Computation of the fractional Fourier transform

@article{Bultheel2004ComputationOT,
  title={Computation of the fractional Fourier transform},
  author={Adhemar Bultheel and Hector Martinez Sulbaran},
  journal={Applied and Computational Harmonic Analysis},
  year={2004},
  volume={16},
  pages={182-202}
}
A New Formulation of the Fast Fractional Fourier Transform
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This work derives a Gaussian-like quadrature of the continuous fractional Fourier transform from a bilinear form of eigenvectors of the matrix associated to the recurrence equation of the Hermite polynomials, which becomes a more accurate version of the FFT and can be used for nonperiodic functions.
Review of Computing Algorithms for Discrete Fractional Fourier Transform
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A comparative analysis of the most famous algorithms for the computation of Discrete Fractional Fourier Transform is presented, to portray the major advantages and disadvantages of the previously proposed algorithms so that appropriate algorithm may be selected as per requirements.
Riesz transform associated with the fractional Fourier transform and applications
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The fractional Riesz transform associated with fractional Fourier transform is introduced, in which the chirp function is the key factor and the technical barriers to be overcome, and the physical and geometric interpretation of the high-dimensional fractional multiplier theorem is given.
Research progress on discretization of fractional Fourier transform
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A summary of discretizations of the fractional Fourier transform developed in the last nearly two decades is presented and it is hoped to offer a doorstep for the readers who are interested in the fractionsal Fouriers transform.
Research progress of the fractional Fourier transform in signal processing
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The fractional Fourier transform has been comprehensively and systematically treated from the signal processing point of view and a course from the definition to the applications is provided, especially as a reference and an introduction for researchers and interested readers.
Image and video processing using discrete fractional transforms
TLDR
Comparison of performance states that discrete fractional Fourier transform is superior in compression, while discrete fractionsal cosine transform is better in encryption of image and video.
The fractional fourier transform and its application to digital watermarking
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  • Computer Science
    2013 8th International Workshop on Systems, Signal Processing and their Applications (WoSSPA)
  • 2013
TLDR
This paper describes the implementation of a watermark embedding technique for images using the discrete fractional Fourier transform to recognize the watermark if there is a strong correlation with the embedded watermark.
Spectrum Estimation of Pseudo-random Nonuniformly Sampled Signals in the Fractional Fourier Transform Domain
  • Xu Huifa, Liu Feng
  • Computer Science
    2010 WASE International Conference on Information Engineering
  • 2010
TLDR
First, the digital spectrum of nonuniformly sampled signals in the Fractional Fourier transform domain is introduced and the result shows that these theories are also effective in the fractional Fouriers transform domain.
Optimal Step Size for the Adaptive Least-Mean Squares Algorithm Applied in the Fractional Fourier Transform Domain for Efficient Signal Estimation in Interference and Noise
© 2015 IEEE. Reprinted, with Permission, from 14 th Canadian Workshop on Information Theory Abstract—The Fractional Fourier Transform (FrFT) has wide applications in communications and signal
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