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2 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.

  • 1 - Introduction

  • Patrick Flandrin
  • Book:
    Explorations in Time-Frequency Analysis
    Published online:
    22 August 2018
    Print publication:
    06 September 2018, pp 1-6

  • Summary

    General considerations are given about signal processing and its place within data science. It is argued that its specificity is rooted in a balanced implication of tools and concepts from physics, mathematics, and informatics. Examples (Fourier, wavelets) are given for supporting this claim, and arguments are detailed for justifying why time-frequency analysis, which is the topic of this book, can be viewed as a natural language for nonstationary signal processing. The Introduction is also the place where to present a roadmap for the way to read the book.