Short-time Variational Mode Decomposition

TL;DR

STVMD is a novel signal decomposition method that uses short-time Fourier transforms within a variational framework to better handle non-stationary signals by segmenting and analyzing signals in short time windows.

Contribution

This paper introduces STVMD, extending VMD with STFT to improve decomposition of non-stationary signals through a new variational optimization approach.

Findings

Non-dynamic STVMD performs comparably to VMD with optimal window size.

Dynamic STVMD effectively tracks non-stationary central frequencies.

Reduced mode function errors in non-stationary signal analysis.

Abstract

Variational mode decomposition (VMD) and its extensions like Multivariate VMD (MVMD) decompose signals into ensembles of band-limited modes with narrow central frequencies. These methods utilize Fourier transformations to shift signals between time and frequency domains. However, since Fourier transformations span the entire time-domain signal, they are suboptimal for non-stationary time series. We introduce Short-Time Variational Mode Decomposition (STVMD), an innovative extension of the VMD algorithm that incorporates the Short-Time Fourier transform (STFT) to minimize the impact of local disturbances. STVMD segments signals into short time windows, converting these segments into the frequency domain. It then formulates a variational optimization problem to extract band-limited modes representing the windowed data. The optimization aims to minimize the sum of the bandwidths of these modes across the windowed data, extending the cost functions used in VMD and MVMD. Solutions are derived using the alternating direction method of multipliers, ensuring the extraction of modes with narrow bandwidths. STVMD is divided into dynamic and non-dynamic types, depending on whether the central frequencies vary with time. Our experiments show that non-dynamic STVMD is comparable to VMD with properly sized time windows, while dynamic STVMD better accommodates non-stationary signals, evidenced by reduced mode function errors and tracking of dynamic central frequencies. This effectiveness is validated by steady-state visual-evoked potentials in electroencephalogram signals.