Butterworth wavelets and adaptive echo cancellation

Butterworth wavelets are introduced for wavelet analysis, and it is shown that they constitute a large class of orthonormal wavelets with some advantages. Wavelet and binary tree representations are compared, and cross terms that decrease the intelligibility are suppressed by carefully adjusting the cut-off frequency. Rational sampling is used to obtain nonaliased frequency bands. Structural freedom of the tree representations can be further increased by using perfect reconstruction filter banks leading to generalized tree structures. Binary tree and filter bank forms are compared for adaptive echo cancellation. The echo suppression rate is improved by decreasing the overlapping frequency bands at the expense of magnitude distortion at these frequencies