Boundary filters for finite-length signals and time-varying filter banks

We examine the question of how to construct time-varying filter banks in the most general M-channel non-orthogonal case. We show that by associating with both analysis and synthesis operators a set of boundary filters, it is possible to make the analysis structure vary arbitrarily in time, and yet reconstruct the input with a similarly time-varying synthesis section. There is no redundancy or distortion introduced. This gives a solution to the problem of applying filter banks to finite length signals; it suffices to apply the boundary filters at the beginning and end of the signal segment. This also allows the construction of orthogonal and non-orthogonal bases with essentially any prescribed time and frequency localization, but which, nonetheless, are based on structures with efficient filter bank implementations