FEATURE EXTRACTION OF ECG SIGNALS BY PCA

A PROJECT REPORT

Submitted by

G. POOJITHA

B. VENKATA RAVINDRA

Under the guidance of

Dr. M. PRADEEPA

in partial fulfillment for the award of the degree

of

BACHELOR OF TECHNOLOGY
in

ELECTRONICS & COMMUNICATION ENGINEERING

NOVEMBER 2018
 BONAFIDE CERTIFICATE

Certified that this minor project report titled “FEATURE EXTRACTION OF ECG
SIGNALS BY PRINCIPLE COMPONENT ANALYSIS” is the bonafide work of
“G. POOJITHA (15UEEC0043), B. VENKATA RAVINDRA (15UEEC0016)” who
carried out the project work under my supervision.

SUPERVISOR HEAD OF THE DEPARTMENT

Dr. M. Pradeepa Dr. G. VAIRAVEL
Associate professor Associate professor
Department of ECE Department of ECE

Submitted for the minor project work viva-voce examination held on ........................

INTERNAL EXAMINER EXTERNAL EXAMINER

i
 ACKNOWLEGEMENT

We express our deepest gratitude to our respected Founder President And Chancellor
Col.Prof.Dr.R.RANGARAJAN, Foundress President Dr.R.SAGUNTHALA
RANGARAJAN, chairperson managing trustee and vice president.

We are very thankful to our beloved chancellor Prof. BEELA SATYANARAYANA

for providing us with an environment to complete our Minor project successfully.

We are very much grateful to our beloved Vice Chancellor Dr.V. RAMACHANDRAN
for providing us with an environment to complete our Minor project successfully.

We thankful to our esteemed director academics Dr. ANNE KOTESWARA RAO. For
providing a wonderful environment to complete our Minor project successfully.

We extremely thankful and pay my gratitude to our dean Dr. JAYASANKAR for his
valuable guidance and support on completion of this Minor project in this presently.

We record indebtedness to or head of the department Dr.G. VAIRAVEL, for immense

care and encouragement towards us throughout the course of the Minor project

ii
 ABSTRACT

The electrocardiogram (ECG) is widely used in medicine to monitor small electrical

changes on the skin of a patient’s body arising from the activities of human heart. It
shows the plot of the bio-potential generated by the activity of the heart and is used by
the doctors to predict and treat various vascular diseases. QRS detection is the main step
in ECG signal processing. The parameters concerned with QRS detection are sensitivity,
accuracy, positive prediction and detection error. There are so many methods used to
detect the QRS complex in ECG signals such as Wavelet transform based QRS detection,
derivative based QRS detection and Pan Tompkins algorithm. In this project we are
going extract the ECG signals by using Pan Tomkins algorithm. Firstly, the signal is
filtered by using a band pass filter which is cascaded by a low pass and high pass filters
and later the signal is differentiated. After that, moving average filter is applied to the
signal for QRS detection. The performance of the proposed algorithm has been
essentially evaluated by the two parameters Sensitivity(Se) and positive
predicitivity(+P). Lastly, Feature Extraction is done by using Principal Component
Analysis (PCA).

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 TABLE OF CONTENT
CHAPTER TITLE PAGE NO
NO
ABSTRACT iii
LIST OF TABLES vi
LIST OF FIGURES vii
1. INTRODUCTION 1
1.1 Introduction 1
1.2 Basics of ECG 2
1.2.1 Importance of ECG 2
1.2.2 Problems identified by ECG 2
1.2.3 ECG waveform 2
1.2.4 Noise present in ECG signal 6
1.2.5 Arrhythmia 7
1.2.6 Types of Arrhythmia 8
2 LITERTURE REVIEW 10
2.1 Development history of Feature extraction 10
3 SOFTWARE AND DATABASE 11
DESCRIPTION
3.1 MATLAB 12
3.1.1 Math Graphics Programming 12
3.1.2 Scale Integrate Deploy 12
3.2 MIT-BIH Arrhythmia database 13
4 PRINCIPAL COMPONENT ANALYSIS 15
4.1 Principal Component Analysis 15
4.1.1 Introduction 15
4.1.2 Objectives of principal component analysis 16

iv
 4.1.3 Assumptions of PCA 16
4.2 Significance of PCA 17
4.3 Applications of PCA 17
4.4 Advantages and Disadvantages of PCA 18
4.4.1 Advantages 18
4.4.2 Disadvantages 18
5 METHODOLOGY 19
5.1 Major steps in the analysis of the ECG 19
signals
5.1.1 ECG Preprocessing 20
5.2 QRS Detection 20
5.2.1 QRS Detection Algorithm 21
5.2.2 Noise elimination from ECG signals 22
5.2.2.1 Band Pass Integer Filter 22
5.2.3 Derivative 24
5.2.4 Squaring 25
5.2.5 Moving Window Integral 25
5.2 Algorithm of PCA 26
6 Results and Discussion 28
7 Conclusion 31
References 32

