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Research Article
Performance Comparison of Wavelet and Multiwavelet
Denoising Methods for an Electrocardiogram Signal
Balambigai Subramanian,1Asokan Ramasamy,2and Kamalakannan Rangasamy1
1Department of Electronics and Communication Engineering, Kongu Engineering College, Perundurai, Erode District,
TamilNadu638052,India
2Kongunadu College of Engineering and Technology, ottiyam, Trichy District, Tamil Nadu 621215, India
Correspondence should be addressed to Balambigai Subramanian; bharathian@yahoo.com
Received January ; Revised April ; Accepted April ; Published May
Academic Editor: Feng Gao
Copyright © Balambigai Subramanian et al. is is an open access article distributed under the Creative Commons
Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is
properly cited.
e increase in the occurrence of cardiovascular diseases in the world has made electrocardiogram an important tool to diagnose
the various arrhythmias of the heart. But the recorded electrocardiogram oen contains artefacts like power line noise, baseline
noise, and muscle artefacts. Hence denoising of electrocardiogram signals is very important for accurate diagnosis of heart diseases.
e properties of wavelets and multiwavelets have better denoising capability compared to conventional ltering techniques. e
electrocardiogram signals have been taken from the MIT-BIH arrhythmia database. e simulation results prove that there is a
.% increase in the performance of multiwavelets over the performance of wavelets in terms of signal to noise ratio (SNR).
1. Introduction
In modern medicine, there are many methods to diagnose
heart disease such as electrocardiogram (ECG), ultrasound,
magnetic resonance imaging (MRI), and computer tomog-
raphy (CT). Among these methods, diagnosis using elec-
trocardiogram has the advantages of convenience and low
cost so that it can be used in a wide area. However, certain
arrhythmia (a fast, slow, or irregular heartbeat) which can
cause abnormal symptoms may occur only sporadically or
may occur only under certain conditions such as stress.
Arrhythmia of this type is dicult to obtain on an electro-
cardiogram tracing that runs only for a few minutes. e
electrocardiogram is the record of variation of bioelectric
potential with respect to time as the human heart beats. Due
toitseaseofuseandnoninvasiveness,electrocardiogram
plays an important role in patient monitoring and diagnosis.
e change in solar activity including electrocardio-
graphicdatawithvariationsingalacticcosmicrays,geomag-
netic activity, and atmospheric pressure suggests the possi-
bility of links among these physical environmental variations
and health risks, such as myocardial infarctions and ischemic
strokes. An increase in the incidence of myocardial infarction
in association with magnetic storms has been reported by
Corn´
elissen et al. [].
Magnetic storms are found to decrease heart rate variabil-
ity (HRV) indicating a possible mechanism since a reduced
HRV is an important factor for coronary artery disease and
myocardial infarction. An increase of % in mortality during
years of maximal solar activity is found when compared with
years of minimal solar activity. ese chronodiagnostics are
particularly important for those venturing into regions away
from hospitals.
Goudarzi et al. []madeaneorttondtheoptimum
multiwavelet for compression of ECG signals to be used
along with SPIHT codec. is work examined dierent
multiwavelets on sets of ECG data with entirely dierent
characteristics selected from MIT-BIH database and assessed
the functionality of the dierent multiwavelets in compress-
ing electrocardiogram signals and their simulation results
showed the cardinal balanced multiwavelet (cardbal) by the
means of identity (Id) preltering method to be the best
eective transformation and the most ecient multiwavelet
was applied for SPIHT coding algorithm on the transformed
signal by this multiwavelet.
Hindawi Publishing Corporation
Journal of Applied Mathematics
Volume 2014, Article ID 241540, 8 pages
http://dx.doi.org/10.1155/2014/241540
Journal of Applied Mathematics
Kania et al. [] studied the application of wavelet denois-
ing in noise reduction of multichannel high resolution ECG
signals. e inuence of the selection of wavelet function
and the choice of decomposition level on eciency of
denoising process was considered and whole procedures of
noise reduction were implemented in MATLAB environment
using the fast wavelet transform. e denoising method was
foundtobeadvantageoussincenoiselevelwasdecreased
in ECG signals, in which noise reduction by averaging had
limited application, that is, in case of arrhythmia.
Helenprabha and Natarajan []proposedatechnique
used for measuring electrical signals generated by foetal heart
as measured from multichannel potential recordings on the
mother’s body surface. ey proposed a new class of adaptive
lter that combines the attractive properties of nite impulse
response (FIR) lter with innite impulse response (IIR)
lter. e maternal ECG and foetal signals were simulated
using MATLAB. e gamma lter design was implemented
in FPGA Spartan E which was programmed using VHDL.
eirresultshavesolvedthecomplexsituationsmorereliably
than normal adaptive methods used earlier for recovering
foetal signals.
