IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 51, NO. 7, JULY 2004 1129 Projective Filtering of Time-Aligned ECG Beats Marian Kotas Abstract—A method of electrocardiographic (ECG) signal processing developed by introduction of time synchronization into the method of nonlinear state-space projections is presented. It can be regarded as an extension of time averaging but contrary to usual averaging it preserves variability of ECG beats morphology. For this purpose, after the respective beats time alignment, the synchronized intervals of the signal undergo processing according to the rules of principal component analysis (PCA). PCA allows for determination of orthogonal basis functions which can be employed for approximation of the respective intervals. The oper- ation is aimed to retain the deviations from the mean which result from the desired component changes and to reject the deviations caused by noise. The method’s capabilities are investigated and some of its applications are presented. Index Terms—Principal component analysis (PCA), state–space projections, time averaging, time alignment. I. INTRODUCTION T HE ELECTROCARDIOGRAPHIC (ECG) signal, repre- senting the electrical activity of the heart, is usually con- taminated by noise of various origin. The predominant types of noise are baseline wander, powerline interference (50 or 60 Hz), electromyographic (emg) noise and electrode motion artifacts. Among them emg and motion artifacts are the most difficult to be suppressed. It stems from the fact that their frequency spec- trum overlaps the spectrum of the desired ECG signal, which makes classical linear bandpass filters ineffective [1]. Several signal-processing tools have been developed for ECG noise suppression without disturbing the desired signal frequency contents. Most of them assumes that the ECG signal is repeatable and that the noise is additive, independent and of zero mean. One of the classical methods is time averaging. It performs time alignment [2] of ECG beats and calculation of an average one. As a result the independent noise is suppressed and the SNR is raised. However, variability of ECG morphology gets suppressed as well. The problem of ECG morphology tracking has been touched on in the works [3], [4] describing application of adaptive triggered filtering to ECG enhance- ment. Since the specific variations of ECG morphology are of diagnostic value [5] the ECG enhancing techniques important feature is the ability to preserve the shapes of individual cardiac beats. The simplest way to raise the averaging techniques ability to follow fast changes of the signal is to decrease the number of beats averaged. This, however, limits the techniques performance [4], [6] (the estimated SNR increase). Similar are Manuscript received April 14, 2003; revised September 23, 2003. The author is with the Division of Biomedical Electronics, Institute of Elec- tronics, Silesian University of Technology, 44-101 Gliwice, Poland (e-mail: mk@boss.iele.polsl.gliwice.pl). Digital Object Identifier 10.1109/TBME.2004.826592 the effects of adaptive filters tuning aimed at raising the speed of adaptation [3], [4]. Variability of ECG beats morphology is particularly incon- venient if the signal is processed in order to suppress the dom- inating repetitive component for the purpose of other compo- nents extraction. Such problem is encountered e.g., in noninva- sive recording of the fetal ECG [7], [8], in atrial fibrillation (AF) analysis [9], or in the analysis of other biosignals contaminated by the undesired ECG [10]. Inability to enhance the dominating component and at the same time to preserve its morphological variability results in difficulties with its suppression. An important cause of ECG morphology changes is patients’ respiration. This activity influences the thorax geometry and the direction of a heart vector [5], [9], and eventually the projection of the heart vector on leads’ vectors. The resulting morpholog- ical variability limits the precision of time alignment and can spoil the effects of averaging. In the case of multilead recordings it is possible to compensate the changes caused by respiration by means of spatial rotation and scaling [5]. The method helps to raise the precision of time alignment and eventually improves results of averaging. Unfortunately, one cannot apply spatial transformations in the case of one-lead signals. Moreover, this technique fails to compensate other morphological variations such as or wave shifts. When some conditions are satisfied all the mentioned types of variability can be preserved by the method of nonlinear state-space projections (NSSP), which was developed for nonlinear deterministic systems analysis [11], and successfully applied to ECG noise reduction [12] and fetal ECG extraction [7]. This method, however, is computationally extremely expen- sive and successful when applied to processing the signals with moderate level of noise only. The goal of this work is to adopt the rules of NSSP in order to develop a method which would be computationally less costly. Our approach allows for effective suppression of the ECG noise and it preserves variability of the desired component. The rest of this paper is organized as follows. Section II describes the basic rules of NSSP as well as the details of a new method developed. In Section III, different factors influence on the method’s performance is investigated and the method’s comparison to some classical techniques is provided. Sec- tion IV presents the method’s applications. Finally, conclusions are drawn in Section V. II. METHODS A. State-Space Projections for ECG Noise Reduction There has for several years been discernible increase of in- terests in applications of nonlinear dynamics methods to pro- cessing and analyzing of real world signals [7], [12]. Although 0018-9294/04$20.00 © 2004 IEEE