v
 LIST OF TABLES
Table Title Page no
No
1.1 Intervals of Normal heart beat 5
6.1 Performance of Pan-Tompkins method on MIT-BIH 29
arrhythmia database

vi
 LIST OF FIGURES

Figure Title Page No

no
1.1 ECG waveform 3
1.2 Types of QRS complex 4
1.3 Noise of ECG signals 7
3.1 MATLAB Layout 13
3.2 MIT-BIH Arrhythmia database 14
3.3 Database record 14
4.1 Principal components 15
4.2 Plot of data showing regression line and orthogonal line 16
5.1 Block Diagram of ECG analysis 19
5.2 Filter stages of QRS detector 21
5.3 Noise removal of the signal by passing through LPF 23
5.4 Noise removal of the signal by passing through HPF 24
5.5 ECG signal after Derivative 24
5.6 ECG signal after squaring 25
5.7 ECG signal after averaging 26
6.1 QRS detection using Pan-Tompkins algorithm 29
6.2 Cumulative variance proportions by each principal 30
component

vii
 CHAPTER 1

INTRODUCTION

1.1 INTRODUCTION
Electrocardiogram is a vital tool that describes the electrical activity of the
heart. Every heart contraction produces an impulse detected by electrodes placed on the
skin. The heartbeat produces a series of waves with a time variant morphology. These
waves are caused by voltage variations of the cardiac cells. Digital signal processing
techniques are used to extract useful information from the input signals received from
the body.

ECG provide information about the heart state. Each heartbeat is produced
after an atrial depolarization (P wave), a ventricular depolarization (QRS wave) and a
ventricular repolarization (T wave). These three stages are continuously repeated.

QRS is the most important wave in an electrocardiogram (ECG) signal,

making this important to analyze its morphology, amplitude, and duration for detecting
cardiac arrhythmias. Computer-based ECG analysis requires an accurate detection of
QRS complex and an accurate detection of the R wave in it. Nevertheless, this is a non-
easy task since real electrocardiogram signal usually faces muscular noise, motion
artifacts, and baseline drifts changes [1]. Other components of an ECG, such as P and T
waves are also found to be high in some cases, and these waves must be differentiated
from the QRS waves. This increases the complexity of QRS detection. False R-wave
undesired results in computer based-based ECG analysis. In addition, the number of false
detections significantly increases in the presence of ECG signals of patients with poor
signal-to-noise (SNR) [1].

1
1.2 Basics of ECG

The ECG which is characterized by five peaks and valleys P, Q, R, S and

T displays as a series of electrical waves which represent the electrical activity of the
heart. The ECG signal has frequency range of 0.05-100 Hz and its dynamic range is 1-
10 mV.

1.2.1 Importance of ECG

1. It can be used to determine the speed of heart beat.
2. Any abnormality in the rhythm of heart beat such as steadiness,
disturbances or irregularities can be deleted.
3. The strength and timing of electrical signals can be detected as they
pass through each part of the heart.
1.2.2 Problems identified by ECG
1. It is used to detect various cardiac disorders including heart attack
and congestive heart failure of a person.
2. It can be used to identify diseases such as an enlarged heart that is
working under strain, fast, slow or irregular heartbeats called
arrhythmias and ventricular tachcycardia.
1.2.3 ECG waveform

A normal ECG signal contains waves, intervals, segments, and one complex defined
below

1. Wave (P, Q, R, S, T and U): A positive or negative deflection from

baseline
2. Interval (PR, QT): The time between two specific ECG events.
3. Segment (ST, TP): The length between two specific points on the
ECG signal which are supposed to be at the baseline amplitude.

2
 4. Complex (QRS): The combination of multiple waves grouped
together.

Figure 1.1 ECG waveform

1. P-wave

ECG interpretation usually starts with assessment of the P-wave. The P-

wave is a small, positive and smooth wave. It is small because the atria make a relatively
small muscle mass. If the rhythm is sinus rhythm (under normal circumstances) the P-
wave vector is directed downwards and to the left in the frontal plane and this yields a
positive P-wave.

2. QRS complex (ventricular complex)

A complete QRS complex consists of a Q, R, S wave. However, all three

waves may not visible. Regardless of which waves are visible, the wave(s) that reflect
ventricular depolarization is always referred to as the QRS complex.

