Analysis of ECG from pole-zero models

Abstract

A complete solution to the fundamental problem of ECG analysis, viz., delineation of the signal into its component waves, is proposed from a system theoretic point of view. The discrete cosine transform of a bell shaped biphasic function is approximated mathematically by a system function with two poles and two zeros, i.e., of order (2, 2). Using this concept as the basis, a pole-zero model of suitable order is derived from the discrete cosine transform (DCT) of the given signal using Steiglitz-McBride method. This model is expanded into a unique set of partial fractions each of order (2, 2), and a biphasic function is recovered from each one of these fractions in the inverse process. Each of the P and T waves usually requires only one biphasic function, while the QRS complex needs two or at most three such fractions. A one-to-one relationship between the pole pattern in the z-plane and component wave pattern in the time signal is established. Results of analysis of continuous strips of ECG show that the delineated component waves are in excellent agreement with the original waves both qualitatively and quantitatively. The method is robust for the analysis of signals with artifacts of various kinds, independent of the sampling rate used, and is free from ad hoc back and forth search procedures.