Gianluca Giacchi: Eardrums writing scores: time-frequency analysis, the handbook of absolute pitches

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Gianluca Giacchi

Eardrums writing scores: time-frequency analysis, the handbook of absolute pitches

A score contains all the information needed to reproduce a music signal in time: the notes representing different frequencies and the octaves being their amplitudes. Time-frequency analysis is a branch of harmonic analysis that studies the relations between tempered distributions and their Fourier transforms that, in this context, precisely represent the amplitude of a signal in time and the amplitude of its frequencies. This seminar aims to provide a brief overview on several aspects of time-frequency analysis: from uncertainty principles, mathematical results providing hindrances to the exact localization of signals, to pseudodifferential operators, whose study fits surprisingly and naturally into a time-frequency analysis setting.