Discrete unitary transforms generated by moving waves

Abstract

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, defined 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 <i>discrete signal-induced heap transforms</i>, are described in detail.