On stochastic representation of residual time series from observed respiratory movements

This paper proposes a stochastic process of the autoregressive moving average (ARMA) type for the parametric representation of time series derived from abdominal or ribcage excursion signals measured by noninvasive respiratory inductance plethysmography (RIP). The RIP output signal is preprocessed by a linear phase bandpass filter, using the least-squares method, based on prior knowledge of the spectrum of infants quiet respiration signals. The residual signal, obtained by subtracting the output of the bandpass filter from that of the RIP, is transformed into a new series that exhibits no apparent deviations from weak stationarity and has a rapidly decreasing sample autocorrelation function. Hence we attempt to approximate the resulting series with a stationary process and to address the related order selection and parameter estimation problems. We illustrate how such a stochastic representation of the residual time series could prove useful in the automated analysis of respiratory or other biomedical signals measured by noninvasive transducers. In particular, this approach could provide a basis for the automated segmentation, which is currently done visually, of long records of respiratory signals into quiet breathing and awakening periods, the latter being mainly corrupted by movement artifacts