Optimal design of orders of DFrFTs for sparse representations

Xiao-Zhi Zhang, Bingo Wing-Kuen Ling*, Ran Tao, Zhi-Jing Yang, Wai Lok Woo, Saeid Sanei, Kok L. Teo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)1023-1033
Number of pages11
JournalIET Signal Processing
Issue number8
Early online date1 Oct 2018
Publication statusPublished - 1 Oct 2018
Externally publishedYes


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