On time-frequency sparsity and uncertainty

Patrick Flandrin
École Normale Supérieure de Lyon

Most structured signals are intrinsically sparse in the time-frequency plane but, at the same time, ultimate localization properties attached to this sparsity is constrained by uncertainty limits. This will be discussed from two different perspectives. First, a non-adaptive "compressed sensing" approach to Wigner-type distributions will be recalled, evidencing the role played by Heisenberg cells in the Fourier transformed domain. Second, sharp localization properties stemming from reassignment techniques will be revisited in terms of spectrogram geometry, leading to adaptive Voronoi descriptions controlled by uncertainty.

Presentation (PDF File)

Back to Adaptive Data Analysis and Sparsity