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Oversampling analysis in fractional Fourier domain

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Abstract

Oversampling is widely used in practical applications of digital signal processing. As the fractional Fourier transform has been developed and applied in signal processing fields, it is necessary to consider the oversampling theorem in the fractional Fourier domain. In this paper, the oversampling theorem in the fractional Fourier domain is analyzed. The fractional Fourier spectral relation between the original oversampled sequence and its subsequences is derived first, and then the expression for exact reconstruction of the missing samples in terms of the subsequences is obtained. Moreover, by taking a chirp signal as an example, it is shown that, reconstruction of the missing samples in the oversampled signal is suitable in the fractional Fourier domain for the signal whose time-frequency distribution has the minimum support in the fractional Fourier domain.

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Authors and Affiliations

  1. Department of Electronic Engineering, Beijing Institute of Technology, Beijing, 100081, China

    Feng Zhang, Ran Tao & Yue Wang

Authors
  1. Feng Zhang
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  2. Ran Tao
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  3. Yue Wang
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Corresponding author

Correspondence to Ran Tao.

Additional information

Supported partially by the National Natural Science Foundation of China for Distinguished Young Scholars (Grant No. 60625104), the National Natural Science Foundation of China (Grant Nos. 60890072, 60572094), and the National Basic Research Program of China (Grant No. 2009CB724003)

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Zhang, F., Tao, R. & Wang, Y. Oversampling analysis in fractional Fourier domain. Sci. China Ser. F-Inf. Sci. 52, 1446–1455 (2009). https://doi.org/10.1007/s11432-009-0118-5

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  • DOI: https://doi.org/10.1007/s11432-009-0118-5

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