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Time–Frequency Analysis

  • Frédéric Cohen Tenoudji
Chapter
Part of the Modern Acoustics and Signal Processing book series (MASP)

Abstract

Fourier analysis is not relevant to describe a signal when some of its properties change over time. This is the case, for example, for the chirp signal that we studied previously whose instantaneous frequency varies with time. This chapter reviews various methods for analyzing nonstationary signals. Multiplication of the signal by a sliding window leads to short-time Fourier analysis and spectrogram. In the Wigner–Ville distribution, the time reversed signal plays the role of a sliding window analyzer. The Continuous Wavelet Transform (CWT) principle is to explore the signal with a window whose width takes successively all possible values. We explain the theoretical basis of this method. Several wavelets are presented: Morlet, Mexican hat, and Shannon wavelets.

Keywords

Instantaneous Frequency Continuous Wavelet Transform Spectral Amplitude Fourier Domain Morlet Wavelet 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Pierre and Marie Curie University, UPMCParisFrance

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