Permutation based design of orthogonal block transforms and filter banks

In this work, a new efficient design technique for orthogonal block transfo rms, lapped orthogonal transforms and 4-channel perfect reconstruction subb and filter banks is developed. The technique consists of permutation and si gn change operations on a reference vector. This approach can be thought of as a generalization of the Hadamard transform in the sense that the refere nce vector 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 t hat are not identically 1's. The design technique, a constructive method ba sed on Hadamard arrays, provides a convenient means to explore new transfor ms. The merit of our method is that the number of unknowns and equality con straints are both reduced significantly which render the design procedure m uch more feasible while guaranteeing at the same time linear phase.