New discrete unitary Haar-type heap transforms
Artyom M. Grigoryan, Merughan M. Grigoryan · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2007
This paper introduces a new class of discrete unitary transformations, the so-called discrete Haar-type heap transformations (DHHT) which are induced by input signals and use the path similar to the traditional Haar transformation. These transformations are fast and performed by simple rotations, can be composed for any order, and their complete systems of basis functions represent themselves variable waves that are generated by signals. The 2r-point discrete Haar transform is the particular case of the proposed transformations, when the generator is the constant sequence {1, 1, 1, ..., 1}. These transformations can be used in many applications and improve the results of the Haar transformation. As an example, the approximation of signals in the simple compression process, when truncating the coefficients of the discrete Haar-type heap transform is illustrated.