Audio Signal Processing and Coding

8.2 DWT AND DISCRETE WAVELET PACKET TRANSFORM (DWPT)

The previous section described subband coding algorithms that utilize banks of fixed resolution bandpass QMF or pseudo-QMF finite impulse response (FIR) filters. This section describes a different class of subband coders that rely instead upon a filter-bank interpretation of the discrete wavelet transform (DWT). DWT-based subband coders offer increased flexibility over the subband coders described previously since identical filter-bank magnitude frequency responses can be obtained for many different choices of a wavelet basis, or equivalently, choices of filter coefficients. This flexibility presents an opportunity for basis optimization. The advantage of this optimization in the audio coding application is illustrated by the following example. First, a desired filter-bank magnitude response can be established. This response might be matched to the auditory filter bank. Then, for each segment of audio, one can adaptively choose a wavelet basis that minimizes the rate for some target distortion level. Given a psychoacoustically derived distortion target, the encoding remains perceptually transparent.

Figure 8.2. Filter-bank interpretation of the DWT.

A detailed discussion of specific technical conditions associated with the various wavelet families is beyond the scope of this book, and this chapter therefore concentrates upon high-level ...