Multi-resolution Fourier Analysis: achieved high resolutions with suppressed finite observation effects

Abstract

In this paper of the series on multi-resolution Fourier analysis, labeled NY-MFA, it is shown that the problem of finite observation and its detrimental consequences on amplitude resolution are eliminated. Obscuring and distorting effects of implicit windowing are suppressed without altering already provided frequency resolution in excess of Gabor–Heisenberg limit. Weak, virtual or spurious spectral lines are detected. Easier and fine frequency estimations are provided. Proposed analysis opens promising perspectives free of finite observation effects helping, by the way, to avoid misleading interpretations and diagnosis errors.

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Acknowledgments

The author would like to thank anonymous reviewers for their suggestions and helpful comments.

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Correspondence to Nourédine Yahya Bey.

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Yahya Bey, N. Multi-resolution Fourier Analysis: achieved high resolutions with suppressed finite observation effects. SIViP 10, 711–718 (2016). https://doi.org/10.1007/s11760-015-0799-8

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Keywords

  • Multi-resolution
  • Windowing effects
  • Finite observation
  • Fourier analysis
  • Amplitude resolution
  • Frequency resolution
  • Frequency estimation
  • Gabor–Heisenberg limit