Chang et al. [] proposed measures to make the optimal
lter design under dierent constraints possible for ECG
signal processing. Experiments have been conducted by them
with articially and practically corrupted ECG signals for
PLI adaptive ltering technique. e assessments included
the convergence time, the frequency tracking eciency,
theexecutiontime,andtherelativestatisticsintimeand
frequency domain. e results demonstrated that there is no
universal optimum approach for this application thus far.
Alfaouri and Daqrouq [] performed wavelet transform
thresholding technique for ECG signal denoising. ey
decomposed the signal into ve levels of wavelet transform
using the Daubechies wavelet (db) and determined a thresh-
oldthroughalooptondthevaluewhereminimumerror
was achieved between the detailed coecients of threshold
noisy signal and the original signal. e threshold value was
accomplished experimentally aer using a loop of calculating
a minimum error between the denoised wavelet subsignals
and the original free of noise subsignals. e experimental
application of the threshold result was better than Donoho’s
threshold particularly in ECG signal denoising.
Zhidong and Chan []proposedanovelmethodforthe
removal of power line frequency from ECG signals based
on empirical mode decomposition (EMD) and adaptive
lter. A data-driven adaptive technique called EMD was
used to decompose ECG signal into a series of intrinsic
mode functions (IMFs). e adaptive power line cancellation
lter was designed to remove the power line interference,
the reference signal of which was produced by selective
reconstruction of IMFs. Clinic ECG signals were used to
evaluate the performance of the lter. Results indicated that
the power line interference of ECG was removed eectively
by the new method.
Kaur and Singh [] proposed a combination method
for power line interference reduction in ECG. e methods
were moving average method and using the IIR notch
characteristics. eir results showed reduction in the power
line noise in the ECG signal using the proposed lter that has
fewer coecients and hence lesser computation time for real
time processing.
Haque et al. [] used wavelet method to detect the small
variations of ECG features. ey simulated standard ECG
signals as well as the simulated noise corrupted signal using
FFT and wavelet for proper feature extraction. ey found
wavelettobesuperiortotheconventionalFFTmethodin
nding the small abnormalities in electrocardiogram signals.
Tan and L ei [ ] used wavelet transform to lter out
noise interferences of electrocardiogram signals for the l-
tering of the myoelectric interference, the power frequency
interference, and the baseline dri. Firstly Coif wavelet was
adapted to decompose electrocardiogram signals containing
noises.Secondly,thesoandhardthresholdvaluequantied
high-frequency coecients of every scale and nally the
electrocardiogram were reconstructed using high-frequency
coecients of every scale which were quantied by the
threshold value. Experiments showed that wavelet transform
had good real time ltering eect and it had more advantages
than traditional methods.
2. Materials and Methods
2.1. Wavelet Method. Awaveletissimplyasmallwavewhich
has energy concentrated in time. It is compactly supported
andhasniteenergyfunction.Itcansatisfyadmissibil-
ity condition and could be amendable for multiresolution
analysis. e wavelet transform is a mathematical tool for
decomposing a signal into a set of orthogonal waveforms
localized both in time and frequency domains. e wavelet
transform is a suitable tool to analyse the electrocardiogram
signal, which is characterized by a cyclic occurrence of
patterns with dierent frequency content (Pwave, QRS
complex, and Twave). It is a decomposition of the signal
as a combination of a set of basic functions, obtained by
means of dilation (a)andtranslation(b) of a single prototype
wavelet; there are several wavelet functions (mother wavelet
with dierent properties) like the Morlet or Mexican Hat
wavelets or complex frequency Bspline wavelets that are used
in study.
Wavelet analysis is done by the breaking up of a signal
into a shied and scaled version of the original wavelet. A
continuouswavelettransformcanbedenedasthesumof
overall time of the signal multiplied by a scaled and shied
version of the wavelet function. e greater the scale factor
“a” is, the wider the basis function is and, consequently,
the corresponding coecient gives information about lower
frequency components of the signal and vice versa.
e wavelet transform is designed to address the problem
of nonstationary signals such as electrocardiogram signals.
It involves representing a time function in terms of simple,
xed building blocks, and termed wavelets. e next step
is the selection of number of decomposition levels of signal
𝑖();seeFigure . First decomposition level is obtained by
using two complementary high- and low-pass lters and
then half of the samples are eliminated. e lters cut
frequency is equal to half of the bandwidth of analysed signal.
