Optimal design of nonuniform multirate filter banks

The design of general nonuniform filter banks is studied. Contrary to unifo rm filter banks, in nonuniform filter banks, it may not be possible to achi eve perfect reconstruction, but in some cases by using optimization techniq ues, we can design acceptable filter banks. Here, the initial finite impuls e response (FIR) analysis filters are designed according to the characteris tics of the input. By the design procedure, the FIR synthesis filters are f ound so that the H-2-norm of an error system is minimized over all synthesi s filters that have a prespecified order. Then, the synthesis filters obtai ned in the previous step are fixed, and the analysis filters are found simi larly. By iteration, the H-2-norm of the error system decreases until it co nverges to its final value. At each iteration, the coefficients of the anal ysis or synthesis filters are obtained by finding the least squares solutio n of a system of linear equations. If necessary, the frequency characterist ics of the filters can be altered by adding penalty terms to the objective function.