Denoising of ECG -- A discrete time approach using DWT

Munzaleen Rashid Bhat Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 5, Issue 5, ( Part -6) May 2015, pp.139-148
www.ijera.com 139 | P a g e
Denoising of ECG -- A discrete time approach using DWT.
Munzaleen Rashid Bhat* Virk Rana**
*(Department of Electronics Communication Engineering, Punjab Technical University Punjab)
** (Department of Electronics Communication Engineering, Punjab Technical University Punjab)
ABSTRACT
This paper is about denoising of ECG signal using DWT transform. In this paper, ECG signals are denoised
using DWT transform.Ecg signals are taken and noise at different frequencies are generated which are
superimposed on this original ecg signal.High frequency noise is of 4000 hertz and power line interference is of
50 hertz.Decomposition of noisy signal is achieved through wavelet packet .wavelet packets are reconstructed
and appropriate wavelet packets are combined to obtain a signal, very similar to original ecg signal.This
technique results in the minimization of mean square error in the filtered signals.
Keywords - CWT,DENOISING,DFT,DWT,ECG,STFT.
I. INTRODUCTION
The ECG is the most commonly performed
cardiac test. This is because the ECG is a useful
screening tool for a variety of cardiac abnormalities;
ECG machines are readily available and the test is
simple to perform, risk-free and inexpensive. As the
heart undergoes depolarization and repolarization, the
electrical currents that are generated spread not only
within the heart, but also throughout the body. This
electrical activity generated by the heart can be
measured by an array of electrodes placed on the
body surface. The recorded tracing is called an
electrocardiogram (ECG, or EKG). From the ECG
tracing, the heart rate, heart rhythm and conduction
abnormalities can be determined thus helping in
diagnosis of any coronary or heart disease.
In first section the human heart is introduced. It
explains the valves present which regulate the flow of
blood through our heart along with the conduction
system of the heart. Furthermore in the second part
the electrical activity of the heart is discussed, which
results due to the action potentials or rather because
of the active sodium-potassium pump (active Na+ -
K+ pump).
Next section discusses the ECG and the noises
that can be present in it. ECG is a quasi-periodical,
rhythmically repeating signal synchronized by the
function of the heart, which acts as a generator of the
bioelectrical events. The different waveforms are
recorded and standardized in terms of amplitude,
time and phase relationship. By looking at a subjects
ECG a physician can diagnose the disease of patient.
Any sort of noise in an ECG signal results in a
deformed ECG, thus making it unsuitable for
diagnosis and even resulting in wrong diagnosis.
The signal processing methods are introduced in
third section of the paper.
Fourth section discusses with the Problem
Considered and the Results obtained. Procedures for
the rectification of the problem to obtain the desired
result have also been discussed.
The last section consists of all the conclusions.
II. HEART
2.1 Heart Anatomy
Figure 2.1: Internal Structure of the Heart
The heart weighs between 7 and 15 ounces (200
to 425 grams) and is a little larger than the size of
your fist. By the end of a long life, a person's heart
may have beat (expanded and contracted) more than
3.5 billion times. In fact, each day, the average heart
beats 100,000 times, pumping about 2,000 gallons
(7,571 liters) of blood.
Your heart is located between your lungs in the
middle of your chest, behind and slightly to the left of
your breastbone (sternum). A double-layered
membrane called the pericardium surrounds your
heart like a sac. The outer layer of the pericardium
surrounds the roots of your heart's major blood
vessels and is attached by ligaments to your spinal
column, diaphragm, and other parts of your body.
The inner layer of the pericardium is attached to the
heart muscle. A coating of fluid separates the two
layers of membrane, letting the heart move as it
beats, yet still be attached to your body.
Your heart has 4 chambers. The upper chambers
are called the left and right atria, and the lower
chambers are called the left and right ventricles. A
RESEARCH ARTICLE OPEN ACCESS

wall of muscle called the septum separates the left
and right atria and the left and right ventricles.
The left ventricle is the largest and strongest
chamber in your heart. The left ventricle's chamber
walls are only about a half-inch thick, but they have
enough force to push blood through the aortic valve
and into your body.
