Time Dependence A Oscillatory Waveforms

Voltage traces of EEG signals recorded from each electrode pair oscillate with mixtures of component waveforms. Each component may be defined in terms of three parameters: its amplitude (Anm), frequency (fm), and phase (fnm). The subscript n denotes the frequency component and the subscript m indicates the electrode pair. The electrical power associated with each frequency component is proportional to the square of the corresponding amplitude. One may express any physical waveform as a sum of components with different frequencies, amplitudes, and phases called a Fourier series. Fourier series are analogous to expressions of music or other sounds as compositions of tones or of white light composed of many colors. The EEG voltage Vm(t) recorded from any electrode pair m may be expressed generally as a sum over frequency components:

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