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2 results

  • 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.

  • 5 - Uncertainty

  • from Part I - Basics and Constraints
  • Patrick Flandrin
  • Book:
    Explorations in Time-Frequency Analysis
    Published online:
    22 August 2018
    Print publication:
    06 September 2018, pp 35-39

  • Summary

    Gaussian functions happen also to be central with respect to the intrinsic conflict that exists between time and frequency and which is referred to as “uncertainty.” This can take various forms depending upon the chosen measure of spread or occupancy in both domains. The striking feature is that most of the intuitive measures such as dispersion or entropy end up with Gaussians as minimizers, making them “quanta” of information (“logons” in Gabor's terminology).