Extending Vaidyanathan’s procedure to improve the performance of unitary filter banks with a fixed lowpass by using additional elementary building blocks

Wavelet decomposition of signals using the classical Daubechies-Wavelets could also be considered as a decomposition using a filter bank with two channels, a low pass and a high pass channel, represented by the father and mother wavelet, respectively. By generalizing this two channel approach filter banks with N ≥ 2 channels can be constructed. They possess one scaling function or father wavelet representing the low pass filter and one, two or more mother wavelets representing band pass filters. The resulting band pass filters do not show a satisfactory selective behavior, in general. Hence, a modification of the generalized design seems appropriate. Based on Vaidyanathan’s procedure we developed a method to modify the modulation matrix under the condition that the low pass is unchanged and the degree of the band pass filters is not increased. This can be achieved by introducing one or more additional elementary building blocks under certain orthogonality constraints with respect to their generating vectors. While the (polynomial) degree of the modulation matrix remains unchanged, its complexity increases due to its increased McMillan degree.