Sampling and sampling rate conversion of band limited signals in the fractional Fourier transform domain

Ran Tao Tao, Bing Deng, Wei Qiang Zhang, Yue Wang

Research output: Contribution to journalArticlepeer-review

143 Citations (Scopus)

Abstract

The fractional Fourier transform (FRFT) has become a very active area in signal processing community in recent years, with many applications in radar, communication, information security, etc., This study carefully investigates the sampling of a continuous-time band limited signal to obtain its discrete-time version, as well as sampling rate conversion, for the FRFT. Firstly, based on product theorem for the FRFT, the sampling theorems and reconstruction formulas are derived, which explain how to sample a continuous-time signal to obtain its discrete-time version for band limited signals in the fractional Fourier domain. Secondly, the formulas and significance of decimation and interpolation are studied in the fractional Fourier domain. Using the results, the sampling rate conversion theory for the FRFT with a rational fraction as conversion factor is deduced, which illustrates how to sample the discrete-time version without aliasing. The theorems proposed in this study are the generalizations of the conventional versions for the Fourier transform. Finally, the theory introduced in this paper is validated by simulations.

Original languageEnglish
Pages (from-to)158-171
Number of pages14
JournalIEEE Transactions on Signal Processing
Volume56
Issue number1
DOIs
Publication statusPublished - Jan 2008

Keywords

  • Fractional Fourier transform (FRFT)
  • Sampling rate conversion
  • Sampling theorem

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