Constrained FIR Filter Design for 2-band Filter Banks and Orthonormal Wavelets
Selesnick, Ivan W.
Odegard, Jan E.
Burrus, C. Sidney
FIR filter banks; orthonormal wavelets; Kuhn-Tucker (KT)
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>Â â ¡</sub> optimization problem and (b) as a constrained L<sub>2</sub> optimization problem which allows arbitrary compromises between an L<sub>2</sub> and an L<sub>Â â ¡</sub> approach with both of them as special cases. Additional flatness constraints can also be easily included. The L<sub>2</sub> and the L<sub>Â â ¡</sub> 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.