Naming of the waves in the QRS complex is easy but frequently

misunderstood. The following rules apply when naming the waves

3
1. A deflection is only referred to as wave if it passes the baseline.
2. If the first wave is negative, then it is referred to as Q-wave. If the
wave is not negative, then the QRS complex does not possess a Q-
wave, regardless of the appearance of the QRS complex.
3. All positive waves are referred t as R-waves. The first positive wave
is simply an “R-wave” (R). The second positive wave is called “R-
prime wave” (R’). If a third positive wave occurs (rare) it is referred
to as “R-bis wave” (R’’).
4. Any negative wave occurring after a positive wave is an S-wave.
5. Large waves are referred to by their capital letters (Q, R, S), and
small waves are referred to by their lower-case letters (q, r, s).

4
 Figure 1.2 Types of QRS complex

3. T-wave

Assessment of the T-wave represents a difficult, but it is a fundamental

part of ECG interpretation. The normal T-wave in adults is positive in most precordial.
The amplitude diminishes with increasing age. The T-wave is normally slightly
asymmetric since its downslope (second half) is steeper than its upslope (first half).

The T-wave should be concordant with the QRS complex, meaning that a
net positive QRS complex should be followed by a positive T-wave, and vice versa.
Otherwise there is discordance which might be due to pathology. A negative T-wave is
also called an inverted T-wave.

Table 1.1 Intervals of Normal Heart Beat

Intervals Normal duration (s) Events on the heart

Average Range during intervals
PR interval 0.18 0.12-0.20 Arial depolarization
QRS duration 0.08 to 0.10 Ventricular
depolarization and atrial
repolarization

5
 QT interval 0.40 to 0.43 Ventricular
depolarization
ST interval 0.32 ... Ventricular
repolarization

1.2.4 Noise present in ECG signal

1. Baseline Drift

It occurs due to respiration and body movement that can produce a low
frequency drift from the desired base line of the signal. It is usually low in frequency,
low in amplitude, and of ongoing duration. Typically, it is a signal <5Hz. This noise can
be removed by implementing a high-pass filter with cut-off frequency at nearly 5Hz.

2. Power line interference

The ECG signal can be affected by power line interference due to the low
output levels of the signal. Induction from neighboring equipment or faulty grounding
of equipment can be led to ECG leads picking up 50Hz interference from neighboring
power line currents. To reduce or remove this unwanted feature, removal of possible
interfering equipment and power cables is an effective approach. It is typically fixed
frequency, high in amplitude, and of ongoing duration. The amplitude of power-line
noise is very large.

3. Electromyography (EMG) noise

EMG interference is the unwanted electrical activity of muscles not related

to the movement of the heart that can interfere with the EMG. It is typically high in
frequency, low in amplitude (10% ECG), and of variable duration. This type of noise can
be lessened by reducing movement of the patient or the use of a low pass filter.

6
 4. Flat line/ missing lead

Due to a bad electrode-to-skin contact or electrodes disconnection.

5. Low amplitude signal

A persistent low amplitude signal in some leads may be produced by an

increased electrode-to-skin impedance. It might appear as sudden changes from normal
to low amplitude.

6. Steep slope/Spike noise

High frequency noise caused by abrupt movement of the electrodes can

produce distorted QRS, known erroneous/spurious beats.

Figure 1.3 Noise of ECG signals (a) Baseline Drift, (b)Power line interference,
(c)EMG noise

7
1.2.5 Arrhythmia

Normally, the Sinoatrial Node (SA) generates the initial electrical impulse
and begins the cascade of events that result in a heart-beat. For a normal healthy person,
the ECG comes off as a nearly periodic signal with depolarization followed by
repolarization at equal intervals. However, sometimes this rhythm becomes irregular.

Cardiac arrhythmia (also dysrhythmia) is term for any of a large and

heterogeneous group of conditions in which there is abnormal electrical activity in the
heart. The heart beat may be too fast or too slow and may be regular or irregular.

Arrhythmia comes in varieties. It may be described as flutter in chest or

sometimes “racing heart”. The diagnosis of Arrhymia requires Electrocardiogram. By
studying ECG, doctors can diagnose the disease.

1.2.6 Types of Arrhythmias

1. Sinus rhythm
This is the normal rhythm of the heart and results from proper
activation of the entire heart in proper sequence. Any variation from
sinus rhythm is termed an arrhythmia.
2. Ventricular Fibrillation
It is a life-threatening arrhythmia which is characterized by rapid,
irregular activation of the ventricles and thereby prevents an
effective mechanical contraction. During ventricular fibrillation,
the ECG has no distinctive QRS complexes but instead consists of
an undulating baseline of variable amplitude. Although the sinus
node continues to function properly, P waves cannot be discerned
in the waveform.

