A New Approach to the Generalized Transfer Function and Its Application to Biomedical Signal Analysis

Abstract

In this paper, we present a method for modeling an electrocardiogram (ECG) signal using time-varying parameters by considering that the signal is generated by a linear, time-varying (LTV) system with a stationary white noise input, and then by estimating the time-varying coefficients of the LTV system. In effect, since the ECG signal is considered to be non-stationary, this method is based on the Wold-Cramer representation of a non-stationary signal. The relationship between the generalized transfer function of an LTV system and the time-varying coefficients of the difference equation of a discrete-time system is not addressed clearly in the literature; in this paper, we propose a new approach to this problem and apply it for modeling a human ECG signal. We first derive a relationship between the system generalized transfer function and the time-varying parameters of the system. Then we develop an algorithm to solve for the system time-varying parameters from the time-frequency kernel of the system output using the time-varying autocorrelation function (TVACF) and by modifying the modified least-square (MLS) and Durbin's approximation algorithms. A comparison between the proposed algorithm and the recursive least-square (RLS) and RLS lattice (RLSL) algorithms is considered. Computer simulations illustrating the effectiveness of our algorithm are presented when the signal is embedded in noise.