2.1.1 Heart Valves
Figure 2.2: Heart Valves
Four valves regulate blood flow through your heart:
1. The tricuspid valve regulates blood flow between
the right atrium and right ventricle.
2. The pulmonary valve controls blood flow from
the right ventricle into the pulmonary arteries,
which carry blood to your lungs to pick up
oxygen.
3. The mitral valve lets oxygen-rich blood from
your lungs pass from the left atrium into the left
ventricle.
4. The aortic valve opens the way for oxygen-rich
blood to pass from the left ventricle into the
aorta, your body's largest artery, where it is
delivered to the rest of the body.
2.2 Conduction System
Figure 2.3: Four Chamber Structure of the Heart
Electrical impulses from your heart muscle (the
myocardium) cause your heart to beat (contract). This
electrical signal begins in the sinoatrial (SA) node,
located at the top of the right atrium. The SA node is
sometimes called the heart's "natural pacemaker."
When an electrical impulse is released from this
natural pacemaker, it causes the atria to contract. The
signal then passes through the atrioventricular (AV)
node. The AV node checks the signal and sends it
through the muscle fibers of the ventricles, causing
them to contract.
The SA node sends electrical impulses at a
certain rate, but your heart rate may still change
depending on physical demands, stress, or hormonal
factors.
2.2.1 Rhythm of the Heart
The word "rhythm" is used to refer to the part of
the heart which is controlling the activation sequence.
The normal heart rhythm, with electrical activation
beginning in the SA node, is called "sinus rhythm".
Electrical activation of heart can sometimes begin in
places other than SA node also.
Figure 2.4: Cardiac Conduction System
The electrical activity of the heart is integral to
the operation of several types of medical instruments,
including the electrocardiograph, the pacemaker, and
the defibrillator. A very small electrical disturbance
can cause this vital organ to cease pumping blood
necessary to sustain life. The heart consists of two
major smooth muscles the atrium, and the ventricle
which form the syncytium, or fusion of cells, that
conducts depolarization from one cell to the next.
Because of the ionic leakage in the smooth muscle
membrane the tissue of the heart depolarizes
spontaneously from its resting state and effectively
oscillates, or beats. The sinoatrial (SA) node beats at
a rate of from 70 to 80 beats per minute (bpm) at rest.
The atrioventricular (AV) node beats at 40 to 60 bpm
and the bundle branch oscillate at 15 to 40 bpm.
The SA node, normally determines the heart rate,
since it beats at the fastest rate and causes stimulation
of the other tissues before it reaches its self-pacing
threshold. Thus, the SA node can be considered the
heart's pacemaker.
The depolarization of the SA node spreads
throughout the atrium and reaches the AV node about
40ms. Because of the low conduction velocity of the
AV node tissue, it requires about 110ms for the
depolarization to reach the bundle branches called the
Purkinje system. The ventricles then contract, the
right ventricle then forcing blood into the lungs, the
left ventricle pushing blood into the aorta and
subsequently through the circulation system. The
contraction period of the heart is called systole.
The action potentials in the ventricle hold for
200 - 250ms. This relatively long time allows the
ventricular contraction to empty blood into the

arteries. The heart then re-polarizes during the rest
period, called diastole, then the cycle repeats.
2.3 Biopotentials in the Heart
The contraction of any muscle is associated with
electrical changes called "depolarization", and these
changes can be detected by electrodes attached to the
surface of the body. Since all muscular contraction
will be detected, the electrical changes associated
with contraction will be detected, the electrical
changes associated with contraction of the heart
muscle will only be clear if the patient is fully
relaxed and no skeletal muscles are contracting.
Although the heart has four chambers, from the
electrical point of view it can be thought as having
only two, because two atria contract together and
then the two ventricles contract together.
The electrical discharge for each cardiac cycle
normally starts in a special area of the right atrium
called the "sinoatrial (SA) node". Depolarization then
spreads through the atrial muscle fibers. There is a
delay while the depolarization spreads through
another special area of atrium, the "atrioventricular
(AV) node". Thereafter, the electrical discharge
travels very rapidly, down specialized conducting
tissue: first a single pathway, the "bundle of His",
which then divides in the septum between the
ventricles into right and left bundle branches. The left
bundle branch itself divides into two. Within the
mass of ventricular muscle, conduction spreads
somewhat more slowly, through specialized tissue
called "purkinje fibers".
