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Optimal overcomplete kernel design for sparse representations via discrete fractional Fourier transforms

Yang, Z, Yang, Z, Qing, C, Ling, BW-K, Woo, WL and Sanei, S (2012) Optimal overcomplete kernel design for sparse representations via discrete fractional Fourier transforms Proceedings of the 2012 8th International Symposium on Communication Systems, Networks and Digital Signal Processing, CSNDSP 2012.

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Abstract

This paper proposes to use a set of discrete fractional Fourier transform (DFrFT) matrices with different rotational angles to construct an overcomplete kernel for sparse representations of signals. The design of the rotational angles is formulated as an optimization problem. To solve the problem, it is shown that this design problem is equivalent to an optimal sampling problem. Furthermore, the optimal sampling frequencies are the roots of a set of harmonic functions. As the frequency responses of the filters are required to be computed only at frequencies in a discrete set, the globally optimal rotational angles can be found very efficiently and effectively. © 2012 IEEE.

Item Type: Article
Authors :
AuthorsEmailORCID
Yang, ZUNSPECIFIEDUNSPECIFIED
Yang, ZUNSPECIFIEDUNSPECIFIED
Qing, CUNSPECIFIEDUNSPECIFIED
Ling, BW-KUNSPECIFIEDUNSPECIFIED
Woo, WLUNSPECIFIEDUNSPECIFIED
Sanei, SUNSPECIFIEDUNSPECIFIED
Date : 2012
Identification Number : https://doi.org/10.1109/CSNDSP.2012.6292655
Depositing User : Symplectic Elements
Date Deposited : 28 Mar 2017 14:13
Last Modified : 28 Mar 2017 14:13
URI: http://epubs.surrey.ac.uk/id/eprint/742471

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