TABLE OF CONTENTS The above discussion is for a single pair of analysis filters. Multiresolution is the process of taking the output from one channel and putting it through another (or more) pair of analysis filters. For the wavelet transform, we do this with the lowpass filter's output. Wavelet packets, however, use an additional filter pair for each channel. We will examine multiresolution starting with the Daubechies four-coefficient wavelet transform, with down-sampling and up-sampling, for two levels of resolution (octaves), as shown in Figure 9.22.
Signals w[ n], w d[ n], z[ n], and z d[ n] are the same as before.
To generate w2[ n], w2 d[ n], z2[ n], and z2 d[ n], we first notice that they have the same relationship to w d[ n] as w d[ n] and z d[ n] have to x[ n]. In other words, we can reuse the above equations, and replace x[ n] with w d[ n]. Also, since there is a down-sampler between w2[ n] and w2 d[ n], every other value of w2[ n] will be eliminated. Signal w2[ n], by definition, is based upon w d[ n], a down-sampled version of w[ n]. Using the original n,...