8
3. Ventricular tachycardia
It is rhythm characterized by wide, bizarre QRS complexes and
frequent ventricular premature contractions in a row. It may be
paroxysmal or chronic and often signifies underlying myocardial
disease.
4. Atrial flutter
It is an AV node-independent intra-atrial macro-reentry rhythm, in
which the atrial anatomy sustains a loop of continuous
depolarization, often around the tricuspid value annulus in the right
atrium. Atrial flutter can be paroxysmal or chronic and may be
associated with extremely rapid ventricular response rates.
5. Atrial fibrillation
It is characterized by rapid, irregular activation of the atria. It causes
can include reentry and abnormal automaticity. It can be
paroxysmal or chronic.

9
 Chapter 2

LITERTURE REVIEW

2.1 Development history of Feature extraction of ECG

A sudden Cardiac Death (SCD), which happens within one hour of onset
of symptoms because of cardiac causes. According to Heart Disease and Stroke Statistics
from the American Heart Association (AHA). That the number is expected to rise to
more than 23.6 million by 2030, the report found. In every year number of deaths are
increases and in most cases is the result of ventricular tachychardia (VT) or ventricular
fibrillation (VF). The implantable cardioverter-defibrillator has been considered as the
best protection against sudden death from ventricular arrhythmias in high-risk
individuals. However, most sudden deaths occur in individuals who do not have high-
risk profiles. This feature extraction finds the amplitudes and intervals in the P-QRS-T
wave’s analysis for classifying the normal and abnormal of the heart beat activity. This
amplitudes and intervals in the P-QRS-T waves concluded the performance of heart of
every human. In ECG, extracting the features of the P-QRS-T waves has been studied
from early time and lots of techniques as well as conversion have been presented for
accurate analysis and ECG feature extraction.

Tien-En Chen et al [2] discussed the first (S1) and second (S2) heart beat
sound recognition based only on sound characteristics. These two assumptions of the
individual periods of S1 and S2 and time durations of S1-S2 and S2-S1 are not involved
in the detection process. These techniques use the deep neural network (DNN) concept
is used for recognized the S1 and S2 heart beat sounds. In DNN, the first heart sound
signals are first converted into a sequence of MFCC and then by using K-means
algorithm are applied to cluster features into individual groups to refine their illustration

10
and discriminative capability. The refined features are then feed to the DNN classifier to
carry out the S1 and S2 identification. The DNN based method can achieve the high
precision with greater than 91 % accuracy.

Farzad et al [3] focused the detection the specific fiducial points of the
Seismocardiogram (SCG) signal with or without using the Electrocardiogram (ECG) R-
wave as the reference point. The identified fiducial points were used to find the cardiac
time intervals. In sensitivity and complexity of the SCG signal, the presented algorithm
was intended to strongly reject the low-quality cardiac cycles, which are the ones that
include unfamiliar fiducial points. This presented algorithm is applied to concurrent ECG
and SCG signals, the desired fiducial points of the SCG signal were effectively estimated
with a high detection rate.

Saxena et al [4] discussed the approach for efficient feature extraction form
ECG signals. He deals with a competent technique which has been created or signal
retrieval, data compression, and feature extraction of ECG signals. After the signal
retrieval from the compressed ECG data, it has been originated that the network not only
compresses the ECG data but is also improves the quality if recovered ECG signal with
respect to elimination of high frequency present in the original ECG signal.

The algorithm proposed by Mallat and Hwang was first applied to QRS
detection. R-peaks are found by scanning for simultaneous modulus maxima in the
relevant scales of the WT. For a valid R-peak the estimated regularity must be greater
than zero; i.e., α > 0.

11
 CHAPTER 3

SOFTWARE AND DATA BASE DESCRIPTION

3.1 MATLAB

Millions of engineers and scientists worldwide use MATLAB to analyze

and design the systems and products transforming our world. MATLAB is in automobile
active safety systems, health monitoring devices, smart power grids, and LTE cellular
networks. It is used for machine learning, signal processing, computer vision,
communications, computational finance, control design, robotics and much more.

3.1.1 Math Graphics Programming

The MATLAB platform is optimized for solving engineering and scientific

problems. The matrix-based MATLAB language is the world’s most natural way to
express computational mathematics. Built-in graphics make it easy to visualize and gain
insights from data. A vast library of pre-built toolboxes lets you get started right away
with algorithms essential to your domain. The desktop environment invites
experimentation, exploration and discovery. These MATLAB tools and capabilities are
all rigorously tested and designed to work together.

3.1.2 Scale Integrate Deploy

MATLAB helps to take the ideas beyond the desktop. It can analyses on
larger data sets and scale up to clusters and clouds. MATLAB code can be integrated
with other languages, enabling to deploy algorithms and applications within web,
enterprise production systems.

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3.1.2.1 Key Features

1. High-level language for scientific and engineering computing.

2. Desktop environment tuned for iterative exploration, designs and
problem- solving.
3. Graphics for visualizing data and tools for creating custom plots.
4. Apps for curve fitting, data classification, signal analysis, control
system tuning and many other tasks.
5. Add- on toolboxes for a wide range of engineering and scientific
applications.

