Permutation Based Design of Orthogonal Block Transformsand Filter Banks

Abstract

In this work, a new efficient design technique for orthogonal block transforms, lapped orthogonal transforms and 4-channel perfect reconstruction subband filter banks is developed. The technique consists of permutation and sign change operations on a reference vector. This approach can be thought of as a generalization of the Hadamard transform in the sense that the reference vector {\mbox{ h }}_{0} (which will be a prototype low-pass filter also forming one of the basis functions of the transform) will in general have components that are not identically 1's. The design technique, a constructive method based on Hadamard arrays, provides a convenient means to explore new transforms. The merit of our method is that the number of unknowns and equality constraints are both reduced significantly which render the design procedure much more feasible while guaranteeing at the same time linear phase.