2.3.1 Sources of Bioelectric Potentials
In carrying out their various functions, certain
systems of body generate their own monitoring
signals, which convey useful information about the
functions they represent. These signals are the
bioelectric potentials associated with nerve
conduction, brain activity, heartbeats, muscle
activity, and so on. BIOELECTRIC
POTENTIALS are actually ionic voltage
produced as a result of the electrochemical activity of
certain special types of cells. Through the use of
transducers capable of converting ionic potentials
into electrical voltages, these natural monitoring
signals can be measured and results displayed in a
meaningful way to aid the physician in his diagnosis
and treatment of various diseases.
The idea of electricity being generated in the
body goes back as far as 1786, when an Italian
anatomy professor, Luigi Galvani, claimed to have
found electricity in the muscle of a frog, s leg. In the
century that followed several other scientists
discovered electrical activity in various animals and
in man. But it was not until 1903, when the Dutch
physician Willem Einthoven introduced the string
galvanometer that any practical application could be
made of these potentials. The advent of the vacuum
tube and amplification and, more recently, of solid-
state technology has made possible better
representation of the bioelectric potentials. These
developments, combined with a large amount of
physiological research activity, have opened many
new avenues of knowledge in the application and
interpretation of these important signals.
2.3.2 Resting and Action Potentials
Certain types of cells within the body, such as
nerve and muscle cell, are encased in a semi
permeable membrane that permits some substances to
pass through the membrane while others are kept out.
Neither the exact structure of the membrane nor the
mechanism by which its permeability is controlled is
known, but the substances involved have been
identified by experimentation.
Surrounding the cells of the body are the body
fluids. These fluids are conductive solutions
containing charged atoms known as ions. The
principal ions are sodium (Na+), potassium (K+), and
chloride (Cl-). The membrane of excitable cells
readily permits entry of potassium and chloride ions
effectively blocks the entry of sodium ions. Since the
various ions seek a balance between the inside of the
cells and the outside, both according to concentration
and electric charge, the inability of the sodium to
penetrate the membrane results in two conditions.
First, the intercellular fluid outside. Since the sodium
ions are positive, this would tend to make the outside
of the cell becomes much lower than in intercellular
fluid outside of the cell more positive than the inside.
Second, in an attempt to balance the electric charge,
additional potassium ions, which are also positive,
enter the cell, causing a higher concentration of the
potassium on the inside than on the outside. This
charge balance cannot be achieved, however, because
of the concentration imbalance of potassium ions.
Equilibrium is reached with a potential difference
across the membrane, negative on the inside and
positive on the outside.
This membrane potential is called the resting
potential of the cell and in maintained until some
kind of disturbance upsets the equilibrium. Since
measurement of the membrane potential is generally
made from inside the cell with respect to the body
fluids, the resting potential of a cell is given as
negative.
Research investigators have reported measuring
membrane potentials in various cells ranging from -
60 to -100 mV. Figure 2.5 illustrates in simplified
from the cross section of a cell with its resting
potential. A cell in resting state is said to be
polarized.

Figure 2.5: Polarized cell with its Resting Potential
When a section of the cell membrane is excited
by the flow of ionic current or by some from of
externally applied energy, the membrane changes its
characteristics and begins to allow some of the
sodium ions to enter. This movement of sodium ions
into cell constitutes an ionic current flow that further
reduces the barrier of the membrane to sodium ions.
The net result is an avalanche effect in which sodium
ions literally rush into the cell to try to reach a
balance with the ions outside. At the same time
potassium ions, which were in higher concentration
inside the cell during the resting state, try to leave the
cell has a slightly positive potential on the inside due
to the imbalance of potassium ions.
This potential is known as the action potential
and is approximately +20 mV. A cell that has been
excited and that displays an action potential is said to
be depolarized; the process of changing from the
resting state to the action potential is called
depolarized. Figure 2.6 shows the ionic movements
associated with depolarization, and Figure 2.7
illustrates the cross section of depolarized cell.
