Instantaneous envelope and phase extraction from real signals: Theory,implementation, and an application to EEG analysis

This paper presents a unified treatment of various important signal processing techniques for the extraction of the instantaneous envelope and phase of a real signal. These techniques include Complex Demodulation, Hilbert Transformation, In-Phase and In-Quadrature Filtering, Phase-Locked Loop Demodulation, and Peak Amplitude and Zero-Crossing Detection. The salient points in the mathematical theory and implementation of these techniques are outlined, as well as their interrelationships via the theory of analytic signals. The advantages and limitations of each of these techniques are elaborated upon, and Complex Demodulation is shown to be the most effective and flexible method from an implementation point of view. The relation of the above techniques to Fourier spectrum analysis is elucidated, and an example is presented of applying Complex Demodulation for the quantification of time nonstationarities in the electrographic morphology of an EEG waveform.