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_{Â â ¡} optimization problem and (b) as a constrained L₂ optimization problem which allows arbitrary compromises between an L₂ and an L_{Â â ¡} approach with both of them as special cases. Additional flatness constraints can also be easily included. The L₂ and the L_{Â â ¡} 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.