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Time-frequency localization from sparsity constraints

Abstract : In the case of multicomponent AM-FM signals, the idealized representation which consists of weighted trajectories on the time-frequency (TF) plane, is intrinsically sparse. Recent advances in optimal recovery from sparsity constraints thus suggest to revisit the issue of TF localization by exploiting sparsity, as adapted to the specific context of (quadratic) TF distributions. Based on classical results in TF analysis, it is argued that the relevant information is mostly concentrated in a restricted subset of Fourier coefficients of the Wigner-Ville distribution neighbouring the origin of the ambiguity plane. Using this incomplete information as the primary constraint, the desired distribution follows as the minimum l1-norm solution in the transformed TF domain. Possibilities and limitations of the approach are demonstrated via controlled numerical experiments, its performance is assessed in various configurations and the results are compared with standard techniques. It is shown that improved representations can be obtained, though at a computational cost which is significantly increased.
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Contributor : Patrick Flandrin Connect in order to contact the contributor
Submitted on : Wednesday, October 3, 2007 - 2:51:40 PM
Last modification on : Wednesday, November 20, 2019 - 2:56:32 AM
Long-term archiving on: : Thursday, September 27, 2012 - 12:41:08 PM


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  • HAL Id : ensl-00176412, version 1



Pierre Borgnat, Patrick Flandrin. Time-frequency localization from sparsity constraints. 2007. ⟨ensl-00176412⟩



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