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Roundoff Error Analysis of the Recursive Moving Window Discrete Fourier Transform


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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Tasche, M., Zeuner, H. Roundoff Error Analysis of the Recursive Moving Window Discrete Fourier Transform. Advances in Computational Mathematics 18, 65–78 (2003).

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