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1 results

  • 12 - Spectrogram Geometry 2

  • 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 106-115

  • Summary

    Spectrograms are revisited from a Bargmann transform point of view, with the time-frequency plane identified to the complex plane. This permits to establish simple phase-magnitude relationships for the Gaussian STFT and to describe reassignment via a vector field which happens to be the gradient of the associated (log-)spectrogram. This also paves the way to variations such as differential or adjustable reassignment. Within this picture, the whole reassignment process can be described in terms of attractors (maxima), repellers (zeros), and basins of attraction (component domains).