In this talk, a new perspective of using trigonometric functions in quantifying nonlinear interaction is introduced. This perspective was pioneered by Norden Huang and emphasizes the multiplicative usage of trigonometric functions in solving problems. The most recent method resulting from this new perspective is Holo-spectrum, a multi-dimensional spectral expression of a time series that explicitly identifies the interactions among different scales and quantifies nonlinear interactions hidden in a time series.
Various enlightening applications of Holo-spectrum analysis, also called Huang transform, in climate studies will also be discussed. As an atmospheric/climate dynamicist and a data analysis method developer who has sided with Norden Huang in their struggles for novel analysis methods in the last fifteen years, the speaker strong believe the Huang transform will help greatly in understanding the complicated climate system.