Figure 3.1 MATLAB Layout

3.2 MIT-BIH ARRHYTHMIA DATABASE

The MIT-BIH Arrhythmia database was first generally available set of

standard test material for evaluation of arrhythmia detectors, and it has been used for that
purpose as well as for basic research into cardiac dynamics. Together with the American

13
Heart Association (AHA) database, it played an interesting role in stimulating
manufactures of arrhythmia analyzers to compete based on objectively measurable
performance, and much of the current appreciation of the value of common databases,
both for basic research and for medical device development and evaluation can be
attributed.

The MIT-BIH database, we selected 48 half-hour excerpts of two-channel,

24-hour, ECG recordings obtained from 47 subjects studied by the BIH Arrhythmia
Laboratory.

Figure 3.2 MIT-BIH Arrhythmia database

Figure 3.3 Database record

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 CHAPTER 4

PRINCIPAL COMPONENT ANALYSIS

4.1 Principal Component Analysis (PCA)

4.1.1 Introduction

Principal Component Analysis (PCA) seeks a linear combination of

variable such that the maximum variance is extracted from the variables. It then removes
this variance and seek a second linear combination which explains the maximum
proportion of the remaining variance. This is called the principal axis method and results
in orthogonal factors.

Figure 4.1 Principal Components

15
4.1.2 Objectives of principal component analysis

1. PCA reduces attribute space from a larger number of variables to

smaller number of factors and as such is a “non-dependent”
procedure.
2. PCA is a dimensionality reduction or data compression method.
The goal is dimension reduction and there is n guarantee that the
dimensions are interpretable.
3. To select a subset of variables from a larger set, based on which
original variables have the highest correlations with the principal
component.

4.1.3 Assumptions of PCA

1. Linearity: PCA assumes the data set to be linear combination of

the variables.
2. Mean and Covariance: It is not necessary that the directions of
maximum variance will contain good features for discrimination.
3. Large Variances have important dynamics: Components with
larger variance correspond to interesting dynamics and lower ones
correspond to noise. Where regression determines a line of best fit
a data set. [5]

Figure 4.2 Plot of data showing regression line and orthogonal line

16
4.2 Significance of PCA

Sometimes it is hard to find pattern in the data where the data is of very
high dimension and that is where the PCA comes into picture. PCA is a powerful
analyzing tool. The goal is to extract the important information from the table of
observations, represent it as set of new orthogonal variables called principal components,
and to display the pattern of similarity or dissimilarity of the observations and of the
variables. PCA, being a simple, non-parametric method of extracting relevant
information form confusing data sets, is used abundantly in all forms of analysis. PCA
shows the way for reducing a complex data set to a lower to reveal the sometimes hidden,
simplified structure that often underlie it.

One major advantage of PCA is that once we have found these patterns in
the data, and we can compress the data, i.e., by reducing the number of dimensions,
without much loss of information. This technique can be used in image compression,
data compression, variable reduction and many other applications [3]. Its goal is the
reduction in the number of dimensions from a numerical measurement of several
variables. With this dimensional reduction, this technique looks for simplifying a
statistical problem with the minimal loss of information. This method is also used in
signal processing for separating a linear combination of signal generated from sources
that are statistically independent. This is performed by representing the data with a new
coordinate system.

4.3 Applications of PCA

There are many different areas of applications where PCA is successfully

employed and has played role of an information extracting tool. Applications like Feature
Extraction, Dimensionality Reduction, Pattern Recognition, Image Compression are
good examples showing PCA as a powerful and reliable date and signal analysis
technique.

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4.4 Advantages and Disadvantages of PCA

4.4.1 Advantages

1. It is a good technique for dimensionality reduction applied on

multivariate analysis
2. It is an optimal and linear scheme for compressing a set of high
dimensional vectors into a set of lower dimensional vectors and
then reconstructing.
3. Also, it computes the model parameters directly from the data.
4. Since the model parameters require only matrix multiplication, the
compression and decompression are easy operations to perform.
5. It is used in many applications that include data compression,
image processing, visualization, probing data analysis, pattern
recognition and time series prediction.

4.4.2 Disadvantages of PCA

1. The PCA technique is non-parametric, so on prior knowledge can

be incorporated.
2. PCA data reduction often incurs a loss of information.
3. The naïve methods for finding the principal component directions
find the trouble with the high dimensional data
4. The standard PCA algorithm is based on assumption that the data
have not been spoiled by outliers.

18
 CHAPTER 5

METHODOLOGY

5.1 Major steps in the analysis of the ECG signals

Noise elimination from ECG using noise filtering techniques

Noise filter removes and reduces the noise components from various sources in the ECG.

