Discrete HARWHT and discrete fractional HARWHT transforms

Authors:
Hongqing Zhu
Affiliations:
Department of Electronics and Communications Engineering, East China University of Science and Technology, Shanghai, China
Venue:
AICI'11 Proceedings of the Third international conference on Artificial intelligence and computational intelligence - Volume Part II
Year:
2011

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Abstract

This paper introduces a new transform known as HARWHT. It results from the Kronecker product of the discrete Hartley transform (DHT) and discrete Walsh-Hadamard transform (WHT). The eigenvectors and eigenvalues of the HARWHT transform matrices are presented using Kronecker product. Then, the results of the eigen decomposition of the transform matrices are used to define discrete fractional HARWHT transform. In addition, the study discusses the properties of discrete fractional HARWHT transform, such as angle additivity. Finally, the study investigates the application of the HARWHT and discrete fractional HARWHT in one and two-dimensional signal processing.