Journal of Signal and Information Processing, 2013, 4, 164-167
doi:10.4236/jsip.2013.43B029 Published Online August 2013 (http://www.scirp.org/journal/jsip)
Comparison of Wavelet Types and Thresholding Methods
on Wavelet Based Denoising of Heart Sounds
Burhan Ergen
Department of Computer Engineering, Firat University, Elazig, Turkey.
Received April, 2013.
ABSTRACT
This paper focuses on the denoising of phonocardiogram (PCG) signals by means of discrete wavelet transform (DWT)
using different wavelets and noise level estimation methods. The signal obtained by denoising from PCG signal con-
taminated white noise and the original PCG signal is compared to determine the appropriate parameters for denoising.
The comparison is evaluated in terms of signal to noise ratio (SNR) before and after denoising . The results showed that
the decomposition lev el is the most important parameter determining the denoising quality.
Keywords: Discrete Wavelet Transform; Denoising; PCG
1. Introduction
The structural defects of the heart are often reflected on
the acoustical vibrations produced as a result of the me-
chanical action of the heart. The proper analysis of heart
sound allows non-invasive detection of coronary artery
stenosis, and valve disorders causing the heart murmurs
[1]. It is possible a computer aided detection of the ab-
normalities by means of processing and analyzing of the
acoustical vibration [2]. A record of the acoustical vibra-
tions acquired by means of microphones, called phono-
cardiogram (PCG), consist of the heart sounds and the
murmurs. While the heart sounds are produced opening
and closing of the heart valves, the murmurs are pro-
duced by the turbulence of blood flow.
The heart sounds have low frequency components, and
the murmurs are high frequency signals occurring gener-
ally between heart sounds. The murmurs can be com-
monly heard in abnormal cardiovascular cases. The fre-
quency components of a PCG signal may achieve around
1 KHz, which seen particularly in abnormal patient due
to the murmurs. On contrary healthy person, the fre-
quency components can exist above 300 Hz in diseased
patients. In normal patients, the spectral energy exists in
the interval of 100 and 200Hz, and rarely reaches up
300Hz [3].
This noise decreases the performance of visual and
computerized analysis. The respiration sounds by lung
mechanical actions, patient movement, and improper
contacts of microphone to the skin, and external noises
from the environments are also added as noise signal into
PCG records. The traditional method to remove the noise
from a PCG signal is to use a low or band pass filter with
cut off frequencies. However the filtering techniques are
able to remove a relevant of the noise, they are incapable
if the noise in the band of the signal to be analyzed.
In the present study, we performed the discrete wave-
let transform (DWT) to overcome the limitations of the
traditional methods. The denoising based on DWT is
consist of three steps; decomposition of the signal, thre-
sholding and reconstruction of the signal. Hard and soft
thresholding approaches are usually applied to eliminate
of small coefficient in denoi sing process.
In the hard thresholding, the wavelet coefficient below
a give value are stetted to zero, while in soft thresholding
the wavelet coefficient are reduced be a quantity to the
thresh value. The thresh old value is the estimation of th e
noise level, which is generally calculated from the stan-
dard derivation of the detail coefficient. The given signal
is decomposed on to a set of orthonormal wavelet func-
tion that constitutes a wavelet basis. The most known
wavelets providing the ortogonality properties are Du-
bechies, Symlets, Coiflets and Discrete Meyer to provide
reconstruction using the fast algorithms.
The result of the DWT is a multilevel decomposition,
in which the signal is decomposed in ‘approximation’
and ‘detail’ coefficients at each level. This is made
through a process that is equivalent to low-pass and high
passes filtering, respectively [4]. DWT decomposition
leads to a tree structure as shown in Figure 1, where ap-
proximation and detail coefficients are presented.
Here, it is studied on the effects of wavelet types, de-

Comparison of Wavelet Types and Thresholding Methods on Wavelet Based Denoising of Heart Sounds 165
composition levels, thresholding techniques and noise
estimation method s.
x
Ax
AAx
AAAx DAAx
DAx
Dx
L1
L2
L3
N
N/2
N/4
N/8
Figure 1. The approximation and the detailed coefficients in
the tree structure of the DWT.
2. Methods
2.1. Discrete Wavelet Transform
The wavelet transform is first introduced for the time-
frequency analysis of transient continuous signal, and
then extended to the theory of multi-resolution wavelet
transform using FIR filter approximation. The discrete
wavelets used in multi- res-
olution analysis constituting an orthonormal basis for
[5,6].
)2(2)( 2/
,ntt mm nm  

)(
2L)(txis decomposed an different scale,
 




 







L
mk k
kLLkmm tkAtkDtx
1,, )()()()()(

(1)
where )(
,t km

is discrete analysis wavelet, and )(
,t kL

is discrete scaling, is the detailed signal at scale
, and is the approximated signal at scale.
and is obtained using the scaling and
wavelet filters [4,8].
)(kDm
m
2(Dm )(kALAL
L
2
)k)k(
)1(
)2(),(2)(
)2(),(2)(
2/1
2/1
nh(-1)
nttng
nttnh
n






