On the design of low delay nearly-PR and PR FIR cosine modulated filter banks having approximate cosine-roll transition band

An efficient method for designing a class of nearly perfect reconstruction (NPR) or perfect reconstruction (PR) cosine modulated filter banks (CMFBs) with prototype filters having an approximate cosine-rolloff transition band is presented. The NPR CMFBs in (Vaidyanathan, 1992) and (Koilpillai and Vaidyanathan, 1991) is first generalized to include low-delay CMFBs. It is shown that a prototype filter with cosine-rolloff transition band will automatically satisfy the flatness condition required by an NPR CMFB. This allows us to formulate the design problem as a convex minimax or least squares problem, and its optimal solution can be solved by the Remez exchange algorithm or more sophisticated semidefinite programming (SDP) method. By using the NPR CMFB so obtained as the initial guess to the nonlinear constrained optimization algorithm such as the Fmincon function of MATLAB, high quality low-delay PR CMFBs can readily be obtained. CMFBs with arbitrary-length linear-phase or low-delay prototype filters can also be obtained readily by this method. Design examples and comparison with existing methods are provided to illustrate the effectiveness of the proposed method.