Fast communication: Reduced biquaternion canonical transform, convolution and correlation

Authors:
Liqiang Guo;Ming Zhu;Xinhong Ge
Affiliations:
Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Science, Changchun 130033, PR China and Graduate School of Chinese Academy of Science, Chinese Academy of Science, Bei ...;Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Science, Changchun 130033, PR China;Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Science, Changchun 130033, PR China and Graduate School of Chinese Academy of Science, Chinese Academy of Science, Bei ...
Venue:
Signal Processing
Year:
2011

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Abstract

The reduced biquaternion canonical transform (RBCT) is defined in this paper, which is the generalization of reduced biquaternion Fourier transform (RBFT). The Parseval's theorem related to RBCT is investigated. The concepts of reduced biquaternion canonical convolution (RBCCV) and reduced biquaternion canonical correlation (RBCCR) are defined, then the convolution and correlation theorem of RBCT are developed in this paper. All these theorems can also be seen as the generalizations of the corresponding theorem related to RBFT. Finally, the discrete form and fast algorithm of RBCT are presented, and the computation complexity is similar to FFT.