  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.
