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Optimal design of orders of DFrFTs for sparse representations

Lookup NU author(s): Dr Wai Lok Woo


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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.

Publication metadata

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


DOI: 10.1049/iet-spr.2017.0283


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