ECG NOISE MODELLING IN TIME-FREQUENCY DOMAIN USING THE POLYNOMIAL EXTRAPOLATION A. Izworski, P. Augustyniak University of Mining and Metallurgy, Institute of Automatics, Kraków, Poland Abstract: The paper presents a new ECG-dedicated noise removal technique. The proposed algorithm makes use of the local bandwidth variability of car- diac electrical representation. Background activities of any origin (muscle, mains interference etc.) are measured in specified regions of the time-frequency plane. Outside of these regions, where normally the cardiac representation components are expected, we use the square polynomial extrapolation to estimate the noise level. The partially measured and partially calculated time-frequency representation of the noise is arithmetically subtracted from the noisy signal and the inverse time-frequency transform yields noise-free cardiac representation. The algorithm was tested with use of the CSE Database records with the addition of the MIT-BIH Database noise patterns. Keywords: electrocardiography, noise removal tech- niques, time-frequency domain Introduction The noise removal is a very important issue for the biomedical signals recording techniques. The primary reason is the unstable recording environment (unwanted signals, poor electrodes, electromagnetic pollution etc.). The second reason is the high importance of these sig- nals for the final diagnosis and treatment of the patient including life-critical circumstances. And the systemati- cally growing importance of the home care in the ageing population, results in technical aspect in moving the typical recording out of the hospital to the unknown and unstable environment. For that reason the traditional approach to the signal de-noising needs to be revised. Usually two principal sources of ECG noise can be distinguished: the "technical" caused by the physical parameters of the recording equipment and the "physio- logical" representing the bioelectrical activity of the cells not belonging to the area of diagnostic interest (called also background activity) [1]. Both sources issue signals of random occurrence overlapping the ECG signal in the time domain and in the frequency domain. Both of them are difficult to eliminate when recorded with the signal, and thanks to the expected gaussian distribution of the noise, averaging technique is usually applied when appropriate [2]. This technique is perfect for the event-triggered potentials (like VEP) thanks to the assumed correlation of two adjacent responses but, unfortunately, it is not applicable when a reliable syn- chronisation point may not be determined. This is the case of noisy electrocardiogram. Traditional de-noising techniques base on the as- sumption that any signal component may occur at any time [3]. Because of the unknown origin of the noise we have to consider it in this way. The electrical cardiac representation, however, is in some way predictable and the local bandwidth varies with the signal contents [4]. The discrete representation contains both of these com- ponents, and fortunately for some time periods (e.g. baseline) above a given frequency the cardiac compo- nents are not expected and thus the noise level can be reliably measured. For the remaining part of the signal it has to be extrapolated from the measured values. Materials and Methods The linearity of the time-frequency domain signals representation motivated us to design, implement and test the algorithm that not only estimates the ECG noise in a quasi-continuous way, but also removes it from the signal. The de-noising algorithm begins with the detec- tion of the P, QRS and T waves with use of a subroutine designed for an interpretative ECG recorder. Next, the segmented signal is transformed to the time-frequency domain by the lifting wavelet transform (LWT) [5] that maps integer signal representation into integer t-f coef- ficients. The time-frequency plane is split into two parts by the standard function of the local bandwidth fitted to the current borders of the waves (fig. 1). Fig. 1 Estimating the ECG local bandwidth with ref- erence to the borders of P, QRS and T waves. The measurement of the noise level is performed for all the t-f atoms belonging to the upper, "signal-free" part of the time-frequency plane. The polynomial ex- trapolation bases on the results of this measurement and