A New Formulation of the Fast Fractional Fourier Transform
- MathematicsSIAM J. Sci. Comput.
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
- Computer Science
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
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
- Computer ScienceScience in China Series F: Information Sciences
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
- Computer ScienceScience in China Series F
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.
Computation of an eigendecomposition-based discrete fractional Fourier transform with reduced arithmetic complexity
- Computer ScienceSignal Process.
Image and video processing using discrete fractional transforms
- Computer ScienceSignal Image Video Process.
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
- Computer Science2013 8th International Workshop on Systems, Signal Processing and their Applications (WoSSPA)
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
- Computer Science2010 WASE International Conference on Information Engineering
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…
SHOWING 1-10 OF 27 REFERENCES
Discrete fractional Fourier transform based on orthogonal projections
- EngineeringIEEE Trans. Signal Process.
The proposed DFRFT has DFT Hermite eigenvectors and retains the eigenvalue-eigenfunction relation as a continous FRFT and will provide similar transform and rotational properties as those of continuous fractional Fourier transforms.
The fractional Fourier transform and time-frequency representations
- EngineeringIEEE Trans. Signal Process.
The authors briefly introduce the functional Fourier transform and a number of its properties and present some new results: the interpretation as a rotation in the time-frequency plane, and the FRFT's relationships with time- frequencies such as the Wigner distribution, the ambiguity function, the short-time Fouriertransform and the spectrogram.
The Fractional Order Fourier Transform and its Application to Quantum Mechanics
We introduce the concept of Fourier transforms of fractional order, the ordinary Fourier transform being a transform of order 1. The integral representation of this transform can be used to construct…
Continuous vs. discrete fractional Fourier transforms
- Physics, Mathematics
The discrete fractional Fourier transform
- Computer Science1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258)
This definition is based on a particular set of eigenvectors of the DFT which constitutes the discrete counterpart of the set of Hermite-Gaussian functions and supports confidence that it will be accepted as the definitive definition of this transform.
Digital Computation of Fractional Fourier Transform
- Engineering, Computer Science
Simulation results indicate that the energy of LFM signal will be collected effectively when the fractional order is matching with its modulation slope and in weak signals detection of underwater acoustic domain, the authors can get high anti-Doppler performance using the Fractional fourier transform algorithm.
A multi-input-multi-output system approach for the computation of discrete fractional Fourier transform
- Engineering, Computer ScienceSignal Process.
Multiplicity of fractional Fourier transforms and their relationships
- MathematicsIEEE Trans. Signal Process.
A general FRT definition is generated, based on eigenfunctions and eigenvalues of the ordinary Fourier transform, which allows us to generate all possible definitions and gives explicit relationships between the different FRTs.
Improved discrete fractional Fourier transform.
- MathematicsOptics letters
An improved DFRFT is proposed that provides transforms similar to those of the continuous fractional Fourier transform and also retains the rotation properties.
Understanding discrete rotations
- Computer Science1997 IEEE International Conference on Acoustics, Speech, and Signal Processing
By studying a 90 degree rotation, an algorithm to compute a prime-length discrete Fourier transform (DFT) based on convolutions and multiplications of discrete, periodic chirps is formulated, providing a further connection between the DFT and the discrete Wigner distribution based on group theory.