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Higher-Order Derivative Sampling Associated with Fractional Fourier Transform

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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.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Beijing Institute of Technology Beijing, No. 5 Zhongguancun South Street, Haidian District, Beijing, 100081, China

    Rui-Meng Jing, Qiang Feng & Bing-Zhao Li

  2. School of Mathematics and Computer Science, Yanan University, Yanan, 716000, Shanxi, China

    Qiang Feng

Authors
  1. Rui-Meng Jing
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  2. Qiang Feng
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  3. Bing-Zhao Li
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Correspondence to Bing-Zhao Li.

Additional information

This work is supported by the National Natural Science Foundation of China (No. 61671063) and (No. 61861044).

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Jing, RM., Feng, Q. & Li, BZ. Higher-Order Derivative Sampling Associated with Fractional Fourier Transform. Circuits Syst Signal Process 38, 1751–1774 (2019). https://doi.org/10.1007/s00034-018-0936-z

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