Contents Introduction Presentation Background, system requirements and installation Introductory examples Example 1 Example 2 Example 3 Non stationary signals Time representation and frequency representation Localization and the Heisenberg-Gabor principle Example 1 Example 2 Instantaneous frequency Group delay About stationarity How to synthesize a mono-component non-stationary signal What about multi-component non-stationary signals ? First class of solutions : the atomic decompositions The Short-Time Fourier Transform Definition An example Some properties Time-frequency resolution Time-scale analysis and the wavelet transform Definitions and interpretation Properties Sampling considerations The discrete STFT The Gabor Representation The discrete wavelet transform From atomic decompositions to energy distributions The spectrogram The scalogram Conclusion Second class of solutions : the energy distributions The Cohen's class The Wigner-Ville distribution The Cohen's class Link with the narrow-band ambiguity function Other important energy distributions Conclusion The affine class Axiomatic definition Some examples Relation with the ambiguity domain The affine Wigner distributions The pseudo affine Wigner distributions Conclusion The reassignment method Introduction The reassignment of the spectrogram Reassignment of the Cohen's class representations Reassignment of the affine class representations Numerical examples Connected approaches Conclusion Extraction of information from a time-frequency image Moments and marginals Moments Marginals More on interferences: information on phase Renyi information Time-frequency analysis: help to decision General considerations An example: detection and estimation of linear FM signals Analysis of local singularities Bibliography Index
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