Solving Puzzles With HHT From a Engineering Perspective

(1)How many dimensions of Hilbert spectrum?

I think it is 3, because it is denoted as $H(w,t)$. The time-frequency distribution of the amplitude is designated as the Hilbert amplitude spectrum $H(w,t)$, or simply the Hilbert spectrum. So for a given time $t$, the instantaneous frequency $w$ and the amplitude are calculated simultaneously so that these values are assigned to Hilbert spectrum, $H(w,t)$. So one can regard $H(w,t)$ as a special 3D plot. The marginal Hilbert Spectrum is defined by $$h(w)=\int_{0}^{T}H(w,t)dt$$, where $T$ is the total data length. It is a measure of total energy contribution from each frequency over the entire data span in a probabilistic sense. It provides a quantitative way to describe the time-frequency-energy representation by integrating the Hilbert spectrum over the entire time span.