Exact reconstruction filter banks using cosine modulation: matrix formalization for arbitrary length prototype filters

This paper describes generalized frequency domain matrix formalizations for two families of filter banks using different structures of polyphase component decomposition that are valid for prototype filters of arbitrary lengths and for an arbitrary number of channels M. In each case, closed form expressions of the polyphase components of the FIR prototype filter are provided and necessary and sufficient conditions on these polyphase components so that the analysis/synthesis system satisfies the perfect reconstruction condition are derived. It is shown that solutions with arbitrary lengths of the form mM-R can be obtained. For both structures, the relations between the polyphase component pairs lead naturally to fast computation algorithms, with very regular structures and low arithmetic complexity