The electrocardiogram signal is considered very important in clinical practice in order to assess the cardiac status of patients. In this paper, a computer aided detection system for R peak localizations is indicated. A four stage architecture is implemented which is able to differentiate R waves from peaked T and P waves with an high degree of accuracy. The performance of the algorithm is tested using ECG waveform records from the MIT-BITH Arrhythmia database. A sensitivity of 96 % and a positive prediction of 99% are achieved.
Signal processing technique has a large number of uses in medical environments
where it is a difficult task the differentiation between real pathological signs and false
alarms because of noise and imperfect signals [
In this paper an improved signal processing technique able to detect R peaks in ECG
signals for heart rate evaluation, is presented. Its variability is linked to various
disorders such as obstructive sleep apnea syndrome, congestive heart failure [
ECG signal is the representation of the heart muscle electrical activity over time. It supplies physicians with useful information and represents an important part of the cardiac patient assessment.
A single normal cycle of ECG represents successive atrial depolarization/repolarization
and ventricular depolarization/repolarization which occur in every heartbeat. In fig.1
an example of the ECG shape is indicated [
The P wave is the first upward pulse of the ECG signal and is generated when the atria contract to pump blood into the ventricles. The PR interval, which is a short period where no electrical activity is seen, is due to a physiological delay; in fact the atrioventricular node slows the electrical depolarization before it proceeds to ventricles. The successive pulse, the QRS complex, is formed when ventricles contract to pump out blood. The next S-T segment represents the early stage of ventricular repolarization and under normal conditions is isoelectric (constant potential). A marked displacement of the S-T segment signifies coronary artery disease. The ventricular repolarization forms the T wave and the cardiac muscle is prepared for the next cycle of the ECG. Therefore, the Q-T interval reflects the total duration of ventricular systole. A long QT interval can be associated with heart failure, ischaemic heart disease, bradycardia, some electrolyte disorders (i.e. hypocalcaemia) and can be consequence of different drugs taking. 3
3.1 Hilbert transform
The Hilbert transform xH(t) of a real function x(t) is defined as [
+∞ ∫−∞ ( ) 1 − Therefore, xH(t) is both a time dependent function and a linear function of x(t). In fact, it is obtained from x(t) applying the convolution with (t)-1. Equation (1) shows that xH(t) is obtained by filtering the signal x(t) through a linear time-invariant filter with impulse response equal to (t)-1. Because of the integrand has a singularity and the limits of integration are finite, the Hilbert transform is properly defined as the Cauchy principal value of the integral in (1), whenever this value exists.
Considering the frequency domain and applying the Fourier transform it results: { ( )} = − { ( )} where +1 −1 > 0 = 0 < 0
3.2 Wavelet transform Therefore, the Hilbert transform shifts all positive frequency components by -90° and all negative frequency components by +90° while the amplitude of F[x(t)] remains constant. Thus it is found that: x(t) and xH(t) are orthogonal and xH(t) represents the harmonic conjugate of x(t). The function x(t) and its transform xH(t) are related to each other and they together create an analytic signal that is expressed as: ( ) = ( ) + ( ) B(t)
x2 (t) xH2 (t)
It is evident that B(t) and x(t) have common tangents and the same values in the points
where xH(t) is zero. Therefore, B(t) have the same slope and magnitude of x(t) at its
Wavelet transform is a suitable tool for studying non-stationary signals. In fact, both
the property of time-frequency localization (which allows us to obtain a signal at a
particular time and frequency or to extract features at various locations in space) and
the multirate filtering option (which permits the differentiation of signals with different
(2)
(3)
(4)
frequencies) make the wavelet transform an effective tool in signal processing analysis.
It decomposes the signal into several components with various scales or resolutions.
Therefore, it can identify useful information for R point detection and discard signal
bands which provide scant contribution to the study [
Since wavelet functions are compact, wavelet coefficients only measure the variations
around a small region of data array. This feature makes wavelet analysis particularly
useful for signal processing; the "localized" nature of the wavelet transform allows us
to pick out features in analyzed data with ease such as spikes (i.e. noise or
discontinuities), discrete objects, edges of objects, and so forth. Moreover, wavelet coefficients at
one location are not affected by coefficients at other locations in data under study. As
the aim of this paper is the implementation of a fast algorithm, a non-redundant wavelet
decomposition has been chosen. Moreover, as the temporal ECG shape is an important
parameter, the wavelet to be adopted should be a symmetrical function to avoid the
introduction of non-linear phase shift.
3.3 Block Diagram
The proposed system is composed of four stages (fig.2).
The first stage is the pre-processing phase in which the ECG signal is derived. This is
done for preparing the signal for Hilbert envelope computation. The second stage
performs the Hilbert transform envelope of the first derivative of ECG waveform. This
envelope represents an enhancement of the signal that can be used for the peak detection
[
For the performance evaluation of the method, sensitivity and positive prediction are taken into account. The Sensitivity (Se) is defined as the probability of detecting a R point when a R point exists really; the positive prediction (+P) represents the probability of detecting a R point among the detected ECG peaks. They are computed adopting the following expressions:
Sensitivity: = (5)
+ Positive Prediction: + =
+ (6) where
TP (the number of true positives) is the number of correct identifications of R points present in the signal under test; - FN (the number of false negatives) is the number of R points present in the signal that the algorithm is not able to detect; - FP (the number of false positive) is the number of R points detected by the algorithm but actually in the signal.
The proposed algorithm is tested on the ECG signals taken from the first channel of
the MIT-BIH arrhythmia database [
In fig.6 are shown the system performance related to the threshold value adopted in the last stage. The threshold value is a percentage of the peak maximum value in the dyadic scales.
30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80% 85%
Threshold value
The algorithm gives Se and +P parameters of about 96% and 99% for a threshold value in the range [45% ÷ 70%] of R* denoting with R* the R point average value in the related dyadic scales.
% 100 90 80 70 60 50 40 30
Sensitivity Positive Predictivity
Real time ECG signal processing is an important diagnostic procedure for the monitoring of heart functional status. The proposed CADe system, makes the localization of R peaks possible even if noisy signals and peaked T and P waves are present. The Hilbert transform envelope and a multiscale analysis is performed for ECG enhancement and R points localization. The parallel behavior of the implemented method optimizes the procedure computational time and makes it suitable for a hardware implementation.