ORTHOGONAL TIME-VARYING FILTER BANKS AND WAVELET PACKETS

We consider the construction of orthogonal time-varying filter banks. By examining the time domain description of the two-channel orthogonal filter bank we find it possible to construct a set of orthogonal boundary filters, which allows us to apply the filter bank to one-sided or finite-length signals, without redundancy or distortion. The method is constructive and complete. There is a whole space of orthogonal boundary solutions, and there is considerable freedom for optimization. This may be used to generate subband tree structures where the tree varies over time, and to change between different filter sets. We also show that the iteration of discrete-time time-varying filter banks gives continuous-time bases, just as in the stationary case. This gives rise to wavelet, or wavelet packet, bases for half-line and interval regions.