Constrained FIR filter design for 2-band filter banks and orthonormal wavelets

Abstract

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/sub /spl infin// optimization problem and (b) as a constrained L/sub 2/ optimization problem which allows arbitrary compromises between an L/sub 2/ and an L/sub /spl infin// approach with both of them as special cases. Additional flatness constraints can also be easily included. The L/sub 2/ and the L/sub /spl infin// 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.<>