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Roundoff Error Analysis of the Recursive Moving Window Discrete Fourier Transform

Advances in Computational Mathematics volume 18, pages 65–78 (2003)Cite this article

Abstract

This paper presents both worst case and average case analysis of roundoff errors occuring in the floating point computation of the recursive moving window discrete Fourier transform (DFT) with precomputed twiddle factors. We show the strong influence of precomputation errors – both within the initial fast Fourier transform (FFT) and the recursion – on the numerical stability. Numerical simulations confirm the theoretical results.

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Authors and Affiliations

  1. Department of Mathematics, University of Rostock, D-18055, Rostock, Germany

    Manfred Tasche

  2. Institute of Mathematics, Medical University of Luebeck, Wallstr. 40, D-23560, Luebeck, Germany

    Hansmartin Zeuner

Authors
  1. Manfred Tasche
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  2. Hansmartin Zeuner
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Tasche, M., Zeuner, H. Roundoff Error Analysis of the Recursive Moving Window Discrete Fourier Transform. Advances in Computational Mathematics 18, 65–78 (2003). https://doi.org/10.1023/A:1021254709641

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  • DOI: https://doi.org/10.1023/A:1021254709641

  • roundoff error analysis
  • worst case study
  • average case study
  • recursive moving window DFT
  • fast Fourier transform
  • discrete windowed Fourier transform