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2 results

  • 14 - More on Maxima

  • from Part II - Geometry and Statistics
  • Patrick Flandrin
  • Book:
    Explorations in Time-Frequency Analysis
    Published online:
    22 August 2018
    Print publication:
    06 September 2018, pp 124-138

  • Summary

    The statistical distribution of the (global and local) extrema are described by an extreme value (Gumbel) distribution. Local maxima can serve as centers for Voronoi cells whose statistics is investigated in terms of density, area, and shape. Following the "musical score" analogy, those local maxima (either isolated or organized along ridges) can be interpreted as "loud" points from which signals embedded in noise can be detected and estimated.

  • 13 - The Noise Case

  • from Part II - Geometry and Statistics
  • Patrick Flandrin
  • Book:
    Explorations in Time-Frequency Analysis
    Published online:
    22 August 2018
    Print publication:
    06 September 2018, pp 116-123

  • Summary

    When applied to white Gaussian noise, Gaussian spectrograms are made of patches whose distribution is controlled by the correlation function of the STFT considered as a 2D homogeneous field, and in turn by the underlying reproducing kernel of the analysis. This can be given a simple model whose basic ingredients are a mean distribution of logons resulting from a circle packing argument due to uncertainty, and an adequate degree of randomness in fluctuations around the mean model and inter-logon phase relationships.