Optimal design of orders of DFrFTs for sparse representations

Zhang, Xiao-Zhi, Ling, Bingo Wing-Kuen, Tao, Ran, Yang, Zhi-Jing, Woo, Wai Lok, Sanei, Saeid and Teo, Kok L. (2018) Optimal design of orders of DFrFTs for sparse representations. IET Signal Processing, 12 (8). pp. 1023-1033. ISSN 1751-9675

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Abstract

This study proposes an optimal design of the orders of the discrete fractional Fourier transforms (DFrFTs) and construct an overcomplete transform using the DFrFTs with these orders for performing the sparse representations. The design problem is formulated as an optimisation problem with an L 1 -norm non-convex objective function. To avoid all the orders of the DFrFTs to be the same, the exclusive OR of two constraints are imposed. The constrained optimisation problem is further reformulated to an optimal frequency sampling problem. A method based on solving the roots of a set of harmonic functions is employed for finding the optimal sampling frequencies. As the designed overcomplete transform can exploit the physical meanings of the signals in terms of representing the signals as the sums of the components in the time-frequency plane, the designed overcomplete transform can be applied to many applications.

Item Type:	Article
Uncontrolled Keywords:	concave programming, discrete Fourier transforms, signal representation, signal sampling
Subjects:	G100 Mathematics H600 Electronic and Electrical Engineering
Department:	Faculties > Engineering and Environment > Computer and Information Sciences
Depositing User:	Paul Burns
Date Deposited:	27 Mar 2019 12:38
Last Modified:	10 Oct 2019 21:01
URI:	http://nrl.northumbria.ac.uk/id/eprint/38569

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