Cardiac cycle detection

Cardiac cycle detection involves detecting the QRS complex peak corresponding to each
beat. QRS Complex detection is implemented using Tompkins QRS complex detection
algorithm.

Feature Extraction

Feature extraction includes formulation and selection of characteristic features such that
they significantly relate to the abnormalities. Additional features are extracted by
performing complexity analysis on the signal.

Block diagram of ECG analysis

Figure 5.1 Block diagram of ECG analysis

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5.1.1 ECG Preprocessing

ECG preprocessing is treating the ECG signal before extracting its useful
information. Different methods are used in the design of the filters used to remove
unwanted parts of signal or the different types of noise present such as power line
interference which is most common ECG noise. Filtering is also used to isolate desired
parts of the signal, such as the components lying within a certain frequency range.

The main task of the ECG pre-processing is the accurate detection of QRS
complex. This is highlighted by the R-peak which is the easiest to detect due to its
greatest magnitude. The R peak is a key indicator of the heart rate and heart rate
variability and can show irregularities such as slow accelerated heart rates. The time
interval between the R-peaks is known as the R-R intervals. It is used to calculate the
heart rate which is calculated by

𝑆𝑎𝑚𝑝𝑙𝑒𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 ∗ 60
= 𝑏𝑝𝑚
𝑅𝑝𝑒𝑎𝑘2 ∗ 𝑅𝑝𝑒𝑎𝑘1

Where bpm is the heart beats per minute and 𝑹𝒑𝒆𝒂𝒌𝟏 and 𝑹𝒑𝒆𝒂𝒌𝟐 are the times of the
consecutive peaks. The normal rate of the heart is from 60 to 100bpm. So, from the
recorded ECG, we can determine whether the heart activity is normal or abnormal.

5.2 QRS Detection

QRS detection algorithm is used to extract the R points of the ECG and it
is an important parameter in obtaining the R-R intervals. For this work, Pan and
Tompkins algorithm were used for QRS detection. This algorithm is chosen in this work
because it has sensitivity of 99.69% and a positive predictivity of 99.77% when tested
using the MIT/BIH database. The QRS detection algorithm developed by Pan and
Tompkins recognizes QRS complex based on analyses of the slope, amplitude and width.

20
5.2.1 QRS Detection Algorithm

The algorithm used to detect QRS complexes is an adaptation of the

commonly used real-time QRS detection algorithm developed by Pan et al and further
described by Hamilton et al. It recognizes QRS complexes based on analysis of the slope,
amplitude and width.

Figure 5.2 Filter stages of QRS detector

Figure 5.2 shows the various processes involved in the analysis of the ECG signal. To
isolate the portion of the wave where QRS energy is predominant, the signal is passed
through a band pass filter composed of cascaded high-pass and low-pass integer filters.
Then the signal is subjected to differentiation, squaring, time averaging and finally peak
is detected by applying threshold. The band pass filter is designed from a special class of
digital filters that require only integer co-efficients. Since it was not possible to directly
design the desired band pass filter with this special approach, the design consists of
cascaded low-pass and high-pass filter sections. Then next processing step is
differentiation, a standard technique for finding the high slopes that normally distinguish
the QRS complexes from other ECG waves. To this point in the algorithm, all the
processes are accomplished by linear digital filters. The differentiated waveform is
subjected to a nonlinear transformation. The nonlinear transformation involves point-by-
point squaring of the signal samples. This transformation serves to make all the data
positive prior to subsequent integration and accentuates the higher frequencies in the

21
signal obtained from the differentiation process. These higher frequencies are normally
characteristic of the QRS complex.

The squared waveform passes through a moving window integrator. This integrator sums
the area under the squared waveform over a 150msec interval, advances 1 sample
interval and integrates the new 150msec window. The width of the window was chosen
to belong enough to include the time duration of extended abnormal QRS complexes,
but short enough so that it does not overlap both the QRS complex and the T wave.
Adaptive amplitude threshold applied to the band pass filtered waveform and to the
moving integration wave form are based on continuously updated estimate of the peak
signal level and the peak noise. After preliminary detection by the adaptive thresholds,
decision processes make the final determination as to whether detected event was a QRS
complex. A measurement algorithm calculates the QRS duration after the detection of
each QRS complex. Thus, two waveform features are available for subsequent analysis,
RR interval and QRS duration.

5.2.2 Noise elimination from ECG using noise filtering techniques

5.2.2.1 Band Pass Integer Filter

The band pass filter for the QRS (heart rate) detection algorithm reduces noise in the
ECG signal by matching the spectrum of the average QRS complex. Thus, it attenuates
T wave interference as well as noise. The pass band that maximizes the QRS energy is
approximately in the 5–15Hz range. The filter implemented in this algorithm is a
recursive integer filter in which poles are located to cancel the zeros on the unit circle of
the z plane. A low pass filter and a high pass filter are cascaded to form the band pass
filter.

