QRS Detection Algorithm Using Savitzky-Golay Filter

ACEEE Int. J. on Signal & Image Processing, Vol. 03, No. 01, Jan 2012

QRS Detection Algorithm Using Savitzky-Golay
Filter
Shreya Das 1, Dr. Monisha Chakraborty*, 1
1
Student, School of Bio-Science and Engineering, Jadavpur University, 188, Raja S. C. Mallik Road, Jadavpur, Kolkata,
India
*, 1
Assistant Professor, School of Bio-Science and Engineering, Jadavpur University, 188, Raja S. C. Mallik Road, Jadavpur,
Kolkata, India
{shreyadas.jadavpuruniv@gmail.com, *monishack@school.jdvu.ac.in}

Abstract: QRS part of an electrocardiogram (ECG) is generated by the depolarisation wave which travels through
physiologically important for cardiac disease detection and the interventricular septum via the bundle of His and bundle
extraction of this waveform from the raw signal is an important branches and reaches the ventricular myocardium via the
part of ECG analysis. Pan Tompkins’ algorithm of QRS Purkinje fibre network. The impulse first depolarises the left
detection is an established method for extraction of this part
side of the septum, and then spreads towards the right. The
of ECG. In this paper, a modification has been done on Pan
Tompkins’ algorithm by using a Savitzky-Golay filter in place left ventricle has larger muscle mass and thus its depolarisation
of the high pass filter and differentiator of Pan Tompkins’ dominates the ECG wave. The QRS complex ends at the J
algorithm. Then QRS detection of normal as well as diseased point and from here starts the ST segment. The ST segment
ECG has been done using both Pan Tompkins’ algorithm and which lies between the J point and the onset of the T wave,
the modified algorithm developed in this work for comparison. represents the period between the end of ventricular
Index Terms- electrocardiogram, QRS, Pan Tompkins’ depolarisation and repolarisation. The T wave is the result of
algorithm, Savitzky-Golay filter ventricular repolarisation. This wave in a normal ECG is
asymmetrical as the first part of this wave is more gradual
I. INTRODUCTION than the subsequent part. The QT interval is measured from
the beginning of the QRS complex to the end of the T wave.
Processing and extraction of features from ECG is of Measurement of this interval is done by taking into account
importance for doctors as many physical conditions and the heart rate as this interval elongates as heart rate decreases.
diseases can be detected using this signal as well as for The last part of the ECG is the U wave which is found just
engineers who obtain ECG by different stimuli and subject it after the T wave ends. It is a small deflection and generally
to various algorithms to obtain information. Also in case of upright [1-2].
ECG it is easy to obtain the signal from the human subject as In this paper, the disease that has been taken is known as
it is non-invasive as well as no drugs or radiations are ventricular tachyarrhythmia and the data is obtained from
required. Cardiologists usually use the time-domain ECG PhysioNet. Filtering of the signals has been done on ten data
signals which are recorded on strip-charts to analyze ECG named cu01 to cu10 [11]. The raw data available in Physionet
signals. For diagnosis purposes, the parts of the waveforms were passed through an active second order low-pass Bessel
present in normal ECGs and their corresponding occurrences filter of cut-off frequency 70 Hz before digitization, and were
in the cardiac system are important. digitised at 250 Hz with 12-bit resolution over a 10 V range (10
The ECG wave consists of certain parts named as the P mV nominal relative to the unamplified signals). Each data is
wave, PR interval, QRS complex, ST segment, T wave, QT approximately 8.5 minutes in duration. These data show the
interval and then the infrequent presence of U wave. The presence of sustained ventricular tachycardia, ventricular
sino- atrial node or the SA node is positioned on the left flutter and ventricular fibrillation [11].
atrium and this initiates the electrical signal causing atrial Ventricular fibrillation is a serious condition of the heart
depolarisation. Although the atrium is anatomically divided which may lead to stoppage of the heart if untreated.
into two parts, electrically they function as one part. Precursor of fibrillation is often ventricular tachycardia or
Atria have very little muscle and produce a wave of small flutter. So it is important to detect flutter and tachycardia in
amplitude called the P wave. The PR segment is the subse- the ECG. Ventricular tachycardia is defined as three or more
quent part after the P wave and occurs as the electrical im- ventricular extrasystoles in succession at a rate of more than
pulse is conducted through the atrio-ventricular node or the 120 beats per minute. The tachycardia may be self terminating
AV node, bundle of His and Purkinje fibres. The PR interval but is described as “sustained” if it lasts longer than 30
can be defined as the time between the onset of atrial seconds [2]. This kind of tachycardia falls under broad
depolarisation and the onset of ventricular depolarisation. category tachycardia which maybe of ventricular or
After the PR interval, QRS complex occurs. This complex is supraventricular in origin but is mostly ventricular. In
ventricular tachycardia the sequence of cardiac activation is
*.1
Corresponding author altered, and the impulse no longer follows the normal
© 2012 ACEEE 55
DOI: 01.IJSIP.03.01.550


