An efficient approach for designing nearly perfect-reconstruction low-delay cosine-modulated filter banks

An efficient approach is described for optimizing the stopband response of the prototype filter for low-delay critically sampled cosine-modulated filter banks in the least-mean-square sense subject to the maximum allowable aliasing and amplitude errors. These low-delay filter banks differ from orthogonal cosine-modulated filter banks, where the filter bank delay is equal to the prototype filter order, in the sense that the order of the prototype filter can be increased while keeping the filter bank delay the same. This results in higher attenuations for the analysis and synthesis filters without increasing the filter bank delay. For designing the prototype filter for these filter banks, a systematic multi-step approach is proposed. In this approach, filter banks having several channels are designed by starting with a filter bank with a small number of channels. Then, the number of channels is gradually increased and a new prototype filter is optimized using the modified version of the prototype filter of the previous step as a good start-up solution. Several examples are included illustrating the flexibility of the proposed approach for making compromises between the required filter orders, the required filter bank delays, and the aliasing and amplitude errors. These examples show that by allowing very small amplitude and aliasing errors, the stopband performance of the resulting filter bank is significantly improved compared to the corresponding perfect-reconstruction filter bank. Alternatively, the filter bank delay and the order of the prototype filter can be significantly reduced while still achieving practically the same filter bank performance.