A two-level method for sparse time-frequency representation of multiscale data Dedicated to Professor LI TaTsien on the Occasion of His 80th Birthday

Based on the recently developed data-driven time-frequency analysis（Hou and Shi, 2013）, we propose a two-level method to look for the sparse time-frequency decomposition of multiscale data. In the two-level method, we first run a local algorithm to get a good approximation of the instantaneous frequency. We then pass this instantaneous frequency to the global algorithm to get an accurate global intrinsic mode function（IMF）and instantaneous frequency. The two-level method alleviates the difficulty of the mode mixing to some extent.We also present a method to reduce the end effects.