper begins with the conditions on the filter coefficients for perfect reconstruction. That part is a brief summary of the exposition in Strang and Nguyen [1].