Processing of finite length signals using unimodular filterbanks without boundary filters

Unimodular filterbanks (UMFBs) have the lowest possible system delay of M - 1 samples, where M is the number of channels. In this paper we make use of this property to show that finite length signals can be processed using UMFBs without any border distortions. More specifically, we show that perfect reconstruction (PR) is achieved without increasing the number of samples at the analysis output, and without any specially designed boundary filters. We provide an extremely simple proof for this remarkable property. We also exploit this property to construct time varying UMFBs without any boundary filters. The UMFB is designed based on a simple canonical structure of an associated nilpotent matrix, with minimum number of free parameters. The optimal set of parameters is obtained through unconstrained optimization. The low computation overhead makes this design suitable for simple and efficient hardware implementation.