Factorization Approach To Unitary Time-Varying Filter Banks

A complete factorization of all optimal (in terms of quick transition) time-varying FIR unitary lter bank tree topologies is obtained. This has applications in adaptive subband coding, tiling of the time-frequency plane and the construction of orthonormal wavelet bases for the half-line and interval 9, 8, 13, 2]. A simple eecient implementation algorithm also comes with the factorization ensuring that even the most complex tree topology can be adapted with minimal overhead. Explicit formulas for entry/exit lters are given for arbitrary tree transitions. The results are independent of the number of channels and the length of the lters (as long as they are FIR), implying that some of the eeciency reasons for considering only binary time-varying trees is not valid any more. Time-varying wavelet bases (diierent bases for diierent segments of the real line) are also constructed.

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