Induced norm optimal multirate filter bank design using LMI constraints

Abstract

The focus of our research was the design of induced norm optimal two-channel multirate filter banks using LMIs. In our research the l2 norm, L∞ norm and H∞ norm were used as the design criteria for two-channel filter bank design. To design QMF banks, we optimized the stopband attenuation level of the individual subband filter, the allowable maximal ripple size of the reconstruction error, and the l2 norm of the impulse response sequence of the FIR lowpass filter. The constraints for the three minimization objectives were converted into LMIs. The H∞ norm was employed when the multirate filter bank design problem was converted into a model-matching design problem. The H∞ optimal model-matching design problem was converted to a series of LMIs. The above LMI constrained optimization problems were solved by semi-definite programmings. The solutions of the l2 and L∞ norm optimal design were globally optimal. The most attractive part of the H∞ optimization result was the stable two-channel filter banks where the passband of the IIR synthesis subband filter was nearly linear phase; the analysis subband filter was an exactly linear phase FIR or a nearly linear phase IIR filter. As a result, the overall filter banks were approximately linear phase. The magnitude, phase and aliasing distortions were all incorporated in the H∞ optimal design procedure.

Date of Award	2002
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology