On the design of cosine modulated filter banks

In this paper, a simple rapidly convergent algorithm is proposed for the design of cosine modulated filter banks. Unlike earlier designs that require right from the start that the prototype mother filter H₀(z), be an exact linear phase FIR filter, the proposed method only require that the resulting analysis/synthesis filter bank constitutes a perfect reconstruction system. It has been shown that the perfect reconstruction requirement results in the mother filter being an exact linear phase one. The algorithm is based on using an efficient polynomial decomposition scheme that ensures that the polyphase components of H₀(z) constitute a unitary matrix. As the prescribed algorithm employs the minimum number of parameters for a specified filter order, convergence is guaranteed to be rapid. The parameters of the analysis filter banks are optimally chosen to produce selective filters satisfying the prescribed specifications. The main feature of the proposed approach apart from simplicity lies in allowing the polyphase components to have its roots distributed all over the complex plane and not restricted to be either minimum or maximum phase polynomials as lattice-based designs did. This means that, one can control the group delay of the analysis filter banks to be nearly constant. An illustrative example is given to verify the design steps of the proposed method.