A method of designing optimal wavelet filter banks

Compactly supported orthogonal wavelets are obtained from two-band paraunitary FIR filter bank solutions, with the additional "flatness" constraint that the low-pass filter should have K zeros at half of the sampling frequency. This constraint is set to obtain a "regular" wavelet, but it is somewhat in contradiction with the requirement of excellent frequency selectivity. Maximally flat filters yielding Daubechies wavelets have the worst frequency selectivity. According to those drawbacks, two design methods based on simple linear optimizations are proposed to generate wavelet filter banks with excellent frequency selectivity by maximizing the energy content in the filter passband. Finally, designed examples are given.