5.2.2.1.1 Low Pass Integer Filter

The transfer function of the second order low pass filter is

22
 (1 − z −6 )2
H(z) =
(1 − z −1 )2

The difference equation of this filter is

y(nT) = 2y(nT−T) −y(nT−2T) +x(nT)−2x(nT−6T) +x(nT−12T)

Figure 5.3 Noise removal of the signal by passing through LPF

5.2.2.1.2 High Pass Integer Filter

The high pass filter is implemented by subtracting a first order low pass filter from an all
pass filter with delay. The low pass filter is an integer co efficient filter with the transfer
function

Y (z) (1−z−32 )
Hlp (z) = =
X (z) (1−z−1 )

The difference equation of the transfer function is

y(nT) = y(nT−T) + x(nT)−x(nT−32T)

The high pass filter is obtained by dividing the output of the low pass filter by its dc gain
and then subtracting from the original signal.

The transfer function of the high pass filter is

23
 P (z) (1−z−32 )
Hhp (z) = =
X (z) (1−z−1 )

The difference equation for this filter is

p(nT) = x(nT−16T) −(1/32) × [y(nT−T) + x(nT)−x(nT−32T)]

Figure 5.4 Noise removal of the signal by passing through HPF

5.2.3 Derivative

After the signal has been filtered it is then differentiated to provide information about
the slope of the QRS complex.

A five-point derivative has the transfer function

𝐻 (𝑧) = 0.1(2 + 𝑧 −1 − 𝑧 −3 − 2𝑧 −4 )

This derivative is implemented with the difference equation

y(nT) = (1/8) ×[2x(nT)+ x(nT−T) + x(nT−3T) −2x(nT−4T)]

The fraction 1/8 approximates the actual gain of 0.1. This derivative approximates the
ideal derivative in the dc through 30Hz frequency range.

Figure 5.5 ECG signal after Derivative

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5.2.4 Squaring

Function The squaring function that the signal passes through is a nonlinear operation.
The equation that implements this operation is

y(nT) = y(nT) = [x(nT)]2

This operation makes all data points in the processed signal positive and it amplifies the
output of the derivative process nonlinearly. It emphasizes the higher frequencies in the
signal that are mainly due to the QRS complex.

Figure 5.6 ECG Signal after Squaring

5.2.5 Moving Window Integral

The slope of the R wave alone is not a guaranteed way to detect a QRS event. Many
abnormal QRS complexes that have large amplitude and long duration (not very steep
slopes) might not be detected using information of the R wave only. Thus, we need to
extract more information from the signal to detect a QRS event. Moving window
integration extracts features in addition to the slope of the R wave. It is implemented
with the following difference equation

y(nT) = (1/N) ×[x(nT−(N−1) T) +x(nT−(N−2) T) +···+x(nT)]

Where N is the number of samples in the width of the moving window. The width of the
window should be approximately the same as the widest possible QRS complex. If the
size of the window is too large the integration waveform will merge the QRS and T
complexes together. On other hand, if the size of the window is too small, a QRS

25
complex could produce several peaks at the output of the stage. The width of the window
should be chosen experimentally.

Figure 5.7 ECG signal after averaging

5.2 Algorithm of PCA

The signal segment of heartbeat is represented by y(k), as in (1)

𝑦 (1)
𝑦 (2)
y(k)=[ ] (1)
⋮
𝑦 (𝑀 )

where M is the samples of the heartbeat. Thus, the heartbeats 𝒚𝟏 , 𝒚𝟐,⋯, 𝒚𝑵 are the N
observations of heartbeats. The entire ensemble of heartbeats is represented by the M×N
matrix[8].

Y=[𝒚𝟏 , 𝒚𝟐,⋯, 𝒚𝑵 ] (2)

The principal component analysis consists of the following steps:

1. Calculate the mean vector: The mean vector of each heartbeat is calculated as in
(3)
1
y= ∑𝑀
𝑖=1 𝑦𝑖 (3)
𝑀

2. Compute the mean adjusted data

𝒚𝒂𝒅𝒋𝑖 = 𝑦𝑖 − 𝑦 (4)

Yadj= [𝐲𝐚𝐝𝐣𝟏 𝐲𝐚𝐝𝐣𝟐 … 𝐲𝐚𝐝𝐣𝑵 ] (5)

26
3. Compute the covariance matrix, as shown in (6)

1
C= ∑𝑀 𝑇
𝑖=1(𝑦𝑖 − 𝑦) (𝑦𝑖 − 𝑦) (6)
𝑀−1

4. Calculate the eigenvectors and eigenvalues of the covariance matrix. The

eigenvalues λ 𝒊 and eigenvectors 𝑒𝑖 , correspond to

C· 𝑒𝑖 = λ 𝒊 · 𝑒𝑖 (7)

