Optimal design of nonuniform multirate filter banks

The design of a general nonuniform filter banks is studied. Contrary to a uniform filter bank, in a nonuniform filter bank, it may not be possible to achieve perfect reconstruction, but in some cases by using optimization techniques, we are able to design acceptable filter banks. Here, the initial analysis filters are designed according to the characteristics of the input. By the design procedure, the analysis filters are first fixed and the FIR synthesis filters are found so that the /spl Hscr//sub 2/-norm of an error system is minimized. Then, the synthesis filters are fixed and the analysis filters are found similarly. By iteration, the /spl Hscr//sub 2/ norm of the error system is decreased until it converges to its final value. In each iteration, the analysis or synthesis filters are obtained by finding the least square solution of a system of linear equations.