Journal of Applied Mathematics
lter
lter
2
2
Low-pass
Low-pass
Low-pass
lter
High-pass
High-pass
High-pass
lter
2
2
lter
lter
2
2
Level 1 Level 2 Level 3
Approximation
Detail
x(n)
cD1
cD2
cD3
cA1
cA2
cA3
F : Diagram of multiresolution analysis of signal 𝑖().
Such algorithm, which is amplication of discrete wavelet
transform, is known as fast wavelet transform.
For analysis the following mother wavelet was used:
Ψ𝑚,𝑛 ()=2−𝑚/2Ψ2−𝑚−, ()
where is coecient of time translation and is coecient
of scale (compression).
In the rst step threshold values for detail coecients at
every level of decomposition are determined according to the
following relationship:
THR𝐽=2log
𝑗
.()
e next step is the modication of values of the jth level
detail coecients basis of appointed threshold. is method
is called so thresholding procedure as follows:
𝑗()=sgn 𝑗()||−THR𝑗; 𝑗()>THR𝑗,
0; 𝑗()≤THR𝑗.()
e nal step of the analysis is reconstruction of signal
𝑖()based of approximation coecients chosen th level of
decomposition (𝑖) and modied detail co ecients from th
(𝑖)aswellashigherlevelsofdecomposition
𝑖()=
𝑛𝑚,𝑛Φ𝑘2−𝑚−
+𝑚𝑘
𝑚=𝑚0
𝑛𝑚,𝑛Ψ𝑚,𝑛 2−𝑚−, ()
where Φ𝑘()is scaling function from kth level of decompo-
sition and Ψ𝑚,𝑛()are wavelet functions for =
0,...,𝑘
levels of decomposition.
e advantages of wavelet methods are possibility of
receiving good quality signal for beat to beat analysis and
possibility of having high quality signal while averaging
technique is impossible, as causing morphology distortion
of electrocardiogram signals, it provides a way for analysing
waveforms bounded in both frequency and duration, it allows
signals to be stored more eciently than by the Fourier
transform,itcanleadtobetterapproximatereal-worldsignals
anditiswell-suitedforapproximatingdatawithsharp
discontinuities. e disadvantage of wavelet method is that
the wavelet transforms ignore polynomial components of the
signal up to the approximation order of the basis.
2.2. Equation for Continuous Wavelet Transform. e wavelet
transform equation is given by
CWTΨ
𝑥(,)=Ψ(,)=1
||𝑡()Ψ∗−
, ()
where () = given signal, =translation parameter, =
scaling parameter =1/,andΨ()=mother wavelet.
2.3. Multiwavelet Method. Multiwavelets constitute a new
chapter which has been added to wavelet theory in recent
years. Recently, much interest has been generated in the study
of the multiwavelets where more than one scaling functions
and mother wavelet are used to represent a given signal. e
rst construction for polynomial multiwavelets was given by
Albert, who used them as a basis for the representation of
certain operators. Later, Geronimo, Hardin, and Massopust
constructed a multiscaling function with components using
fractal interpolation.
In spite of many theoretical results on multiwavelet,
their successful applications to various problems in signal
processing are still limited. Unlike scalar wavelets in which
Mallet’s pyramid algorithm have provided a solution for good
signal decomposition and reconstruction, a good framework
for the application of the multiwavelet is still not available.
Nevertheless, several researchers have proposed method of
Journal of Applied Mathematics
how to apply a given multiwavelet lter to signal and image
decomposition.
2.4. Multiscaling Functions and Multiwavelets. e concept
of multiresolution analysis can be extended from the scalar
case to general dimension N. A vector valued function
=[
12,...,𝑟]𝑇belonging to 2()𝑟and Niscalleda
multiscaling function if the sequence of closed spaces
𝑗=span 2𝑗/2𝑖2𝑗−:1≤≤,∈.()
∈constitute a multiresolution analysis (MRA) of
multiplicity for 2(). e multiscaling function must
satisfy the two-scale dilation equation
()=2
𝑘𝑘(2−).()
Now let 𝑗denote a complementary space of 𝑗in 𝑗+1.e
vector valued function Ψ=[Ψ
1Ψ2,...,Ψ𝑟]𝑇such that
𝑗=span 2𝑗/2𝑖2𝑗−:1≤≤,∈.()
∈is called a multiwavelet. e multiscaling function must
satisfy the two-scale equation
Ψ()=2
𝑘𝑘(2−).()
𝑘∈
2()𝑟×𝑟 is an ×matrix of coecients. e two-
scale equations ()and()canberealizedasamultilterbank
operating on input data streams and ltering them in two
routput data streams, each of which is downsampled by a
factor of two. If ()isthegivensignalanditisassumedthat
()∈ 0,then
()=2
𝑘𝑇
0,𝑘(−).()
And the scaling coecient 𝑇
1,𝑘 of the rst level can be consid-
ered as a result of low-pass multiltering and downsampling
as follows:
1,𝑘 =
𝑚𝑚−2𝑘0,𝑚.()
Analogously, the rst level multiwavelet coecients 1,𝑘 are
obtained using high-pass multiltering and downsampling as
follows:
1,𝑘 =
𝑚𝑚−2𝑘0,𝑚.()
Full multiwavelet decomposition of the signal () can be
found by iterative ltering of the scaling coecient as follows:
𝑗,𝑘 =
𝑚𝑚−2𝑘𝑗−1,𝑚,
𝑗,𝑘 =
𝑚𝑚−2𝑘𝑗−1,𝑚.()
Note that 𝑗,𝑘 and 𝑗,𝑘 are ×1column vectors.
