On a Novel Model for ECG Signals and its Statistical Properties

Abstract

An accurate mathematical ECG model helps comprehend the heart’s workings, which in turn helps identify various heart-related abnormalities. A typical ECG waveform consists of recurrent QRS complexes at almost regular intervals. In the most general scenario, the amplitude, the period after which it repeats, and the shape of the QRS complex may change from pulse to pulse. This paper proposes a mathematical model for the ECG signals capable of capturing these features. Since statistical analysis of the the general model is more complex, we make certain assumptions to make the problem analytically tractable. With these assumptions at our disposal, we provide closed-form expressions for time-varying covariance/spectra of the process generated by the proposed model. In order to demonstrate the approximation capability of the model, that is, the ability to model ECG signals, we synthesize ECG signals for different health states by first extracting the QRS complex of that health state and using the mean time period also extracted from the realization of the same health state. We find that the degree of non-stationarity of the real-world ECG and the one generated by the model match closely. In reality, the signal for each state appears to be a close match. Based on our experimental findings, we observe that the measure of the degree of non-stationarity interestingly falls in different ranges, depending upon the type of heart-related abnormality. This observation makes our conjecture that this measure can serve as a biomarker for various related abnormalities.

Keywords

• Electrocardiogram
• almost-cyclostationary
• time-varying covariance
• time-varying spectrum