Fractional Fourier transform as a signal processing tool: An overview of recent developments

By Ervin Sejdic, Igor Djurovic, Ljubisa A. Stankovic. Signal Processing, 2011

430 citations recorded by the source corpus.

Fractional Fourier transform (FRFT) is a generalization of the Fourier transform, rediscovered many times over the past 100 years. In this paper, we provide an overview of recent contributions pertaining to the FRFT. Specifically, the paper is geared toward signal processing practitioners by emphasizing the practical digital realizations and applications of the FRFT. It discusses three major topics. First, the manuscripts relates the FRFT to other mathematical transforms. Second, it discusses various approaches for practical realizations of the FRFT. Third, we overview the practical applications of the FRFT. From these discussions, we can clearly state that the FRFT is closely related to other mathematical transforms, such as time-frequency and linear canonical transforms. Nevertheless, we still feel that major contributions are expected in the field of the digital realizations and its applications, especially, since many digital realizations of the FRFT still lack properties of the continuous FRFT. Overall, the FRFT is a valuable signal processing tool. Its practical applications are expected to grow significantly in years to come, given that the FRFT offers many advantages over the traditional Fourier analysis.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Signal Processing

View Paper: https://www.semanticscholar.org/paper/a3e15a23c8baf381ac8e5cb6e404a41fd4f537e5

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In Computer Vision and Pattern Recognition

1. Jian Zhao
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Citations in the corpus

• Application of the Fractional Complex Transform to Fractional Differential Equations (2011, neutral): “Many useful transforms for solving various problems were appeared in open literature, such as the travelling wave transform [1], the Laplace transform [2], the Fourier transform [3], the Bäcklund transformation [4], the integral transform [5], and the local fractional integral transforms[6].”
• Orthogonal Chirp Division Multiplexing (2016, background): “Both the Fresnel and Fourier transforms are linear canonical transform [51]–[54].”
• Fractional Fourier transforms on $L^p$ and applications (2020, neutral): “, [3, 13, 16, 20, 21, 23]).”