chapter  7
20 Pages

Practical Computation

As explained in section 6.2, the discrete multiwavelet transform (DMWT) is based on the decomposition

A function can be expanded either as

or as

where

(and likewise for ), and

The multiscaling and multiwavelet functions are column vectors. The coefficients are row vectors. The notation s, d originally stood for sum and difference, which is what they are for the Haar wavelet.

You can also think of them as standing for the smooth part and the fine detail of s. The original function s (x) is the signal.