2.5. Advantages of Wavelets and Multiwavelets Compared to
Conventional Filtering Techniques
(i) e Fourier transform fails to analyze the nonsta-
tionary signal, whereas wavelet transform allows the
components of a nonstationary signal to be analyzed.
(ii) Wavelet transform holds the property of multires-
olution to give both time and frequency domain
information in a simultaneous manner.
(iii) A set of wavelets which are complementary can
decompose the given data without gaps or overlap so
that the decomposition process becomes mathemati-
cally reversible.
2.6. Comparison between Wavelet and Multiwavelet. Multi-
wavelets contain multiple scaling functions, whereas scalar
wavelets contain one scaling function and one wavelet.
is leads to more degrees of freedom in constructing
wavelets. erefore, opposed to scalar wavelets, properties
such as compact support, orthogonality, symmetry, vanishing
moments, and short support can be gathered simultaneously
in multiwavelets which are fundamental in signal processing.
e increase in degree of freedom in multiwavelets is
obtained at the expense of replacing scalars with matrices,
scalar functions with vector functions, and single matrices
with block of matrices. However, preltering is an essential
task which should be performed for any use of multiwavelet
in signal processing.
3. Results and Discussions
3.1. Data Collection
3.1.1. MIT-BIH Arrhythmia Database. MIT-BIH arrhythmia
database consists of -half-hour electrocardiogram record-
ings. e recordings were digitized at Hz (samples per
secondperchannel)with-bitresolutionovermV.e
simulations were carried out in MATLAB environment
Rb. Various benchmark records from the MIT-BIH
database were considered for this study.
(A) Performance Analysis of Wavelet Based Denoising Method
for Electrocardiogram
Wav e l e t D e n o i s i n g Usin g B i o r t h o g o n a l 1 D Wavelet. Figure
shows the wavelet denoising for the record m in which
level approximation coecient 1for Biorthogonal wavelet
shows that there is maximum noise in it. Hence reconstruc-
tion of the original signal to obtain the denoised electrocar-
diogram from 1coecients will also contain the maximum
noise. e level decomposition contains the least noise and
hence reconstruction is done using 4.
Original and Denoised Signals Using Biorthogonal Wavelet.
Figure shows the comparison of the original signal and
the denoised signal using Biorthogonal wavelet at level
decomposition for the record m. In this the signal to
noise ratio obtained is . dB and the power line noise
Journal of Applied Mathematics
500 1000 1500 2000 2500 3000 3500
0
100
950
1000
1050
1100
1150
1000
s
a4
d4
d
2
−4
500
1
00
0
1500
2
000
2
500
3000
3500
0
100
95
0
1
000
1
05
0
11
00
11
5
0
1
000
4
4
2
−
4
F : Wavelet denoising for ECG record no m using Biorthogonal D wavelet.
500 1000 1500 2000 2500 3000 3500
900
1050
1100
1150
1200
1250
1300
Original and denoised signals
Original ECG signal
Denoised ECG signal
5
0
0
1
000
1
50
0
200
0
250
0
3
000
3
500
90
0
1050
1
1
0
0
1
1
50
1
2
00
1250
1300
O
ri
g
inal and denoised si
g
nal
s
F : Original and denoised signals for ECG record no m using Biorthogonal wavelet.
is reduced for this record. Figure shows the approximation
and coecient details aer the signal in record m has
been subjected to the Biorthogonal wavelet transform and
Figure shows the original and denoised electrocardiogram
in the record m. e signal to noise ratio obtained is
.dB. is shows that the noise has to be removed further
to enhance the quality of the obtained electrocardiogram.
