From atomic decompositions to energy distributions Up to this point, we presented time-frequency representations that decompose the signal into elementary components, the atoms, well localized in time and in frequency. These representations were linear transforms of the signal. Another approach to this problem, which will be developed in the next chapter, consists in distributing the energy of the signal along the two variables time and frequency. This gives rise to energy time-frequency distributions, which are naturally quadratic transforms of the signal. We present in this section a natural transition between these two classes of solutions through the spectrogram (for the Weyl-Heisenberg group) and the scalogram (for the affine group).
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