Multi-resolution fourier analysis: extraction and missing signal recovery of short buried signals in noise

Abstract

In this paper, proposed multi-resolution Fourier analysis, relabeled NY-MFA, recovers as a function of resolution levels brief duration signals defined for low signal-to-noise ratios. These short noisy signals are restored with their missing parts independently of the nature of noise and its frequency extent. It is shown that the variance of resolved spectral estimates is reduced proportionally to the chosen level of frequency resolution. Extraction ability of NY-MFA using no more than a single realization of noisy simulated or experimental signals outperforms that of wavelets. Moreover, missing signal recovery of buried signals in the time domain, called here natural extrapolation, is achieved without errors. It is shown that NY-MFA is a promising signal processing tool.

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Acknowledgments

The author would like to thank anonymous reviewers for their pertinent questions, helpful comments and valuable discussions.

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Correspondence to Nouredine Yahya Bey.

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Yahya Bey, N. Multi-resolution fourier analysis: extraction and missing signal recovery of short buried signals in noise. SIViP 8, 1483–1495 (2014). https://doi.org/10.1007/s11760-012-0383-4

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Keywords

  • Multi-resolution
  • Denoising
  • Short stationary signals
  • Spectral analysis
  • Missing parts
  • Signal recovery
  • Doppler velocimetry