(B) Performance Analysis of Multiwavelet Based Denoising
Method for Electrocardiogram
Biothogonal Based Multiwavelet Denoising. e multiwavelet
denoising for the record m shown in Figure yields
a signal to noise ratio of . dB in which the power
line noise gets removed. Figure shows the multiwavelet
denoising for the record m and the signal to noise ratio
obtained is . dB because of the removalof power line
noise.
3.2. Performance Comparison of Wavelet and Multiwavelet
Methods. Comparison of signal to noise ratio for wavelet
and multiwavelet based denoising techniques for various
electrocardiogram records.
4. Conclusion
e inference from Tables ,,,andis that the output signal
tonoiseratiovalueofmultiwaveletdenoisingfunctionsis
Journal of Applied Mathematics
3500
−5
0
5
−20
0
20
−100
−50
0
50
−100
0
100
200
1000
1100
1200
1300
1000
1200
1400
s
.
a4
d4
d3
d2
d1
Decomposition at level 4:s=a
4+d
4+d
3+d
2+d
1
3
5
00
−
5
0
5
−2
0
0
2
0
−1
00
−
50
0
50
−1
00
0
1
00
2
00
1
000
11
00
12
00
1
300
1
00
0
12
0
0
140
0
s
a
4
d
4
d
3
d
2
d
1
F : Wavelet denoising for ECG record no m using Biorthogonal D wavelet.
500 1000 1500 2000 2500 3000 3500
1000
1050
1100
1150
1200
1250
1300
1350
1400
1450
Denoised signal
500
1000
1500
2
000
2
500
3000
3500
100
0
105
0
1
1
00
1
1
50
1
2
00
1
2
50
1300
1350
1
4
0
0
1
4
5
0
D
enoised si
g
nal
Original ECG signal
Denoised ECG signal
F : Original and denoised signals for ECG record no m using Biorthogonal wavelet.
T : Performance comparison of wavelet and multiwavelet for
record m.
Wav e l e t f a m i l y
SNR (dB)
Record no m
Wavelet Multiwavelet
Bio . . .
Db . .
Db . .
Coif . .
Sym . .
greater than the signal to noise value of wavelet functions. e
table also indicates that the Daubechies wavelet has better
denoising capability than when compared to corresponding
values of the wavelet denoising as the shape of this wavelet
T : Performance comparison of wavelet and multiwavelet for
record m.
Wav e l e t f a m i l y
SNR (dB)
Record no m
Wavelet Multiwavelet
Bio . . .
Db . .
Db . .
Coif . .
Sym . .
is more close to the shape of electrocardiogram. e increase
in signal to noise ratio value indicates that there is no loss in
the information contained in the original electrocardiogram
signal and multiwavelet has better denoising capability to
Journal of Applied Mathematics
500 10001500 2000 2500 3000 3500
900
950
1000
1050
1100
1150
1200
1250
1300
1
Signals
500 10001500 2000 2500 3000 3500
D1 D2 D3 D4 A4
500 10001500 2000 2500 3000 3500
850
900
950
1000
1050
1100
1150
1200
1250
1300
1350 Denoised signals
Coecients
F : Multiwavelet denoising for ECG record no m using Biorthogonal D wavelet.
1000
1050
1100
1150
1200
1250
1300
1350
1400
1450
1
D1 D2 D3 D4 A4
500 10001500 2000 2500 3000 3500500 10001500 2000 2500 3000 3500500 10001500 2000 2500 3000 3500 900
1000
1100
1200
1300
1400
1500
Signals Denoised signals
Coecients
F : Multiwavelet denoising for ECG record no m using Biorthogonal D wavelet.
T : Performance comparison of wavelet and multiwavelet for
record m.
Wav e l e t f a m i l y
SNR (dB)
Record no m
Wavelet Multiwavelet
Bio . . .
Db . .
Db . .
Coif . .
Sym . .
T : Performance comparison of wavelet and multiwavelet for
record m.
Wav e l e t f a m i l y
SNR (dB)
Record no m
Wavelet Multiwavelet
Bio . . .
Db . .
Db . .
Coif . .
Sym . .
Journal of Applied Mathematics
remove the power line noise in the various electrocardiogram
records.
Conflict of Interests
e authors declare that they have no conict of interests
regarding the publication of this paper.
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http://www.hindawi.com Volume 2014
Decision Sciences
Advances in
Discrete Mathematics
Journal of
Hindawi Publishing Corporation
http://www.hindawi.com
Volume 2014
Hindawi Publishing Corporation
http://www.hindawi.com Volume 2014
Stochastic Analysis
International Journal of
