Audio Signal Processing and Coding

6.5 TREE-STRUCTURED QMF AND CQF M-BAND BANKS

Clearly, audio coders require better frequency resolution than either the QMF or CQF two-band decompositions can provide in order to realize sufficient coding gain for spectrally complex signals. Tree-structured cascades are one straight-forward method for creating M-band filter banks from the two-band QMF and CQF prototypes. These are constructed as follows. The two-band filters are connected in a cascade that can be represented well using either a binary tree or a pruned binary tree. The root node of the tree is formed by a single two-band QMF or CQF section. Then, each of the root node outputs is connected to a cascaded QMF or CQF bank. The cascade structure may be continued to the depth necessary to achieve the desired magnitude response characteristics. At each node in the tree, a two-channel QMF or CQF bank operates on the output from a higher-level two-channel bank. Thus, frequency subdivision occurs through a series of two-band splits. Tree-structured filter banks have several advantages. First of all, the designer can approximate an arbitrary partitioning of the frequency axis by creating an appropriate cascade. Consider, for example, the uniform subband tree (Figure 6.8) or the octave-band tree (Figure 6.9). The ability to partition the frequency axis in a nonuniform manner also has implications for multi-resolution temporal analysis, or nonuniform tiling of the time-frequency plane. This property can be advantageous if the ...