Arbitrary-length spectral factor applied to the design of pseudo-QMF cosine-modulated filter banks

The main advantage of pseudoquadrature mirror filter cosine modulated filter banks with a spectral factor of a 2Mth band filter is that the optimization stage can be avoided when designing the prototype filter. However, these filter banks are constrained by the condition that the order of the prototype filter has to be an integer multiple of the M-number of channels in the bank. In this paper, we set the conditions that must be imposed to cosine-modulation phase factors so as to cancel the most significant terms of aliasing using a prototype filter of arbitrary length. An example is included to confirm the validity of the theory.