Journal ArticleDOI
The fractional Fourier transform: theory, implementation and error analysis
V. Ashok Narayanan,K.M.M. Prabhu +1 more
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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Journal ArticleDOI
Invariant quadratic operators associated with linear canonical transformations and their eigenstates
TL;DR: In this article , the authors identify invariant quadratic operators associated with linear Canonical Transformations (LCTs) which could play important roles in physics, and the eigenstates of these operators are also identified.
Journal ArticleDOI
On an αth-order fractional Radon transform and a wave type of equation
TL;DR: In this article, a fractional Radon transform for which a sort of Fourier slice theorem also holds was considered, and the Fourier slices theorem was shown to hold for the classical Radon transformation.
Proceedings ArticleDOI
Application of hybrid ATI/DPCA method for moving human target detection in forest environments
TL;DR: Moving human target sensing for airborne foliage-penetration (FOPEN) radar applications is considered and the processing algorithm is evaluated using the scattering returns from large-scale, full-wave electromagnetic simulations of a scene consisting of a walking human embedded in a forest stand.
Journal ArticleDOI
A Comparative Study of LFM Reverberation Suppression Schemes
TL;DR: The simulation results with LFM reverberation data verify that the proposed dechirping transformation based and FrFT based MA and ARMA prewhitening models improves the target detection performance of active sonar systems.
Book ChapterDOI
Multivariate Harmonic Analysis
TL;DR: In this article, multivariate harmonic analysis technique has been employed widely in determining cyclic variations of multivariate time series and it has been shown that it can be used to determine cyclic variation of time series.
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.