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3 results

  • 4 - On Time, Frequency, and Gauss

  • 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 29-34

  • Summary

    Gaussian functions are central throughout the book. They are introduced as basic elementary waveforms whose versatility can be used for establishing a continuum of representations between the "natural" (Shannon-Nyquist-like) representation in time to the dual (Fourier) representation in frequency. This allows for a first introduction of a joint (Gabor) time-frequency representation.

  • 7 - Uncertainty Revisited

  • 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 50-55

  • Summary

    As Fourier images of (modified) ambiguity functions, time-frequency energy distributions obey uncertainty relations that can take different forms, depending on the chosen measure of spread in the plane (e.g., norms, support, variance, or entropy). In complement to classical formulations of uncertainty, this reinforces the role played by Gaussians and Gaussian STFTs/spectrograms.