(2)
The wavelet coefficient can be computed by means of
a pyramid transfer algorithm. The algorithms refer to a
FIR filter bank with low-pass filter h, high-pass filter g,
and down sampling by a factor at each stage of the
filter bank [6]. Figure 1 shows the tree structure of DWT
decomposition for three levels.
2
2.2. Threshold Estimation
The main idea of the wavelet denoising to obtain the
ideal components of the signal from the noisy signal re-
quires the estimation of the noise level. There are many
possible approaches to the estimation of the noise level,
and a systematic investigation about their performance [8,
9]. In this work, four different threshold options were
applied to assess their effectiveness.
Rigresure is adoptive threshold selection using the
Stein’s unbiase d ri sk estimation criteria;
)loglog(2 2NNThValue   (3)
where is the length of the signal, and N

is the stan-
dard deviation of the noise. The latter is estimated from
the detail coefficient at the first level of signal decompo-
sition; 674.0/)(Dxmedian

Sqtwolog is defined as the universal threshold;
)(log2 NThValue e   (4)
Heursure is the heuristic version that uses a mixture of
the previous rules.
Minimaxi is a threshold selection using the minmax
principle. A fixed threshold is selected to get the min-
mum of the maximum mean square error, obtained the
worst function in given set, when compared against a
ideal procedure.
2.3. Assessments for Comparison
The studies were made on a heart sounds contaminated at
a desired SNR level by white Gaussian noise. Measuring
the performance of the denoising method by calculation
of the residual SNR (SNR) gi ven as;

  
0
12
10 12
0
01
10log logn
N
N
dn
n
xn
SNR xnx n










 (5)
where is the original sign al, is the denoised
signal. The comparison between the initial SNR and the
result SNR may be used as the performance indicator.
][nx ][nxdn
3. Experiments and Results
The assessments were made of the behavior of different
mother wavelets and four different threshold estimation
techniques in order to find the most reliable parameters
for DWT denoising of heart so unds. These hav e drowned
from the most used wavelet families, Daubechies, Sym-
lets, Coiflets, and Discrete Meyer.
The PCG signal was contaminated at SNR=5dB in or-
der to test the performance of the wavelets and the thre-
shold estimation techniques. A normal PCG signal gen-
erally contains only two heart sounds, first and second
heart sounds. Figure 2 illustrates a sample PCG signal,
the noisy signal, a denoised sample using DWT, and the
error between the original and the denoised PCG signals.
The frequency components of a normal PCG signals
can be rise up 200 Hz, and the energy of the most sig-
nificant components concentrates around the frequency
band 100 - 150 Hz. The frequency ban ds of the signal are
important in point of the denoising technique using DWT
approaches. Because the DWT approaches decomposes

Comparison of Wavelet Types and Thresholding Methods on Wavelet Based Denoising of Heart Sounds
166
the signal into frequency bands to eliminate the detail
components assumed as noise, the decomposition level
reflects directly on the frequency components that cause
the smoothed version of the signal.
(a) (b)
(c) (d)
Figure 2. Wavelet denoising of a PCG signal, a) Original
signal, b) Noisy signal, c) Denoised signal, d) Error between
the original and the denoised signal.
The effected components are related to not only de-
composition level but also sampling frequency. The de-
composition level, l, influences the frequency bands by
dividing the sampling frequency respect to 2l. In our ex-
periments, choosing l=5 causes the proceeding of the
denoising process down to 150 Hz due to the sampling
frequency is 11.5 Hz.
Therefore, the most important factor determining the
SNR level is the depth of the decomposition. Table 1
presents the SNR results respect to the decomposition
level with by using symlet8 and rigresure estimation for
hard and soft tresholding. For the both tresholding tech-
niques, it is seen that the highest SNR values obtained
when the composition level is 5 due to the reason ex-
pressed above.
Table 1. SNR level respect to the depth of decomposition.
Level Hard Soft
1 8.1209 7.8843
2 11.1471 10.9218
3 14.3251 14.0031
4 17.2973 16.9275
5 20.1305 19.4396
6 13.2248 13.2472
7 12.1531 9.8726
8 10.8010 8.3255
9 10.4986 8.1632
10 10.4912 8.1593
The other parameters to obtain best SNR level are the
kind of the wavelet and the thresholding rule. Table 2
presents the SNR leve ls using different wavelet when the
decomposition level is 5. In Table 2, there is no signifi-
cant difference in SNR in terms of wavelet type s. Never-
theless, it is attracting that the mother wavelets having
high oscillation number produces better SNR results.
Table 2. SNR values respect to wavelet types (Rigrsure,
level = 5).
Wavelet Type Hard Soft
Daubechies2 16.5378 16.5057
Daubechies3 18.9391 18.8353
Daubechies4 19.8138 19.8002
Daubechies5 19.8747 19.7425
Symlet2 16.3487 16.4181
Symlet3 18.5401 18.7874
Symlet4 19.5732 19.8002
Symlet5 19.4795 19.5458
Coiflet1 16.7746 16.7658
Coiflet2 19.4866 19.4501
Coiflet 3 19.7812 19.6252
Discrete Meyer 19.9018 19.7154
It is attracting that the wavelets having higher oscilla-
tion frequency gives better SNR results. For example, the
symlet wavelet having eight oscillations in its mother
wavelet produces better SNR level than the lower ones.
The very lower oscillation frequency causes the lower
SNR results.
The estimation techniques show the same performance
for the level 5 respects to the initial SNR level. For the
comparison, the initial SNR level before denoising is
increased from 1dB to 30dB, and the result SNR level
after denoising is calculated using Equation (5). Figure 3
presents a comparison of the four noise estimation me-
thods for level 5 and 8 by using Symlet8.
We have observed no distinguishing evidence among
the noise level estimation methods until level 6. After
this level, rigresure method has produced better SNR
values. And it is observed that rigresure preserve the
second heart sound in PCG signals while the other me-
thods destroying. This situation is clearly seen in Figure
4.
The signal part belonging to second heart sound taking
place at around 0.7 s in Figure 4 (a) cannot be seen in
the other figures. This also proves that the rigresure pre-
serve the main characteristic of the signal. Therefore, we
can conclude that the rigresure is the best noise estima-
tion method.

