An efficient approach for designing nearly perfect-reconstruction cosine-modulated and modified DFT filter banks

Efficient two-step algorithms are described for optimizing the stopband response of the prototype filter for cosine-modulated and modified DFT filter banks either in the minimax or in the least-mean-square sense subject to the maximum allowable aliasing and amplitude errors. The first step involves finding a good start-up solution using a simple technique. This solution is improved in the second step by using nonlinear optimization. Several examples are included illustrating the flexibility of the proposed approach for making compromises between the required filter lengths 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 orders and, consequently, the overall delay can be significantly reduced to achieve practically the same performance.