intraventricular conduction pathway. As a consequence, the The transfer function of the high pass filter is as shown in
morphology of the QRS complex is bizarre, and the duration equation (4).
of the complex is prolonged [2]. The ECG waveform which is Hhp(z)= P(z)/X(z)= z-16 – Hlp(z)/32 (4)
obtained is overshadowed with noise signal due to which It is finally obtained as in equation (5).
essential features cannot be identified from it. There are many Hhp(z)= (-z32 + 32z16 – 32z15 + 1)/(32z32 – 32z31) (5)
algorithms present for denoising an ECG signal and popular The difference equation of the filter is as in equation (6).
among them is the Pan- Tompkins’ algorithm [3,9]. In this p (nT)= x(nT – 16T) – 0.0313[y(nT – T) + x(nT) – x(nT –
algorithm feature extraction is restricted to QRS detection 32T)] (6)
from the original signal by passing the signal through a band The low cut off frequency of the filter is about 5 Hz and delay
pass filter and a differentiator and then squaring of the is 80 ms. The gain of this filter is 1 [9].
resulting signal. The band pass filter is the one which ii) Derivative
eliminates noise and the differentiator is used to provide To provide information about the slope of the QRS
information about the slope of the QRS complex. Squaring of complex, differentiation of the signal is done, after it has been
the signal is done so that all negative values in the waveform through the band pass filter [9]. A five point derivative is
are changed to positive values. This process is a nonlinear implemented using the transfer function as shown in equation
operation which amplifies the output of the differentiator (7).
nonlinearly. Then the signal is passed through a moving H(z)= 0.1(2 + z-1 – z-3 – 2z-4 ) (7)
integrator to obtain the QRS waves [3,9]. The difference equation for this transfer function is as shown
This paper shows an alternative way of QRS detection in equation (8).
from the ECG signal using Savitzky-Golay filter in place of y (nT)= (1/8)*[2x(nT) + x(nT – T) – x( nT – 3T) – 2x(nT –
the band pass filter of the Pan Tompkins’ algorithm. A normal 4T) (8)
as well as a diseased ECG data showing ventricular The fraction 1/8 in equation (8) is an approximation of the actual
tachyarrythmic ECG data are taken and Pan Tompkins’ gain of 0.1. This derivative approximates the ideal derivative in
algorithm using Savitzky-Golay filter is implemented. The the dc through 30 Hz frequency range, and it has a filter delay of
respective QRS detected signals have been obtained from 10 ms [9].
both types of data. iii) Squaring
Now, the signal is to be squared. This is the non linear
II. THEORY processing of the signal. It is done to get all positive values so
that later these values can be processed to get the corresponding
A. Pan Tompkins’ Algorithm
squared waves. Also this processing emphasizes the higher
i) Band pass filter frequencies of the ECG signal which are due to the presence of
The band pass filter that has been used has been done the QRS complexes [9]. Point by point squaring of the signal
by using a low pass filter and then a high pass filter in cascade. obtained from the differentiator is implemented by equation (9).
The purpose low pass filter is to suppress high frequency y ( nT)= [x(nT)]2 (9)
noise [9]. Filter design using digital filters having integer
coefficients allows real time processing speeds. No floating iv) Moving Integrator
point processing required so speed is high. This band pass The slope of the R wave is not the absolute way to detect
filter for QRS detection algorithm reduces noise in the ECG QRS complexes in an ECG. There may be many long duration
signal by matching the spectrum of average QRS complex, and large amplitude QRS waves in the ECG which is abnormal.
eliminating noise due to muscle artefacts, 60 Hz power line Only slope of R wave cannot detect these waves [9]. So a moving
interference, baseline wandering and T wave interference. QRS window integrator is used so that these waves can be detected
energy is maximised by the pass band of approximately in the as well. The difference equation for this moving window
5 to 15 Hz range. The filter is an integer filter which has poles integrator is as shown in equation (10).
located such so as to cancel out the zeroes [9]. The second y(nT)= (1/N) [(x(nT) – (N-1)T) + (x(nT) – (N-2)T) +…+x(nT)]
order low pass filter has the transfer function of as shown in (10)
equation (1). It is important to choose an appropriate value for N, which is the
H(z)= (1- z-6)2/(1- z-1)2 (1) number of samples in the width of the moving window [9].
The cut- off frequency of the filter is 11 Hz, delay is 5 samples B. Savitzky-Golay Filter
and the gain is 36 [9]. The difference equation of the filter is as
Savitzky-Golay filter has been used both for ECG noise
shown in equation (2).
reduction and compression [4-8]. It has been used because of
y (nT)= 2y(nT- T) - y(nT - 2T) + x(nT) – 2x(nT – 6T) + x(nT –
its signal following capabilities by least squares approach [8,10].
12T) (2)
The Savitzky-Golay filter that has been used in this paper is of
The high pass filter is implemented by subtracting a first order zero order and of frame length 41.
low pass filter from an all pass filter with delay [9]. The transfer
function of the low pass filter is as shown in equation (3).
Hlp(z)= Y(z)/X(z)= (1 – z-32)/(1 – z-1) (3)
© 2012 ACEEE 56
DOI: 01.IJSIP.03.01. 550


