Using HOS for characterization of periodical and time-varying waveform

We applied an approach based on high order statistics (HOS) to classification of time series. This is different from most of the prior analyses in which signal features have been compared. In our approach, we investigate an input signal deformed non-linearly in time and contaminated with additional different forms of noise, e.g. Gaussian, non-Gaussian and their mixed form. The bispectrum-averaging technique (third order statistics) which preserves information about both amplitude and phase of the Fourier transform is studied for the reconstruction of the predictable waveform. The technique does require neither an initial estimate nor a peak-to-peak synchronization of the realizations. Thus, the normal waveform is considered ideally to be smooth and entirely predictable. The residual is characterized by subtracting the predictable part from the original waveform. Under non-linearity assumption, we propose that the Volterra process tool is suitable for analysis and differentiation between the patterns contained in the time series residual. We present and classify some results of the output of the linear transfer function of the process. The approach is numerically tested with the use of computer-generated data. Its effectiveness in dealing with electrocardiogram (ECG)-related data is also demonstrated.