How phase is calculated in linear decomposition

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Mathematical proof



Suppose we have any linearly decomposed (PCA, ICA, etc.) three channel EEG recording into three components (three is to keep the example simple) and identified Comp.2 as a signal we wish to remove (e.g. eye movement). Removing a component changes a channel signal's phase (e.g. that of Fz) in the following way:


The phase difference in channel Fz's signal caused by removing Comp.2 is shown as φ_diff. Note that Comp.1, Comp. 2, and Comp.3 here each represents that component's projection onto channel Fz. This difference in phase is not collateral distortion, but a direct and expected result of removing that component. In other words, this is a due change in phase and nothing surprising.

Empirical demonstration

See this page for the demo.


See this page.

(This page was written by Makoto Miyakoshi, Hirokazu Tanaka, and Luca Pion-Tonachini)