A systematic technique for designing prototype filters for perfect reconstruction cosine modulated and modified DFT filter banks

Optimizing the angles for the lattice structures in the prototype filter for perfect-reconstruction cosine-modulated and modified DFT filter banks is a very difficult task because there exist several local optima. In order to get around this problem, this paper describes an efficient systematic technique for designing prototype filters in the least-mean-square sense. First, the few angles for the two-channel case are optimized using various techniques for numerous filter lengths and stop-band edge frequencies. The resulting angles are expressed as polynomials of the stop-band edge for later use, After knowing the angles for the two-channel case, corresponding filter banks having several channels can be effectively generated by gradually increasing the number of channels and by properly using the result of the previous step as a start-up solution for the present step. This approach allows us to design, very fast at least, good locally optimized prototype filters for banks having many channels and long channel filters.