Comparison of Wavelet Types and Thresholding Methods on Wavelet Based Denoising of Heart Sounds
167
(a)
(b)
Figure 3. The SNR values after denoising before denoising
for level 5 and 8.
(a) (b)
(c) (d)
Figure 4. The denoised signal using four different threshold
rules at eighth level.
4. Conclusions
The wavelet denoising techniques were studied on a
noised PCG signal in this work. The performances of
several variations of denoising including thresholding
rules and the type of wavelet were compared to produce
the best denoising results of the methods.
We conclude that reasonable decomposition level is
bsolutely depending on the sampling frequency and the
frequency band of the signal. Just in this study, the de-
composition level of 5 produced reasonable results be-
cause the frequency band of a normal PCG signal is
around 150 - 200 Hz and the sampling frequency is 11.5
KHz. Since the noise level method is one of the impor-
tant parameter in wavelet denoising, it is examined for
different levels. We have not seen any noteworthy dif-
ferences in the methods from level 1 to level 6. After this
level, rigresure method has showed superiority to the
other methods in terms of SNR level. Consequently, it is
determined that the wavelet type is not very important if
the oscillation number is not very low, th e decomposition
level is absolutely depends on the frequency band of the
PCG signal and its sampling frequency, and rigresure
method is best of the noise estimation techniques.
REFERENCES
[1] M. Akay, J. L. Semmlow, W. Welkowitz, M.D. Bauer
and J. B. Kostis, “Detection of Coronnary Occlusion Us-
ing Autoregressive Modeling Diastolic Heart Sounds,”
IEEE Transactions on Biomedical Engineering, Vol. 37,
1990, pp. 336-273.doi:10.1109/10.52343
[2] L.G. Durand, M. Blanchard, G. Cloutier, H. N. Sabbah
and P.D. Stein, “Comparison of Pattern Recognition Me-
thods for Computer-Assisted Classification of Spectra of
Heart Sounds in Patient with Porcine Bioprosthetic Valve
Implanted in the Mitral Position,” IEEE Transactions on
Biomedical Engineering, Vol. 37, 1990, pp.
1121-1129.doi:10.1109/10.64456
[3] B. Ergen and Y. Tatar, “The Analysis of Heart Sounds
Based on Linear and High Order Statistical Methods,”
Proceedings of the 23rd Annual EMBS International Con-
ferences, 2001, pp. 2139-2141.
[4] P. E. Tikkanen, “Nonlinear Wavelet and Wavelet Packet
Denoising of Electrocardiogram Signal,” Biological Cy-
bernetics, Springer-Verlag, 1999.
[5] S. G. Mallat, “A Theory for Multiresolution Signal De-
composition: The Wavelet Representation,” IEEE Trans-
actions on Pattern Anal. And Mach. Int., Vol. 11, No. 7,
1989, pp. 674-693.
[6] O. Rioul, “Discrete-Time Multiresolution Theory,” IEEE
Trans. on Signal Processing, Vol. 41, No. 8, 1993, pp.
2591-2605. doi:10.1109/78.229891
[7] E. Erçelebi, “Electrocardiogram Signals Denoising Using
Lifting Based Discrete Wavelet Transform,” Comp. in
Biol. and Med., Vol. 34, 2004, pp. 479-493.
doi:10.1016/S0010-4825(03)00090-8
[8] H. F. C-Greiff, R. R-Garcia and J. V. L-Ginori, “Signal
De-noising in Magnetic Resonance Spectroscopy Using
Wavelet Transforms,” Vol.14, No. 6, 2002, pp. 388-401.
[9] A. Effern, K. Lehnertz, T. Schreiber, T. Grundwald, P.
David and C. E. Elger, “Nonlinear Denoising of Transient
Signals with Application to Event-related Potentials,”
Physica, Vol. 140, 2000, pp. 257-266.
a