New sampling formulae for the fractional Fourier transform
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Digital watermarking in the fractional Fourier transformation domain
Journal of Network and Computer Applications
Understanding Discrete Rotations
ICASSP '97 Proceedings of the 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '97)-Volume 3 - Volume 3
Sampling and series expansion theorems for fractional Fourier and other transforms
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Time-frequency signal analysis based on the windowed fractional Fourier transform
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Adaptive fractional Fourier domain filtering
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Discrete Fractional Fourier Transform Based on New Nearly Tridiagonal Commuting Matrices
IEEE Transactions on Signal Processing
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Lv's distribution for time-frequency analysis
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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.