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Circuits, Systems, and Signal Processing

, Volume 38, Issue 4, pp 1751–1774 | Cite as

Higher-Order Derivative Sampling Associated with Fractional Fourier Transform

  • Rui-Meng Jing
  • Qiang Feng
  • Bing-Zhao LiEmail author
Article
  • 58 Downloads

Abstract

The uniform and recurrent nonuniform higher-order derivative sampling problems associated with the fractional Fourier transform are investigated in this paper. The reconstruction formulas of a bandlimited signal from the uniform and recurrent nonuniform derivative sampling points are obtained. It is shown that if a bandlimited function f(t) has \(n - 1\) order derivative in fractional Fourier transform domain, then f(t) is determined by its uniform sampling points \(f^{(l)}(knT)(l=0,1,\ldots ,n-1)\) or recurrent nonuniform sampling points \(f^{(l)}(n(t_{p}+kNT))(l=0,1,\ldots ,n-1;p=1,2,\ldots ,N)\), the related sampling rate is also reduced by n times. The examples and simulations are also performed to verify the derived results.

Keywords

Derivative sampling Fractional Fourier transform Uniform sampling Recurrent nonuniform sampling 

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsBeijing Institute of Technology BeijingBeijingChina
  2. 2.School of Mathematics and Computer ScienceYanan UniversityYananChina

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