Figure 2.6: Depolarization of a cell Na+ ions rush
into the cell while K+ ions attempt to leave
Figure 2.7: Depolarized cell during an Action
Potential
Once the rush of sodium ions through the cell
membrane has stopped (a new state of equilibrium is
reached), the ionic currents that lowered the barrier to
sodium ions are no longer present and the membrane
reverts back to its original, selectively permeable
condition, wherein the passage of sodium ions from
the outside to the inside of the cell is again blocked.
Were this the only effect, however, it would take a
long time for a resting potential to develop again. But
such is not the case. By an active process, called a
sodium pump, the sodium ions are quickly
transported to the outside of the cell, and the cell
again becomes polarized and assumes its resting
potential. This process is called re depolarization.
Although little is known of the exact chemical steps
involved in the sodium pump, it is quite generally
believed that sodium by some form of high-energy
phosphate compound. The rate of pumping is directly
proportional to the sodium concentration in the cell.
It is also believed that the operation of this pump is
linked with the influx of potassium existed.
Figure 2.8 shows a typical action-potentials
waveforms, beginning at the resting potential
after repolarization. The time scale for the action
potentials depends on the type of cell producing
the potential. In nerve and muscle, on the other
hand, repolarizes much more slowly, with the
action potential for heart muscle usually lasting
from 150 to 300 msec.
Figure 2.8: Waveform of the Action Potential
Regardless of the method by which a cell is
excited or the intensity of the stimulus (provided it is
sufficient to activate the cell), the action potential is
always the same for any given cell. This is known as
the all-or-nothing law. The net height of the action
potential of the depolarized membrane at the peak of
the action potential and the resting potential.
2.3.3 Cardiac Action Potentials
The cardiac action potential differs from the
neuronal action potential by having an extended
plateau, in which the membrane is held at a high
voltage for a few hundred milliseconds prior to being
repolarized by the potassium current as usual. This
plateau is due to the action of slower calcium
channels opening and holding the membrane voltage
near their equilibrium potential even after the sodium
channels have inactivated.

The cardiac action potential plays an important
role in coordinating the contraction of the heart. The
cardiac cells of the sinoatrial node provide the
pacemaker potential that synchronizes the heart. The
action potentials of those cells propagate to and
through the atrioventricular node (AV node), which
is normally the only conduction pathway between the
atria and the ventricles. Action potentials from the
AV node travel through the bundle of His and thence
to the Purkinje fibers. Conversely, anomalies in the
cardiac action potential-whether due to a congenital
mutation or injury-can lead to human pathologies,
especially arrhythmias. Several anti-arrhythmia drugs
act on the cardiac action potential, such as quinidine,
lidocaine, beta blockers, and verapamil.
Figure 2.9: Action Potential
III. ELECTROCARDIOGRAM
3.1 .Electrocardiogram
Figure 3.1: Electrocardiogram
During diastole, while the heart is at rest, all of
the cells are polarized so that the potential inside each
cell is negative with respect to the outside. Normally,
depolarization occurs first at the SA node, making the
outside of the tissue negative with respect to the
inside of the cells and making it negative with respect
to the tissues not yet depolarized. This imbalance
results in an ionic current, I, causing the left arm to
measure positive with respect to the right arm. The
resulting voltage is called the P wave.
After about 90 ms, the atrium is completely
depolarized, and the ionic current measured by lead I
reduces to zero. The depolarization then passes
through the AV node causing a delay of 110ms. The
depolarization then passes to the right ventricular
muscle depolarizing it and making it negative relative
to the still polarized left ventricular muscle. Again
the direction of I causes a + to - voltage from LA to
RA called the R-wave.
The complete wave form is called an
electrocardiogram with labels P, Q, R, S, and T
indicating its distinctive features. The P wave arises
from the depolarization of the atrium. The QRS
complex arises from depolarization of the ventricles.
The magnitude of the R-wave within this complex is
approximately 1mV. The T wave arises from re-
polarization of the ventricle muscle. The U wave that
sometimes follows the T-wave is second order effect
of uncertain origin and is of little diagnostic
significance.
