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dc.contributor.authorZhang, X.
dc.contributor.authorLing, B.
dc.contributor.authorTao, R.
dc.contributor.authorYang, Z.
dc.contributor.authorWoo, W.
dc.contributor.authorSanei, S.
dc.contributor.authorTeo, Kok Lay
dc.identifier.citationZhang, X. and Ling, B. and Tao, R. and Yang, Z. and Woo, W. and Sanei, S. and Teo, K.L. 2018. Optimal design of orders of DFrFTs for sparse representations. IET Signal Processing. 12 (8): pp. 1023-1033.

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.

dc.publisherThe Institution of Engineering and Technology
dc.titleOptimal design of orders of DFrFTs for sparse representations
dc.typeJournal Article
dcterms.source.titleIET Signal Processing
curtin.departmentSchool of Electrical Engineering, Computing and Mathematical Science (EECMS)
curtin.accessStatusFulltext not available

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