Journal ArticleDOI
Tuning of FIR filter transition bandwidth using fractional Fourier transform
TLDR
An alternative methodology to tune the transition bandwidth of window-based FIR filters, based on FRFT, is developed and introduces a comparative ease in tuning by eliminating the need to re-compute the impulse response coefficients.About:
This article is published in Signal Processing.The article was published on 2007-12-01. It has received 19 citations till now. The article focuses on the topics: Window function & Kaiser window.read more
Citations
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Journal ArticleDOI
A SVDD approach of fuzzy classification for analog circuit fault diagnosis with FWT as preprocessor
Hui Luo,Jiang Cui Youren Wang +1 more
TL;DR: A new approach of fault diagnosis in analog circuits, which employs the Fractional Wavelet Transform (FWT) to extract fault features and adopts a fuzzy multi-classifier based on the Support Vector Data Description (SVDD) to diagnose circuit faults, is proposed.
Journal ArticleDOI
Caputo-Based Fractional Derivative in Fractional Fourier Transform Domain
TL;DR: An application example of a low-pass finite impulse response fractional order differentiating filter in the FrFT domain based on the definition of Caputo fractional differintegral method has been investigated taking into account amplitude-modulated signal corrupted with high-frequency chirp noise.
Journal ArticleDOI
The discrete fractional Fourier transform based on the DFT matrix
Ahmet Serbes,Lutfiye Durak-Ata +1 more
TL;DR: It is shown that this DFrFT definition based on the eigentransforms of the DFT matrix mimics the properties of continuous fractional Fourier transform (FrFT) by approximating the samples of the continuous FrFT.
Journal ArticleDOI
Analysis of Dirichlet and Generalized Hamming window functions in the fractional Fourier transform domains
TL;DR: A new mathematical model for obtaining the fractional Fourier transforms of Dirichlet and Generalized ''Hamming'' window functions is presented and contains an adjustable parameter with which the main lobe width and correspondingly the minimum stop band attenuation of the resulting window function can be controlled.
Journal ArticleDOI
Closed-Form Analytical Expression of Fractional Order Differentiation in Fractional Fourier Transform Domain
TL;DR: A closed-form analytical expression for fractional order differentiation in the fractional Fourier transform (FrFT) domain is derived by utilizing the basic principles of fractional orders calculus, derived in terms of the well-known confluent hypergeometric function.
References
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Journal ArticleDOI
On the use of windows for harmonic analysis with the discrete Fourier transform
TL;DR: A comprehensive catalog of data windows along with their significant performance parameters from which the different windows can be compared is included, and an example demonstrates the use and value of windows to resolve closely spaced harmonic signals characterized by large differences in amplitude.
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.
Journal ArticleDOI
The Fractional Order Fourier Transform and its Application to Quantum Mechanics
TL;DR: In this article, a generalized operational calculus is developed, paralleling the familiar one for the ordinary transform, which provides a convenient technique for solving certain classes of ordinary and partial differential equations which arise in quantum mechanics from classical quadratic hamiltonians.
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
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.