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
A review and evaluation of numerical tools for fractional calculus and fractional order control
TL;DR: In this article, the authors present a survey of the available tools for fractional integration/differentiation, and the simulation of fractional order systems, in order to benefit researchers with different academic backgrounds.
Journal ArticleDOI
Automatic musical instrument classification using fractional fourier transform based- MFCC features and counter propagation neural network
TL;DR: A novel feature extraction scheme for automatic classification of musical instruments using Fractional Fourier Transform (FrFT)-based Mel Frequency Cepstral Coefficient (MFCC) features that shows significant improvement in classification accuracy and robustness against Additive White Gaussian Noise compared to other conventional features.
Journal ArticleDOI
Analysis of financial data series using fractional Fourier transform and multidimensional scaling
TL;DR: In this paper, the analysis of the dynamical properties of financial data series from worldwide stock market indexes during the period 2000-2009 is presented, under a regional criterium, ten main indexes at a daily time horizon.
Journal ArticleDOI
Research progress on discretization of fractional Fourier transform
Ran Tao,Feng Zhang,Yue Wang +2 more
TL;DR: 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.
Journal ArticleDOI
A Comparison of ECG Signal Pre-processing Using FrFT, FrWT and IPCA for Improved Analysis
TL;DR: A new fractional wavelet transform (FrWT) has been proposed as a pre-processing technique in order to overcome the disadvantages of other existing commonly used techniques viz. wavelettransform (WT) and the fractional Fourier transform ( FrFT).
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.