Two-dimensional discrete fractional Fourier transform-based content removal algorithm

Tian, Nili; Zhang, Xiaozhi; Ling, Bingo Wing‐Kuen; Yang, Zhijing

doi:10.1007/s11760-016-0946-x

Cited by 2 publications

(1 citation statement)

References 10 publications

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“…FRT is of importance for signal processing [6][7][8][9][10][11][12][13], time/space-frequency representations [5,[14][15][16], image processing [17][18][19][20], video processing [21,22], pattern recognition [23], radar/sonar signal processing [24,25] and beamforming [26,27]. FRT finds applications in wave and beam propagations, diffraction and generally in Fourier optics [1,28,29].…”

Section: Introductionmentioning

confidence: 99%

Operator theory-based discrete fractional Fourier transform

Koç

2019

SIViP

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The fractional Fourier transform is of importance in several areas of signal processing with many applications including optical signal processing. Deploying it in practical applications requires discrete implementations, and therefore defining a discrete fractional Fourier transform (DFRT) is of considerable interest. We propose an operator theory-based approach to defining the DFRT. By deploying hyperdifferential operators, a DFRT matrix can be defined compatible with the theory of the discrete Fourier transform. The proposed DFRT only uses the ordinary Fourier transform and the coordinate multiplication and differentiation operations. We also propose and compare several alternative discrete definitions of coordinate multiplication and differentiation operations, each of which leads to an alternative DFRT definition. Unitarity and approximation to the continuous transform properties are also investigated in detail. The proposed DFRT is highly accurate in approximating the continuous transform.

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Section: Introductionmentioning

confidence: 99%

Operator theory-based discrete fractional Fourier transform

Koç

2019

SIViP

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Optimal Fractional Fourier Filtering for Graph Signals

Ozturk

Özaktaş

Gezici

et al. 2021

IEEE Trans. Signal Process.

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Graph signal processing has recently received considerable attention. Several concepts, tools, and applications in signal processing such as filtering, transforming, and sampling have been extended to graph signal processing. One such extension is the optimal filtering problem. The minimum mean-squared error estimate of an original graph signal can be obtained from its distorted and noisy version. However, the best separation of signal and noise, and thus the least error, is not always achieved in the ordinary Fourier domain, but rather a fractional Fourier domain. In this work, the optimal filtering problem for graph signals is extended to fractional Fourier domains, and theoretical analysis and solution of the proposed problem are provided along with computational cost considerations. Numerical results are presented to illustrate the benefits of filtering in fractional Fourier domains.

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Two-dimensional discrete fractional Fourier transform-based content removal algorithm

Cited by 2 publications

References 10 publications

Operator theory-based discrete fractional Fourier transform

Operator theory-based discrete fractional Fourier transform

Optimal Fractional Fourier Filtering for Graph Signals

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