Recursive relations and fast flow diagram for nonlinear quantised transform

Abstract

A nonlinear quantised transform called a sign transform is introduced. Besides transforming uniquely between ternary data and the ternary spectral domain, the transform also converts to and from the sign Haar and sign Walsh spectral domains. Recursive equations defining forward and inverse transforms are presented. It is possible to calculate the new transform using recursive definitions of a new type of matrix called a sign matrix. New properties of, and operations on, such a type of matrix are shown. The fast flow diagram for efficient calculation of the new transform is introduced, implemented in the form of a locally connected flexible parallel architecture. The computational advantages of new algorithms developed for sign transform, and their comparison with known fast sign Haar and fast sign Walsh transforms, are also discussed.