5. Choosing components and forming a feature vector. The eigenvector with the
highest value is the principal component. Then, the eigenvectors are ordered by
eigenvalues from highest to lowest, which returns the components in order of
significance.
6. Subsequently, the dimensionality is reduced by selecting K-principal components
that retain the physiological information. Thus, the percentage of variance, 𝒓𝒌 , of
each eigenvalue is obtained by applying (8)

𝟏 ∑𝑲
𝒊=𝟏 λ 𝒊
𝒓𝒌 = (8)
𝑴−𝟏 ∑𝑵
𝒊=𝟏 λ 𝒊

7. Furthermore, we select the Principal Components whose percentage of variance

is higher than the percentage threshold, th, that is 0.9 or 0.95 as shown in (9)

𝑟𝑘 = (𝑟𝑘 ≥ th) (9)

8. Deriving the new data set, the final datadet is obtained by (10)
𝑌𝑝𝑐𝑎(𝑘) = 𝑟𝑘 Yadj𝑇 (10)

27
 CHAPTER 6

RESULTS AND DISCUSSION

The QRS automatic detection and extraction methods have been validated using the
MIT-BIH arrhythmia database[8][9]. The MIT-BIH arrhythmia database contains
records sampled at 360 Hz, with 11-bit resolution over 5mV range. Each record contains
a duration of 30minutes. For QRS detection, only the first channel of each record has
been considered. A total of 11 records have been considered. These records contain
inverted QRS polarity and low amplitude QRS, ventricular ectopic beats with low SNR,
premature ventricular beats, and premature atrial beats. The performance of the proposed
algorithm has been essentially evaluated by two parameters Sensitivity (Se)(1) and
positive predictivity(+P)(2).

𝑇𝑃
Se(%) = × 100 (1)
𝑇𝑃+𝐹𝑁

𝑇𝑃
+P(%)= × 100 (2)
𝑇𝑃+𝐹𝑃

Where TP (true positive) is the number of heartbeats properly detected (i.e., QRS
complexes properly detected), FN (false negative) indicates the number of heartbeats
that were not detected by this method (i.e., QRS complexes that were not detected), and
FP (False positive) indicates the false heartbeats detected (i.e., QRS complexes detected
by the method when no QRS complexes are present).

The sensitivity parameter (Se) indicates the percentage of heartbeats that were correctly
detected by the algorithm. The positive predictivity (+P) indicated the percentage of

28
heartbeats detections which were real true heartbeats. The table represents the results of
the method applied to the records extracted from the MIT-BIH arrhythmia database.

Table 6.1 Performance of Pan-Tompkins method on MIT-BIH arrhythmia

database.

Record No of TP FP FN Se +P
beats
100 2273 2273 0 0 100.00 100.00
101 1865 1863 9 1 99.94 99.51
103 2084 2082 0 1 99.95 100.00
105 2412 2359 5 28 96.13 99.93
111 1774 1494 1 0 100.00 99.84
112 2539 2539 5 4 98.82 99.78
118 1535 1535 1 0 100.00 99.73
203 2136 2094 1 21 99.00 99.80
223 2605 2552 0 26 98.99 99.47
232 1573 1569 1 2 99.87 99.93
Total 20796 20360 23 83 90.25 90.72
The results of our method to detect QRS complexes are significantly precise. Our method
scored Se =90.25% and +P = 90.72% over 20796 heartbeats.

Figure 6.1 QRS Detection using Pan-Tompkins algorithm

29
After the QRS detection, 90 samples were selected from the left side of R-peak and 90
samples after the R-peak point. Then, the PCA technique has been applied to select useful
features which can be used for further ECG recognition,

The linear dimensionality reduction of the input Y(k) is obtained by the PCA technique.
This technique provides projection of Y(k) in the direction of highest variance. Figure
6.2 shows the fraction of total variance in the data as explained by each principal
component. As it can be seen the first four principal components account for around 99%
of the variance.

Figure 6.2 Cumulative variance proportions by each principal component.

30
 CHAPTER 7

CONCLUSION

This project has presented a novel approach for QRS detection of electrocardiogram
signals by applying the Pan-Tompkins technique. In addition, Principal Component
Analysis is implemented for feature extraction of QRS complex.

Our approach for QRS complexes detection introduces a technique to

improve the accuracy of QRS complexes detection in records with ventricular ectopic,
negative QRS polarities, low signal-to-noise ratio and low amplitude R-peaks. Our
experiments showed that our proposed approach achieves precise detection rates with an
overall positive predictivity of 90.72% and a sensitivity of 90.25%.

As future work we propose to automate the classification of cardiac

arrhythmias using multilayer perceptron neural network with a backpropagation learning
technique.

31
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