RECURSIVE RELATIONS AND FAST-FLOW DIAGRAM FOR NONLINEAR QUANTIZED TRANSFORM

A nonlinear quantised transform called a sign transform is introduced. Besides transforming uniquely between ternary data and the ternary sp ectral domain, the transform also converts to and from the sign Haar a nd sign Walsh spectral domains. Recursive equations defining forward a nd inverse transforms are presented, It is possible to calculate the n ew transform using recursive definitions of a new type of matrix calle d a sign matrix. New properties of, and operations on, such a type of matrix are shown. The fast flow diagram for efficient calculation of t he new transform is introduced, implemented in the form of a locally c onnected flexible parallel architecture. The computational advantages of new algorithms developed for sign transform, and their comparison w ith known fast sign Haar and fast sign Walsh transforms, an also discu ssed.