Exact perfect reconstruction of filter window bank with application to incompatible nonuniform filter banks

Abstract

This paper proposes a filter window bank structure. It consists of a bank of single input single output analysis linear time invariant filters, a bank of analysis periodic windows, a bank of single input single output synthesis linear time invariant filters and a bank of synthesis periodic windows. Since the joint downsampling functions and the upsampling functions in conventional uniform filter banks, conventional nonuniform filter banks, conventional uniform block filter banks and conventional nonuniform block filter banks are particular types of periodic window functions, these conventional filter banks are particular types of the proposed filter window banks. This paper derives the exact perfect reconstruction conditions for the proposed filter window banks with both the constant and the time varying synthesis periodic window functions. Finally, the filter window banks with both the constant synthesis periodic window functions and the time varying periodic window functions are compared to conventional nonuniform filter banks and conventional nonuniform block filter banks.