The dynamical model

where , , and is the angular velocity of the trajectory as it moves around the limit cycle. Baseline wander was introduced by coupling the baseline value in (1) to the respiratory frequency using

where mV. These equations of motion given by (1) were integrated numerically using a fourth order Runge-Kutta method [15] with a fixed time step where is the sampling frequency. Visual analysis of a section of typical ECG from a normal subject was used to suggest suitable times (and therefore angles ) and values of and for the PQRST points. The times and angles are specified relative to the position of the R-peak as shown in Table I. A trajectory generated by equation (1) in three-dimensions corresponding to is illustrated in Fig. 2. This demonstrates how the positions of the events act on the trajectory in the -direction as it precesses around the unit circle in the -plane. The variable from the three-dimensional system (1) yields a synthetic ECG with realistic PQRST morphology (Fig. 3). The similarity between the synthetic ECG and the real ECG may be seen by comparing Fig. 3 with Fig. 1. Note that noise has not been added to the model at this point.

Index (i) | P | Q | R | S | T |

Time (secs) | -0.2 | -0.05 | 0 | 0.05 | 0.3 |

(radians) | 0 | ||||

1.2 | -5.0 | 30.0 | -7.5 | 0.75 | |

0.25 | 0.1 | 0.1 | 0.1 | 0.4 |

with means and standard deviations . Power in the LF and HF bands are given by and respectively whereas the variance equals the total area , yielding an LF/HF ratio of . Fig. 4 shows the power spectrum given by , , , and . The Gaussian frequency distribution is motivated by the typical power spectrum of a real RR tachogram [7]. A RR-interval time series with power spectrum is generated by taking the inverse Fourier transform of a sequence of complex numbers with amplitudes and phases which are randomly distributed between 0 and . By multiplying this time series by an appropriate scaling constant and adding an offset value, the resulting time series can be given any required mean and standard deviation. Suppose that represents the time series generated by the RR-process with power spectrum . The time-dependent angular velocity of motion around the limit cycle is then given by

(4) |