Convex Optimization approach to signals with fast varying instantaneous frequency

Matthieu Kowalski, Adrien Meynard, Hau tieng Wu

Research output: Contribution to journalArticlepeer-review


Motivated by the limitation of analyzing oscillatory signals composed of multiple components with fast-varying instantaneous frequency, we approach the time-frequency analysis problem by optimization. Based on the proposed adaptive harmonic model, the time-frequency representation of a signal is obtained by directly minimizing a functional, which involves few properties an “ideal time-frequency representation” should satisfy, for example, the signal reconstruction and concentrative time-frequency representation. FISTA (Fast Iterative Shrinkage-Thresholding Algorithm) is applied to achieve an efficient numerical approximation of the functional. We coin the algorithm as Time-frequency bY COnvex OptimizatioN (Tycoon). The numerical results confirm the potential of the Tycoon algorithm.

Original languageEnglish (US)
Pages (from-to)89-122
Number of pages34
JournalApplied and Computational Harmonic Analysis
Issue number1
StatePublished - Jan 2018


  • Chirp factor
  • Convex optimization
  • Instantaneous frequency
  • Time-frequency analysis

ASJC Scopus subject areas

  • Applied Mathematics


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