A novel method to represent ECG signals via predefined personalized signature and envelope functions

In this paper, a new method to model ECG signals by means of "Predefined Personalized Signature and Envelope Functions" is presented. ECG signals are somewhat unique to a person. Moreover, it presents quasi-stationary behavior. Therefore in this work, on a frame basis, personal ECG signals X_i(t) is modeled by the form of X_i(t)≈C_iφ_i(t) α_i(t). In this model, φ_i(t) is defined as the Personalized Signature Function (PSF); α_i(t) is referred to as Personalized Envelope Function (PEF) and C_i is called the Frame-Scaling Coefficient (FSC). It has been demonstrated that for each person, the sets Φ={φ_k(t)} and A={α_r(t)} constitute a "Predefined Personalized Functional Bases or Banks (PPFB)" to describe any measured ECG signal. Almost optimum forms of (PPFB), namely {α_r(t)}, {φ_k(t)} pairs are generated in the Least Mean Square (LMS) sense. Thus, ECG signal for each frame is described in terms of the two indices "R" and "K" of PPFB and the frame-scaling coefficient Ci. It has been shown that the new method of modeling provides significant data compression. Furthermore, once PPFB are stored on each communication node, transmission of ECG signals reduces to the transmission of indexes "R" and "K" of [α_r(t), φ_k(t)] pairs and the coefficients C_i, which also result in considerable saving in the transmission band.