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).