A general formulation of modulated filter banks

This paper presents a general framework for maximally decimated modulated f ilter banks, The theory covers the known classes of cosine modulation and r elates them to complex-modulated filter banks, The prototype filters have a rbitrary lengths, and the overall delay of the filter bank is arbitrary Wit hin fundamental limits. Necessary and sufficient conditions for perfect rec onstruction (PR) are derived using the polyphase representation. It is show n that these PR conditions are identical for all types of modulation-modula tion based on the discrete cosine transform (DCT), both DCT-III/DCT-IV and DCT-I/DCT-II, and modulation based on the modified discrete Fourier transfo rm (MDFT). A quadratic-constrained design method for prototype filters yiel ding PR with arbitrary length and system delay is derived, and design examp les are presented to illustrate the tradeoff between overall system delay a nd stopband attenuation (subchannelization).