7. Time-Frequency Analysis and Wavelet Packets
Society for Industrial and Applied Mathematics eBooks · 2001
7.1 Heuristic considerations A time-frequency analysis of a signal is a representation of the signal as a linear combination of time-frequency atoms. These time-frequency atoms are essentially characterized by an arbitrary duration t2 − t1 and an arbitrary frequency ω. The instant t1 is the moment when the signal is first heard (if it is a speech signal, for example), and t2 is the instant when it ceases to be heard. The frequency ω is an average frequency; this is the frequency of the emitted tone in the case of a musical signal, while the frequency spectrum given by Fourier analysis takes into consideration the parasitic frequencies created by the note's attack and decay. We also think of a time-frequency atom as occupying a symbolic region in the time-frequency plane (Figure 7.1). This symbolic region is a rectangle R with area 2π, which expresses the Heisenberg uncertainty principle.