3.1.1 ECG Waves and Intervals
1. P wave: the sequential activation (depolarization)
of the right and left atria
2. QRS complex: right and left ventricular
depolarization (normally the ventricles are
activated simultaneously)
3. ST-T wave: ventricular repolarization
4. U wave: origin for this wave is not clear-but
probably represents "after depolarizations" in the
ventricles
5. PR interval: time interval from onset of atria
depolarization (P wave) to onset of ventricular
depolarization (QRS complex)
6. QRS duration: duration of ventricular muscle
depolarization
7. QT interval: duration of ventricular
depolarization and repolarization
8. RR interval: duration of ventricular cardiac cycle
(an indicator of ventricular rate)
9. PP interval: duration of atrial cycle (an indicator
of atrial rate)
3.2 Generation of ECG Signal
The heart is innervated by the autonomic nervous
system, which increases or decreases heart rate; it
does not initiate contraction. The heart can go on
beating without any direct stimulus from the nervous
system. This is possible because the heart has an
intrinsic regulating system called the conduction
system. The conduction system is composed of
specialized muscle tissue that generates and
distributes the action potentials that stimulate the
cardiac muscle fibers to contract.
These tissues are found in the
1. Sinoatrial (SA) node,
2. Atrioventricular (AV) node,

3. Atrioventricular (AV)
4. Bundle (bundle of His),
5. Bundle branches, and
6. Conduction myofibres (Purkinje fibers).
All cardiac muscle is capable of self-excitation;
that is, it spontaneously and rhythmically generates
action potentials that result in contraction of the
muscle.
The normal resting rate of self-excitation of the
sinoatrial node is about 75 times per minute in adults.
Since this rate occurs faster than that of other
cardiac muscle fibres, the SA node is called the
"pacemaker". The onset of depolarisation in the heart
begins within a focus of pacemaker cells found at the
upper right border of the heart, just below the
opening to the superior vena cava. These cells which
give the initial activation are collectively known as
the sinoatrial node
Since the SA node spontaneously generates
action potentials faster than other components of the
conduction system, nerve impulses from the SA node
spread to the other areas and stimulate them so
frequently they are not able to generate action
potentials at their own inherent rates.
Thus the faster SA node sets the rhythm for the
rest of the heart. The rate set by the SA node may be
altered by nerve impulses from the autonomic
nervous system or by chemicals such as thyroid
hormones and epinephrine.
The conduction continues to travel in a wave
downwards, leftwards and posteriorly, through both
atria, depolarising each cell in turn. It is this
propagation of charge that can be seen as the P wave
on the electrocardiograph
Figure 3.2: Atrial Depolarization
Eventually this conduction of depolarisation
meets the atrioventricular node near the centre of the
heart at the top of the interventricular septum. It is the
atrioventricular node that is the main cause of delay
in conducting the impulse from the atria to the
ventricles. Since the atrioventricular node is small no
depolarisation voltage is recorded and an isoelectric
PR segment is seen on the electrocardiograph
Figure 3.3: Atrioventricular Nodal
Depolarization and Activation of Bundle of His
The depolarization continues down the septum, along
the bundle of His, before splitting to follow the left
and right bundle branches and onwards to the
conduction myofibres (Purkinje fibres) which
distribute the action potential and thus depolarize the
myocardial cells of the ventricles. Since the left
bundle branch is activated first, the septal
depolarisation proceeds from left to right and gives
rise to a small negative deflection within the
electrocardiograph - the Q wave.
As the impulse travels down the septum the atria
and sinoatrial node start to polarize.The wave of
depolarisation continues down the septum and into
the ventricular free wall. Since the left ventricular
wall mass is significantly greater than the right, the
mean vector of depolarisation of the ventricular free
wall is to the left. The depolarisation takes place from
the endocardium to the epicardium and is seen as the
R wave.
Atrial, atrioventricular nodal and bundle of His
polarization continue but are obscured by the higher
the rim of the ventricular muscle below the
atrioventricular groove is the last to be depolarized.
The direction of depolarisation leads to the S wave.
Figure 3.4: Ventricular Systole
Polarization is the return of the membrane
potential to the baseline. This gives a deflection in
the same direction as depolarisation because both
polarity and direction are negated - the T wave.
