Improved procedure of complex demodulation and an application to frequency analysis of sleep spindles in EEG

Complex demodulation is a local version of harmonic analysis that enables the amplitude and phase of particular frequency components of a time series to be described as functions of time. The paper presents a computational procedure involving complex demodulation with interpolation of data in the frequency domain. A computational procedure comprising repeated use of complex demodulation is also presented. This is used to estimate the optimum choice of the demodulating frequency which considerably influences the measurement of the instantaneous amplitude and phase of the underlying process. The usefulness of this procedure is verified by computer simulation. An example of applying this procedure to the estimation of the centre and the instantaneous frequencies of sleep spindles in the EEG (electroencephalogram) is presented. By using the procedure developed here, several partially overlapping sleep spindles are detected and correctly separated. The paper also presents an approach to separating and analysing transient time series (such as overlapping sleep spindles) by using an accurate frequency processing technique.