Constrained FIR Filter Design for 2-band Filter Banks and Orthonormal Wavelets

M. Lang, I. Selesnick, J. E. Odegard, and C. S. Burrus

Department of Electrical and Computer Engineering - MS366
Rice University, Houston, TX-77251

Abstract

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2-band paraunitary FIR filter banks can be used to generate a multiresolution analysis with compactly supported orthonormal (ON) wavelets.  The filter design problem is formulated and solved (a) as a constrained L_oo optimization problem and (b) as a constrained L_2 optimization problem which allows arbitrary compromises between an L_2 and an L_oo approach with both of them as special cases. Additional flatness constraints can also be easily included.  The L_2 and the L_oo design are based on the Kuhn-Tucker (KT) conditions and the alternation theorem, respectively.  Therefore, optimality of the solution is guaranteed. The method (a) is a simpler alternative to a known method.  The method (b) solves a more general problem than the approaches known in the literature including all of them as special cases.