Because the bundle of His has the greatest
capacitance within the conduction cycle, it is the final
part of the heart to polarize. The positive deflection
caused by this is so small that it is often unclear.
When detected it is referred to as the U wave.
Figure 3.5: Ventricular
Figure 3.6: Bundle of His

Figure: 3.7 Explanations of the ECG Waves
3.4 Noises in ECG Signal
Electrocardiographic signals (ECG) may be
corrupted by various kinds of noise. Typical
examples are:
1. Power Line Interference
2. Electrode Contact Noise.
3. Motion Artifacts.
4. Muscle Contraction.
5. Base Line Drift.
6. Instrumentation Noise generated by Electronic
Devices.
7. Electrosurgical Noise.
3.4.1 Power Line Interference
It consists of 50-60Hz pickup and harmonics,
which can be modeled as sinusoids.
Characteristics, which might need to be varied in
a model of power line noise, of 60Hz component (as
most of the signals of study were digitized in USA)
include the amplitude and frequency content of the
signal. The amplitude varies up to 50 percent of the
peak to peak ECG amplitude. It is shown in Figure
3.13 where power signal is affecting the signal
between 1000 to 3000 units of time.
3.4.2 Electrode Contact Noise
It is a transient interference caused by loss of
contact between the electrode and the skin that
effectively disconnects the measurement system from
the subject. The loss of contact can be permanent, or
can be intermittent as would be the case when a loose
electrode is brought in and out of contact with the
skin as a result of movements and vibration. This
switching action at the measurement system input can
result in large artifacts since the ECG signal is
usually capacitively coupled to the system.
It can be modeled as randomly occurring rapid
base line transition, which decays exponentially to
the base line value and has a superimposed 60 Hz
component. Typically the values of amplitude may
vary to the maximum recorder output.
IV. SIGNAL PROCESSING
A general transform equation can be written as:-
∞
X ( a , b) = ∫ x (t ) Ψa , b (t ) dt (4.1)
−∞
The signal to be processed is given as x (t).
Depending on the function Ψa,b(t) chosen, one gets
different transforms. In order to evaluate the integral,
certain conditions have to be imposed on this
function. In this paper, we shall consider only three
such transforms and these are the Fourier Transform,
Short-Time Fourier
Transform and the Wavelet Transform.
Tne of the major Signal Processing tools is the
Fourier Analysis, which has different forms like
Fourier Series, Fourier Transform, Discrete Fourier
Transform, and so on. Fourier analysis methods use
orthogonal sets of functions in order to expand a
given periodic function into an infinite series.
4.2 Fourier Transform
Fourier analysis is extremely useful for data analysis,
as it breaks down a signal into constituent sinusoids
of different frequencies. For sampled vector data,
Fourier analysis is performed using the Discrete
Fourier transform (DFT).
The Fourier transform, in essence, decomposes or
separates a waveform or function into sinusoids of
different frequency which sum to the original
waveform. It identifies or distinguishes the different
frequency sinusoids and their respective amplitudes.
The Fourier Transform of f (x) is defined as:
∞
F ( s ) =∫ f ( x ) e − j 2 πxs dx−∞ (4.2)
4.2.2 Drawbacks of Fourier Transform
1. One of the shortcomings of the Fourier
Transform is that it does not give any
information on the time at which a frequency
component occurs.
2. This is not a problem for "stationary" signals but
does leave room for improvement when "non-
stationary" signals are involved. (A stationary
signal is one in which frequency content remains
unchanged in time while in a non-stationary
signal frequency changes with time).
3. The biggest problem is that frequency
components in a signal cannot be localized in
time.
4. FT is a "global" analysis. A small perturbation of
the function at any one point on the time-axis
influences all points on the frequency-axis and
vise versa.
5. It can only be computed for one frequency at a
time.
6. It cannot be computed in real-time.
7. Time-domain information is difficult to be
interpreted from the spectrum.

8. It cannot display time-frequency information
effectively.
9. FT Only Gives what Frequency Components
Exist in the Signal.
10. The Time and Frequency Information can not be
Seen at the Same Time.
