Journal ArticleDOI
The fractional Fourier transform: theory, implementation and error analysis
V. Ashok Narayanan,K.M.M. Prabhu +1 more
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TLDR
It is hoped that this implementation and fixed-point error analysis will lead to a better understanding of the issues involved in finite register length implementation of the discrete fractional Fourier transform and will help the signal processing community make better use of the transform.About:
This article is published in Microprocessors and Microsystems.The article was published on 2003-11-03. It has received 128 citations till now. The article focuses on the topics: Fractional Fourier transform & Non-uniform discrete Fourier transform.read more
Citations
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Proceedings ArticleDOI
Chirp signal analysis based on PWD in fractional Fourier transform domain
Li Jing,Wang Shuxun,Wang Fei +2 more
TL;DR: In this paper, a pseudo Wigner distribution in the fractional Fourier transform (FT) domain is proposed to analyze single or multi-component chirp signals, which preserves the WD auto-terms and cancels the cross-terms when there are several signal components.
Journal ArticleDOI
Gear Fault Signal Detection based on an Adaptive Fractional Fourier Transform Filter
TL;DR: In this article, an adaptive fractional Fourier transform filter is proposed to suppress noise in gear vibration signals and hence to highlight signal components originated from gear fault dynamic characteristics, while the transform orders are selected when the signal has the highest energy gathering and the filter parameters are determined by evolutionary rules.
Journal ArticleDOI
Classical ghost-imaging spectral ellipsometer.
TL;DR: A novel approach for the spectral characterization of inhomogeneous thin films and interfaces by means of an imaging ghost ellipsometer operating with classical light of Gaussian statistics, which shows that the device output provides the ellipsometric information associated with the fractional Fourier transforms of the sample's reflection coefficients.
Journal ArticleDOI
Asymptotic behavior of fractional Laplacians in the half space
TL;DR: The estimation of the asymptotic behavior is the generalization of the argument reported in Qiao and Deng (2010) and the weighted boundary limits of modified fractional Laplacians are discussed.
Journal ArticleDOI
QPSK Training Sequence-Based Both OSNR and Chromatic Dispersion Monitoring in DWDM Systems
TL;DR: In this article, a quadrature phase-shift keying training sequence (QPSK-TS) was designed for monitoring both optical signal-to-noise ratio (OSNR) and chromatic dispersion (CD) in a dense wavelength division multiplexing (DWDM) system.
References
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Journal ArticleDOI
The fractional Fourier transform and time-frequency representations
TL;DR: 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.
Book
The Fractional Fourier Transform: with Applications in Optics and Signal Processing
TL;DR: The fractional Fourier transform (FFT) as discussed by the authors has been used in a variety of applications, such as matching filtering, detection, and pattern recognition, as well as signal recovery.
Journal ArticleDOI
Digital computation of the fractional Fourier transform
TL;DR: An algorithm for efficient and accurate computation of the fractional Fourier transform for signals with time-bandwidth product N, which computes the fractionsal transform in O(NlogN) time.
Journal ArticleDOI
The discrete fractional Fourier transform
TL;DR: This definition is based on a particular set of eigenvectors of the DFT matrix, which constitutes the discrete counterpart of the set of Hermite-Gaussian functions, and is exactly unitary, index additive, and reduces to the D FT for unit order.
Journal ArticleDOI
Effects of finite register length in digital filtering and the fast Fourier transform
Alan V. Oppenheim,C. Weinstein +1 more
TL;DR: The groundwork is set through a discussion of the relationship between the binary representation of numbers and truncation or rounding, and a formulation of a statistical model for arithmetic roundoff, to illustrate techniques of working with particular models.