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
Pansharpening scheme using filtering in two-dimensional discrete fractional Fourier transform
TL;DR: The proposed pansharpening scheme based on two-dimensional discrete fractional Fourier transform (2D-DFRFT) has improved spectral and spatial resolution as compared to the existing schemes.
Journal ArticleDOI
A novel feature extraction-based ECG signal analysis
TL;DR: A novel technique, i.e., fractional wavelet transform (FrWT) is proposed to be used as a feature extraction technique and results establish robustness of the proposed technique will go a long way in assisting the cardiologists in improving overall health care system in hospitals.
Journal ArticleDOI
Linear Canonical Transformations in Relativistic Quantum Physics
TL;DR: In this article, the possibility of considering LCTs to be the elements of a symmetry group for relativistic quantum physics is studied using the principle of covariance, which may help in the establishment of a unified theory of fundamental interactions.
Proceedings ArticleDOI
Improved Chirp Modulation Spread Spectrum Receiver Based on Fractional Fourier Transform for Multiple Access
TL;DR: In this article, the fractional Fourier transform (FRFT) is one of the most efficient techniques for digital signal processing of linear frequency modulated (LFM) signal applications.
Journal ArticleDOI
A secure image encryption algorithm based on fractional transforms and scrambling in combination with multimodal biometric keys
Jobanpreet Kaur,Neeru Jindal +1 more
TL;DR: Experimental results like histogram analysis, correlation analysis, peak signal-to-noise ratio, mean square error, structural similarity index measure, spectral distortion, information entropy, key sensitivity analysis, differential attacks and spoofing attacks verify the efficacy of proposed algorithm.
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.