Permutation Based Design of Orthogonal Block Transforms and Filter Banks

In this work, a new efficient design techniquefor orthogonal block transforms, lapped orthogonal transformsand 4-channel perfect reconstruction subband filter banks isdeveloped. The technique consists of permutation and sign changeoperations on a reference vector. This approach can be thoughtof as a generalization of the Hadamard transform in the sensethat the reference vector h ₀ (which will be a prototype low-pass filteralso forming one of the basis functions of the transform) willin general have components that are not identically 1's. Thedesign technique, a constructive method based on Hadamard arrays,provides a convenient means to explore new transforms. The meritof our method is that the number of unknowns and equality constraintsare both reduced significantly which render the design proceduremuch more feasible while guaranteeing at the same time linearphase.