20 September 2007 Discrete unitary transforms generated by moving waves
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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 discrete signal-induced heap transforms, are described in detail.
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Artyom M. Grigoryan, Merughan M. Grigoryan, "Discrete unitary transforms generated by moving waves", Proc. SPIE 6701, Wavelets XII, 670125 (20 September 2007); doi: 10.1117/12.728383; https://doi.org/10.1117/12.728383
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