The Properties and Fast Algorithm of Quaternion Linear Canonical Transform

Author: Ye Zhang, Guanlei Xu

ABSTRACT
The quaternion linear canonical transform (QLCT) is defined in this paper, with proofs given for its reversibility property, its linear property, its odd-even invariant property and additivity property. Meanwhile, the quaternion convolution (QCV), quaternion correlation (QCR) and product theorem of LCT are deduced. Their physical interpretation is given as classical convolution, correlation and product theorem. Moreover, the fast algorithm of QLCT (FQLCT) is obtained, whose calculation complexity for different signals is similar to FFT. In addition, the paper presents the relationship between the convolution and correlation in LCT domains, and the convolution and correlation can be calculated via product theorem in Fourier transform domain using FFT.

Source:

Journal: Journal of Signal and Information Processing
DOI: 10.4236/jsip.2018.93012 (PDF)
Paper Id: 86760 (metadata)

See also: Comments to Paper

About scirp

(SCIRP: http://www.scirp.org) is an academic publisher of open access journals. It also publishes academic books and conference proceedings. SCIRP currently has more than 200 open access journals in the areas of science, technology and medicine. Readers can download papers for free and enjoy reuse rights based on a Creative Commons license. Authors hold copyright with no restrictions. SCIRP calculates different metrics on article and journal level. Citations of published papers are shown based on Google Scholar and CrossRef. Most of our journals have been indexed by several world class databases. All papers are archived by PORTICO to guarantee their availability for centuries to come.
This entry was posted in JSIP. Bookmark the permalink.

Leave a Reply

Your email address will not be published. Required fields are marked *