Multiresolution Mode Decomposition for Adaptive Time Series Analysis

摘要: This paper proposes the \emph{multiresolution mode decomposition} as a novel model for adaptive time series analysis. The main conceptual innovation is introduction of intrinsic function} (MIMF) form \[ \sum_{n=-N/2}^{N/2-1} a_n\cos(2\pi n\phi(t))s_{cn}(2\pi N\phi(t))+\sum_{n=-N/2}^{N/2-1}b_n \sin(2\pi n\phi(t))s_{sn}(2\pi N\phi(t))\] to nonlinear and non-stationary data with time-dependent amplitudes, frequencies, waveforms. %The MIMF explains difficulty in concentrating time-frequency representation provides new direction decomposition. multiresolution expansion coefficients $\{a_n\}$, $\{b_n\}$, shape function $\{s_{cn}(t)\}$ $\{s_{sn}(t)\}$ provide innovative features For complex signals that are superposition several MIMFs well-differentiated phase functions $\phi(t)$, recursive scheme based on Gauss-Seidel iteration diffeomorphisms proposed identify these MIMFs, their coefficients, series. Numerical examples from synthetic natural phenomena given demonstrate power this method.