Modeling the time-varying microstructure of simulated sleep EEG spindles using time-frequency analysis methods

The time-varying microstructure of sleep spindles may have clinical significance and can be quantified and modeled with a number of techniques. In this paper, sleep spindles were regarded as AM-FM signals modeled by six parameters. The instantaneous envelope (IE) and instantaneous frequency (IF) waveforms were estimated using four different methods, namely Hilbert Transform (HT), Complex Demodulation (CD), Wavelet Transform (WT) and Matching Pursuit (MP). The six model parameters were subsequently estimated from the IE and IF waveforms. The average error, taking into account the error for each model parameter, was lowest for HT, higher but still less than 10% for CD and MP, and highest (greater than 10%) for WT, for three different spindle model examples. The amount of distortion induced by the use of a given method is also important; distortion was the greatest (0.4 sec) in the case of HT. Therefore, in the case of real spindles, one could utilize CD and MP and, if the spindle duration is more than 1 sec, HT as well.