How phase is calculated in linear decomposition

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.

Comments

See this page.

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