4.2 Wavelet Transforms
The basic idea which lies behind wavelets is the
representation of an arbitrary function as a
combination of simpler functions, generated as scaled
and dilated versions of a particular oscillatory mother
function.
This mother wavelet is used to generate a set of
daughter functions through the operations of scaling
and dilation applied to the mother wavelet. This set
forms an orthogonal basis that allows, using inner
products, to decompose any given signal much like in
the case of Fourier analysis. Wavelets, however, are
superior to Fourier analysis for time information is
not lost when moving to the frequency domain. This
property makes them suitable for applications from
diverse fields where the frequency content of a signal
as well as the energy's temporal location is valuable.
The wavelets application of interest for this work
is their use for data analysis, especially for signals
denoising. Denoising stands for the process of
removing noise, i.e. unwanted information, present in
an unknown signal.
The term wavelet is mostly used for denoting a
particular wave whose energy is concentrated in a
specific temporal location. A wavelet is therefore a
known signal with some peculiar characteristics that
allow it to be employed for studying the properties of
other signals simultaneously in the frequency and
time domains.
V. RESULTS
Problem considered 1:
Muscle contractions cause artifactual milli-volt
level potentials to be generated. The base line
electromyogram is usually in the micro-volt range
and therefore is usually insignificant. It is simulated
by adding random noise to the ECG signal. The
maximum noise level is formed by adding random
single precision numbers of ±50% of the ECG
maximum amplitude to the uncorrupted ECG.
We have a high frequency noise which is
superimposed on ECG signal each which is to be
denoised using wavelet transform.
Frequency of noise: 4000 Hz
Number of Samples in single ECG signal: 4096
Result:
We generated a high frequency cosine signal and
superimposed it on a pure ECG signal and hence
generated a noisy ECG signal as illustrated in the
Figure 5.1.
Figure 5.1: Noisy Signal for High Frequency Noise
of Frequency 4000 Hz
Course of Denoising:
Wavelet used: - Daubechies wavelet (db7) up to level
12
In discrete wavelet transform the signal is analyzed at
different frequency bands with different resolution by
decomposing the signal into a coarse approximation
and detail information. The coarse approximation is
then further decomposed using the same wavelet
decomposition step. This is achieved by successive
high pass and low pass filtering of the time domain
signal.
Approximations (Ai) signify low frequency
components and details (Di) signify high frequency
components of the signal.
Signal ‘S' is decomposed into high frequency
component (detail D1) and low frequency component
(approximation A1). Now approximation ‘A1' is
further decomposed into high frequency component
(detail D2) and low frequency component
(approximation A2). Similarly the decomposition of
approximations is continued up to 12th level.
Using Matlab, when we program to decompose the
noisy signal we obtain co-efficients of the
approximations and details. These are reconstructed
to obtain approximation and detail information.
To remove the high frequency noise we need to
remove the detail components from the signal as they
are high frequency component of the signal.
After removing high frequency detail components
from the signal or equivalently adding all the low
frequency approximation and detail components we
obtain the filtered signal which is similar to the
original ECG signal.

Figure 5.2: Signal Processing using Wavelets
Figure 5.3: Filtered Signal in comparison to High
Frequency Noisy Signal
In the figure red colour represents noisy signal
and the blue colour represents the reconstructed
signal.
Mean Square Error of 16384 samples with
respect to the original signal is 0.3524 Frequency
Response of Reconstructed approximation and detail
vectors for High Frequency Noise
The drift of the base line with respiration can be
represented by a sinusoidal component at the
frequency of respiration added to the ECG signal.
The amplitude and the frequency of the sinusoidal
component should be variables. Extraneous low
frequency components can severely influence the
visual interpretation of an ECG as well as the results
obtained from computer based ECG analysis.
Removal of base line wander is therefore required in
the analysis of the ECG signals to minimize the
changes in beat morphology with no physiological
counterpart. Respiration and electrode impedance
changes due to perspiration are important sources of
base line wander in most types of ECG recordings.
