Design of special structure FIR filters and two-channel quadrature mirror FIR filter bank with sparse coefficients

Abstract

The sparse design of special structure FIR filters (e.g., matrix-decomposition based FIR filter and frequency response mask based FIR filter) or special purpose FIR filters (e.g., the prototype FIR filter in the two-channel quadrature mirror FIR filter bank) is scarcely addressed previously. In this study, we deal with the sparse design of special structure/purpose FIR filters. A convergent scheme for the sparse design of special structure/purpose FIR filters is proposed. Its technical essence is a convergent scheme for minimizing the ℓk (k=1,2,…,∞) norm of the variable coefficients while the design error satisfying the desired requirement. The basic idea of the proposed scheme, for minimizing the ℓk norm of the variable coefficients, is approximately transforming all the sub-functions in the design error expression into linear ones using Taylor-Series. Thereby, the original non-convex design error turns to be convex. As part of the proposed scheme for the sparse design of special structure/purpose FIR filters, three new criteria of obtaining one more sparse coefficient are proposed. Simulation results validate the effectiveness of the proposed scheme in minimizing the ℓk norm of the variable coefficients and obtaining sparse coefficients in the sparse design of special structure/purpose FIR filters.