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© The Institution of Engineering and Technology 2018. 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 L1-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.
Author(s): Zhang X-Z, Ling BW-K, Tao R, Yang Z-J, Woo W-L, Sanei S, Teo KL
Publication type: Article
Publication status: Published
Journal: IET Signal Processing
Year: 2018
Volume: 12
Issue: 8
Pages: 1023-1033
Print publication date: 15/10/2018
Online publication date: 25/07/2018
Acceptance date: 26/04/2018
ISSN (print): 1751-9675
ISSN (electronic): 1751-9683
Publisher: Institution of Engineering and Technology
URL: https://doi.org/10.1049/iet-spr.2017.0283
DOI: 10.1049/iet-spr.2017.0283
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