CHAPTER 4 Time Meets Frequency

When we listen to music, we clearly “hear” the time variation of the sound “frequencies.” These localized frequency events are not “pure” tones but packets of close frequencies. The properties of sounds are revealed by transforms that decompose signals over elementary functions that have a narrow localization in time and frequency. Windowed Fourier transforms and wavelet transforms are two important classes of local time-frequency decompositions. Measuring the time variations of “instantaneous” frequencies illustrates the limitations imposed by the Heisenberg uncertainty. Such frequencies are detected as local maxima in windowed Fourier and wavelet dictionaries and define a signal-approximation support. Audio-processing ...

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