Fig 2: Block diagram showing QRS detection using Savitzky-Golay filter

IV. RESULTS
III. PROCEDURE
The established Pan Tomkins’ algorithm as shown in Fig. 1
On both the normal and diseased data, Pan Tompkins’
has been applied on normal and ventricular tachyarrythmic ECG
algorithm has been implemented using the conventional
data and the final QRS detected signals obtained are shown in
algorithm and then using Savitzky-Golay filter in place of the
Fig. 3 and Fig. 5 respectively. The results obtained after applying
high pass filter and differentiator. The block diagrams of these
the developed algorithm using Savitzky-Golay filter is shown
two methods are shown in Fig. 1 and Fig.2 respectively.
in Fig. 4 and Fig. 6 for normal and diseased ECG data
respectively. The different blocks of the algorithm have
applied as shown in Fig. 2 and the final QRS detected signals
are obtained.

Fig. 3: Result of the last block of Pan Tompkins’ algorithm for normal ECG data

Fig. 4: Result of the last block of Pan Tompkins’ algorithm for Fig. 5: Result of the last block of Pan Tompkins’ algorithm with
diseased ECG (data cu04) Savitzky-Golay filter for normal ECG data

© 2012 ACEEE 57
DOI: 01.IJSIP.03.01.550


V. CONCLUSION [1] [4] Dotsinsky, G. Mihov, “A simple approach for tremor
suppression in electrocardiograms”, in Int. J. Bioautomation, 2010,
From the results obtained using the developed algorithm, 14(2), 129-138.
it can be observed that QRS detection is possible with higher [5] C.M. Fira, Liviu Goras, “An ECG signals compression method
amplitudes of the detected QRS peaks. This algorithm also and its validation using NNs”, in IEEE Trans. Biomed. Eng. 2008,
eliminates the need of the high pass filter and the differentiator vol.55, no.- 4.
blocks as present in Pan Tompkins’ algorithm. [6] M. Lascu, D. Lascu, “ Electrocardiogram compression and
optimal ECG filtering algorithms”, in WSEAS Transactions on
Computers, Issue 4, Volume 7, April 2008.
REFERENCES [7] K. Pandia, S. Ravindran, R. Cole, G. Kovacs, L. Giovangrandi,
[1] Gary D. Clifford, Francisco Azuaje, Patrick E. McSharry, “ Motion artefact cancellation to obtain heart sounds from a single
Advanced Methods and Tools for ECG Data Analysis. Engg. in chest- worn accelerometer” in IEEE ICASSP 2010.
Medicine & Biology, Boston, London, 2006. [8] S. Hargittai, “ Savitzky-Golay least squares polynomial filters
[2] Francis Morris, June Edhouse, William J. Brady, John Camm, in ECG signal processing” in IEEE, Computers in Cardiology, 2005.
ABC of Clinical Electrocardiography.BMJ Books, London, 2003. [9] W.J. Tompkins, Biomedical Digital Signal Processing.
[3] J. Pan, W.J. Tompkins, “A real-time QRS detection algorithm”, Englewood Cliffs, NJ, Prentice Hall, 1993.
IEEE Trans. Biomed. Eng. 1985, vol.32, pp. 230-236. [10] Sophocles J. Orfanidis, Introduction to Signal Processing.
Prentice Hall, 2010.
[11] www.physionet.org/physiobank/database/cudb/

© 2012 ACEEE 58
DOI: 01.IJSIP.03.01. 550

QRS Detection Algorithm Using Savitzky-Golay Filter

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