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 nonorthogonal 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 nonorthogonal bases with essentially any prescribed time and frequency localization, but which, nonetheless, are based on structures with efficient filter bank implementations