Discrete Unitary Transforms Generated by Moving Waves

摘要

This paper describes a new class of discrete heap transforms which are unitary energy-preserving transforms and induced by input signals. These transforms have a simple form of composition and fast algorithms for any size of processed signals. We consider the heap transforms, denned by two-dimensional elementary rotations, as satisfying the given decision equations. The main feature of each heap transform is the corresponding system of basis functions, which represent themselves a family of interactive waves which are moving in the field generated by the input signal. Properties and examples of heap transforms, which we also call discrete signal-induced heap transforms, are described in detail.