An Efficient Algorithm to Design Nearly Perfect-Reconstruction Two-Channel Quadrature Mirror Filter Banks

Abstract

In this paper, a novel technique for the design of two-channel Quadrature Mirror Filter (QMF) banks with linear phase in frequency domain is presented. To satisfy the exact reconstruction condition of the filter bank, low-pass prototype filter response in pass-band, transition band and stop band is optimized using unconstrained indirect update optimization method. The objective function is formulated as a weighted sum of pass-band error and stop-band residual energy of low-pass prototype filter, and the square error of the distortion transfer function of the QMF bank at the quadrature frequency. The performance of the proposed algorithm is evaluated in terms of Peak Reconstruction Error (PRE), mean square error in pass-band and stop-band regions and stop-band edge attenuation. Design examples are included to illustrate the performance of the proposed algorithm and the quality of the filter banks that can be designed.

Keywords

• Nearly Perfect-Reconstruction
• Optimization
• Phase Distortion
• Two-Channel Filter Banks.