The frequency content of the base line wander is
usually in a range well below 0.5Hz. The variations
could be reproduced by amplitude modulation of the
ECG by the sinusoidal component added to the base
line. Reduction of ECG baseline wandering is very
important for the measurement of the S-T segment
with high accuracy, which is used for diagnosing
ischemia, myocardial infarction and indicating the
imbalance of myocardial oxygen supply.
We have a low frequency noise which is
superimposed on ECG signal which is to be denoised
using wavelet transform.
Frequency of noise: 0.4 Hz
Result:
We generated a low frequency cosine signal and
Figure 5.5.
Figure 5.4: Noisy Signal for Baseline Wandering
Noise of Frequency 0.4 Hz
Wavelet used: - Daubechies wavelet (db7) up to level
12
Referring to the explanation of discrete wavelet
transform in the previous problem
To remove the low frequency noise we need to
remove the approximation components from the
signal as they are low frequency component of the
signal.
After removing low frequency approximation
components from the signal or equivalently adding
all the high frequency detail components we obtain
the filtered signal which is similar to the original
ECG signal.
The filtered signal is as in the Figure-5.6 along with
the noisy signal.
Power Line Interference consists of 50-60Hz
pickup and harmonics, which can be modeled as
sinusoids. Characteristics, which might need to be
varied in a model of power line noise, of 60Hz
component (as most of the signals of study were
digitized in USA), include the amplitude and
frequency content of the signal. The amplitude varies
up to 50 percent of the peak to peak ECG amplitude
where power signal is affecting the signal between
1000 to 3000 units of time.
We have a high frequency noise which is
superimposed on ECG signal which is to be denoised
using wavelet transform.
Frequency of noise: 50 Hz

Result:
We generated a high frequency sinusoidal signal and
Figure-5.8.
Figure 5.8: Noisy Signal for Power Line Interference
of Frequency 50 Hz
Wavelet used: - Daubechies wavelet (db22) up to
level 12
Referring to the explanation of discrete wavelet
transform in the first problem
To remove the high frequency noise we need to
remove the detail components from the signal as they
are high frequency component of the signal.
After removing high frequency detail
components from the signal or equivalently adding
all the low frequency approximation and detail
components we obtain the filtered signal which is
similar to the original ECG signal.
VI. CONCLUSION
We have taken three ECG signals, which are
superimposed by three different noises, viz., baseline
wander, power line interference and muscle
contraction, thereby obtaining noisy ECG signals.
Then we have decomposed them using wavelet
decomposition.
The signals are reconstructed by adding
‘selected' appropriate approximation and detail
information.
Finally comparing the reconstructed ECG signals
with the original ECG signal, error is obtained, which
is very low, as specified in the results in the above
section.
REFERENCES
[1] Gargour, C.S. and Ramachandran, V., "A
Scheme for Teaching Wavelets at the
Introductory Level," Concordia University,
Montreal, Canada.
[2] Daqrouq,K., "ECG Baseline Wandering
Reduction Using Discrete Wavelet
Transform," Asian Journal of Information
technology, 4(11), 989-995, 2005.
[3] Qaio, F.,"Introduction to Wavelet - A
Tutorial," Workshop 118 on Wavelet
Application in Transportation Engineering,
January 09, 2005.
[4] Mahmoodabadi, S.Z., Ahmadian, A. and
Abolhasani, M.D., "ECG Extraction using
Daubechies Wavelets," Proceedings of the
fifth IASTED International Conference on
Visualisation, Imaging, and Image
processing, Benidorm, Spain, September 07-
09, 2005.
[5] Mozaffary, B. and Tinati, M.A., "ECG
Baseline Wander Elimination using Wavelet
Packets," Proceedings of World Academy of
Science, Engineering and Technology,
vol(3), January 03, 2005.
[6] Jamshaid, K., Akram, O., Sabir, F., Shah,
S.I., and Ahmed, J., "Application of
Adaptive and Non-Adaptive Filters in ECG
Signal Processing," GIK Institute of
Engineering Sciences and Technology.
[7] Polikar, R., "The Wavelet Tutorial", Iowa
State University, [http://engineering.rowan.
edu/~polikar/WAVELETS/WTtutorial.html],
1996.

Denoising of ECG -- A discrete time approach using DWT

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