Journal ArticleDOI
Generalized Sampling Expansion for Bandlimited Signals Associated With the Fractional Fourier Transform
Deyun Wei,Qiwen Ran,Yuan-Min Li +2 more
TLDR
By designing fractional Fourier filters, the potential application of the GSE is presented to show the advantage of the theory and reconstruction method for sampling from the signal and its derivative based on the derived GSE and the property of FRFT is obtained.Abstract:
The aim of the generalized sampling expansion (GSE) is the reconstruction of an unknown continuously defined function f(t), from the samples of the responses of M linear time invariant (LTI) systems, each sampled by the 1/M th Nyquist rate. In this letter, we investigate the GSE in the fractional Fourier transform (FRFT) domain. Firstly, the GSE for fractional bandlimited signals with FRFT is proposed based on new linear fractional systems, which is the generalization of classical generalized Papoulis sampling expansion. Then, by designing fractional Fourier filters, we obtain reconstruction method for sampling from the signal and its derivative based on the derived GSE and the property of FRFT. Last, the potential application of the GSE is presented to show the advantage of the theory.read more
Citations
More filters
Journal ArticleDOI
Generalized Sampling Expansions with Multiple Sampling Rates for Lowpass and Bandpass Signals in the Fractional Fourier Transform Domain
Deyun Wei,Yuan-Min Li +1 more
TL;DR: This paper investigates the GSE for lowpass and bandpass signals with multiple sampling rates in the fractional Fourier transform (FRFT) domain and derives the periodic nonuniform sampling scheme and the derivative interpolation method by designing different fractional filters and selecting specific sampling rates.
Journal ArticleDOI
A Convolution and Correlation Theorem for the Linear Canonical Transform and Its Application
Deyun Wei,Qiwen Ran,Yuan-Min Li +2 more
TL;DR: The convolution theorem in FT domain is shown to be a special case of the achieved results, and the correlation theorem is derived, which is also a one dimensional integral expression.
Journal ArticleDOI
Multichannel Sampling and Reconstruction of Bandlimited Signals in Fractional Fourier Domain
TL;DR: The classical multichannel sampling theorem and the well-known sampling theorem for the FRFT are shown to be special cases of it and the validity of the theoretical derivations is demonstrated via simulations.
Journal ArticleDOI
Convolution and Multichannel Sampling for the Offset Linear Canonical Transform and Their Applications
Deyun Wei,Yuan-Min Li +1 more
TL;DR: New convolution and product theorems for the OLCT are proposed, which state that a modified ordinary convolution in the time domain is equivalent to simple multiplication operations for theOLCT and the Fourier transform (FT) and a practical multichannel sampling expansion constructed by the new convolution structure is introduced.
Journal ArticleDOI
Reconstruction of multidimensional bandlimited signals from multichannel samples in linear canonical transform domain
Deyun Wei,Yuan-Min Li +1 more
TL;DR: This study proposes the multidimensional multichannel sampling (MMS) for the bandlimited signal in the LCT domain based on a basis expansion of an exponential function and obtains the reconstruction method for theMultidimensional derivative sampling and the periodic non-uniform sampling by designing the system filter transfer functions.
References
More filters
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 Shannon sampling theorem—Its various extensions and applications: A tutorial review
TL;DR: In this paper, the authors present the various contributions made for the sampling theorems with the necessary mathematical details to make it self-contained, including sampling for functions of more than one variable, random processes, nonuniform sampling, nonband-limited functions, implicit sampling, sampling with the function and its derivatives as suggested by Shannon in his original paper, and sampling for general integral transforms.
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.