| The electrocardiogram (ECG) is used as a means to detect various cardiac abnormalities for diagnostic and prognostic purposes. This thesis explores the statistical and mathematical characteristics of the electrocardiogram, and consequently generates new approaches that would improve the effectiveness of the use of the ECG.; We commence by doing an extensive survey of the abnormal rhythms detection and classification techniques. We divide these techniques into different classes and describe each technique in some detail followed by our own critique.; We next look at the issue of QRS template generation. We show that the sequence of points in the ECG that are one period apart are practically normally distributed and white. Also, we show that the random amplitude modulations between one depolarization and another are also white. Consequently, the sample average may be used to generate a QRS template. But as the sample average gives the same weight to new data as old data, we look for a new method that would allow template updating based on giving more weight to the newer depolarizations. Our analysis leads us to conclude that exponential smoothing is the practical method to update the template. With appropriate choice of the gain factor one finds that exponential smoothing generates a template with lower variance than that produced by the sample average; moreover the gain factor is constant which makes it ideal for use in pacemakers.; Next we present our model of the ECG and prove that this model is cyclostationary by showing that it is periodic both in the mean and in the autocorrelation function. We then investigate the validity of this model on real ECG data.; Next we investigate the rhythmic variation of the ECG. We review the classical hypothesis of Integral Pulse Frequency Modulation (IPFM), in addition to other techniques. Afterwards, we propose our novel approach to the modeling and analysis of the RR interval based on the cyclostationarity of the point process representing the depolarizations arrival times. We derive a closed-form solution to the mean and autocorrelation function of this point process and show that they are periodic. We validate our theoretical results on ECG data of 20 patients. We plot the spectral correlation matrix contours and show that differences occur between one group of patients and another.; Next we look at the spectral correlation of the ECG, which includes both the morphological and timing information. We derive the spectral correlation matrix of the ECG and analyze the influence of morphology.; The major contributions of this thesis are related to (1) template updating, (2) modeling of the ECG that captures its periodic characteristics, (3) a closed-form solution to many of the ECG model properties, and (4) the use of spectral correlation of the ECG as a predictive and non-invasive tool in some cardiac illnesses. |
