Convex Optimization approach to signals with fast varying instantaneous frequency
نویسندگان
چکیده
Motivated by the limitation of analyzing oscillatory signals composed of multiple compo-nents with fast-varying instantaneous frequency, we approach the time-frequency analysisproblem by optimization. Based on the proposed adaptive harmonic model, the time-frequency representation of a signal is obtained by directly minimizing a functional, whichinvolves few properties an “ideal time-frequency representation” should satisfy, for exam-ple, the signal reconstruction and concentrative time frequency representation. FISTA(Fast Iterative Shrinkage-Thresholding Algorithm) is applied to achieve an efficient nu-merical approximation of the functional. We coin the algorithm as Time-frequency bYCOnvex OptimizatioN (Tycoon). The numerical results confirm the potential of theTycoon algorithm.
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