Thesis - Instituto de Telecomunicações

88 CHAPTER 4. SIGNAL PROCESSING AND FEATURE EXTRACTION(a) Normalizing an ECG signal.By producing the amplitude histogram of a completeacquisition of ECG signals, the R wave is clearly visible as being the top area of thehistogram with considerable mass density. In figure 4.13 we show an example of an ECGsignal we acquired, where some noise is visible (left). In the middle we see the histogram ofthe signal, where the influence of the noise is limited. On the right the inverted cumulativesum is depicted; the point detected as the R wave mean amplitude is marked with a circle.To compute the R wave reference amplitude for each user, we use the histogram of thesignal to create an algorithm with some immunity to noise. We define the vector c as theamplitude histogram of the input ECG signal, e, such that c(a) is the histogram value foramplitude a.∑ t=nst=t iWe use an inverted cumulative sum of the ECG signal histogram, defined as icumsum(t i )=c(t), and search for the first point in the vector higher than a threshold (β). Thecorresponding amplitude at this point is defined as R ref , the R wave reference amplitude.This threshold β was easily tuned for all users, so that the detection algorithm correctlyidentifies most of the R waves of the collected data.Figure 4.13: Histogram of a noisy ECG signal. On the left the ECG signal. In the middlethe filled black area presents the histogram. A dashed line represents the histogram scaled10 times. On the right the solid line represents the inverted cumulative sum and a scaledversion to identify the point where the R reference wave is detected (marked with a circle).We assume that noise exists in only a fraction of the entire data collection so that when