Abstract
We consider the problem of estimating time-localized cross-dependence in a collection of nonstationary signals. To this end, we develop the multivariate locally stationary wavelet framework, which provides a time-scale decomposition of the signals and, thus, naturally captures the time-evolving scale-specific cross-dependence between components of the signals. Under the proposed model, we rigorously define and estimate two forms of cross-dependence measures: wavelet coherence and wavelet partial coherence. These dependence measures differ in a subtle but important way. The former is a broad measure of dependence, which may include indirect associations, i.e., dependence between a pair of signals that is driven by another signal. Conversely, wavelet partial coherence measures direct linear association between a pair of signals, i.e., it removes the linear effect of other observed signals. Our time-scale wavelet partial coherence estimation scheme thus provides a mechanism for identifying hidden dynamic relationships within a network of nonstationary signals, as we demonstrate on electroencephalograms recorded in a visual-motor experiment.
Original language | English (US) |
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Article number | 6868283 |
Pages (from-to) | 5240-5250 |
Number of pages | 11 |
Journal | IEEE Transactions on Signal Processing |
Volume | 62 |
Issue number | 20 |
DOIs | |
State | Published - Oct 15 2014 |
Externally published | Yes |
Keywords
- Coherence
- local stationarity
- multivariate signals
- partial coherence
- wavelets
ASJC Scopus subject areas
- Signal Processing
- Electrical and Electronic Engineering