Multiresolution mode decomposition for adaptive time series analysis

This paper proposes the multiresolution mode decomposition (MMD) as a novel model for adaptive time series analysis. The main conceptual innovation is introduction of intrinsic function (MIMF) form∑n=−N/2N/2−1ancos⁡(2πnϕ(t))scn(2πNϕ(t))+∑n=−N/2N/2−1bnsin⁡(2πnϕ(t))ssn(2πNϕ(t)) to nonlinear and non-stationary data with time-dependent amplitudes, frequencies, waveforms. expansion coefficients {an}, {bn}, shape {scn(t)} {ssn(t)} provide innovative features For complex signals that are superposition several MIMFs well-differentiated phase functions ϕ(t), new 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.