Analysis of Optimization Algorithms for Non-Uniform Filter Bank Design

This paper deals with design algorithms for filter banks based on optimization. The design specifications consist of the perfect reconstruction (PR) and frequency response specifications for finite impulse response (FIR) analysis and synthesis filters. The PR conditions are formulated as a set of linear equations with respect to the analysis filters’ coefficients and the synthesis filters’ coefficients. Two design algorithms are presented; the first is based on an unconstrained optimization of a performance index, which includes the PR error and the error in the frequency specifications. The second algorithm is formulated as a constrained optimization problem with the PR error as the performance index and the frequency specifications as constraints. The performance of the two algorithms is evaluated and compared using two examples; these examples include a compatible nonuniform filter bank (NUFB) and an incompatible NUFB design. The results show that the two algorithms can achieve almost PR and can meet the frequency response specifications in the compatible NUFB. In the case of the incompatible NUFB, PR is more difficult to be achieved.