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arXiv · 1503.07591

Convex Optimization approach to signals with fast varying instantaneous frequency

Matthieu Kowalski·Adrien Meynard·Hau-tieng Wu
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Abstract

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 {\it Time-frequency bY COnvex OptimizatioN} (Tycoon). The numerical results confirm the potential of the Tycoon algorithm.

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Matthieu Kowalski, Adrien Meynard, Hau-tieng Wu. 2015-03-26. Convex Optimization approach to signals with fast varying instantaneous frequency. https://arxiv.org/abs/1503.07591

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