ECG signal denoising using a novel approach of adaptive filters for real-time processing

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 11, No. 2, April 2021, pp. 1243~1249
ISSN: 2088-8708, DOI: 10.11591/ijece.v11i2.pp1243-1249  1243
Journal homepage: http://ijece.iaescore.com
ECG signal denoising using a novel approach of adaptive filters
for real-time processing
Amean Al-Safi
Department of Electrical and Electronics Engineering, University of Thi-Qar, Thi-Qar, Iraq
Article Info ABSTRACT
Article history:
Received Aug 16, 2019
Revised Jul 14, 2020
Accepted Sep 22, 2020
Electrocardiogram (ECG) is considered as the main signal that can be used to
diagnose different kinds of diseases related to human heart. During the
recording process, it is usually contaminated with different kinds of noise
which includes power-line interference, baseline wandering and muscle
contraction. In order to clean the ECG signal, several noise removal
techniques have been used such as adaptive filters, empirical mode
decomposition, Hilbert-Huang transform, wavelet-based algorithm, discrete
wavelet transforms, modulus maxima of wavelet transform, patch based
method, and many more. Unfortunately, all the presented methods cannot be
used for online processing since it takes long time to clean the ECG signal.
The current research presents a unique method for ECG denoising using a
novel approach of adaptive filters. The suggested method was tested by using
a simulated signal using MATLAB software under different scenarios.
Instead of using a reference signal for ECG signal denoising, the presented
model uses a unite delay and the primary ECG signal itself. Least mean
square (LMS), normalized least mean square (NLMS), and Leaky LMS were
used as adaptation algorithms in this paper.
Keywords:
Adaptive filters
ECG
ECG signal denoising
Leaky LMS
LMS
NLMS
This is an open access article under the CC BY-SA license.
Corresponding Author:
Amean Al-Safi
Department of Electrical and Electronics Engineering
University of Thi-Qar
Thi-Qar, Iraq
Email: ameen-sh@utq.edu.iq, ameansharea.ghazi@wmich.edu
1. INTRODUCTION
Electrocardiograms (ECG) signals contain different kinds of information that can be used to
diagnose various heart related diseases. They reflect the electrical activity of the human heart. ECG signals
are usually contaminated by various types of noise and artifacts. Power line interference (PLI), baseline
wander, drift in electrodes connections (electrode misconduct noise and electrode displacement artifacts), and
muscle artifacts are the most effective ones. They make the diagnosing process and obtaining the required
signal information a hard task to reach [1, 2]. Performing any kinds of physical analysis to ECG signals
should be proceeded by signal denoising process since this kind of analysis might result in wrong diagnosis
of cardiac arrhythmias [3-8]. In order to remove the contamination noise (denoising) from the recorded ECG
signal, several methods have been presented.
ECG signal denoising techniques have been designed based on median filters, adaptive filters,
Wiener filters, switching Kalman filters, polynomial filters, frequency-selective filters, singular value
decomposition (SVD), discrete wavelet transform (DWT), discrete cosine transform (DCT), empirical mode
decomposition (EMD), nonlinear Bayesian filter (NBF), mathematical morphological (MM) operators,
principal component analysis (PCA), independent component analysis (ICA), nonlocal mean (NLM)

 ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 11, No. 2, April 2021 : 1243 - 1249
1244
technique, variational mode decomposition (VMD), and EMD based technique for single and combined noise
sources removal which might be considered as the most recent technique for ECG signal denoising [9, 10].
The current existing denoising methods have a high capability rate of suppressing noises and
artifacts that might vary the ECG signal morphology. The ST-segment shown in Figure 1 might get distorted
during the filtering process if the baseline wander removal methods are used. This issue represents the main
concern in using baseline wander removal techniques [11, 12]. In most cases, simple digital or analog filters
might not be adequate for removing electromyogram (EMG) signal without affecting the peaks, period,
interval, and featuring shapes of the ECG signal [13, 14]. In fact, some of the currently used method for ECG
signal denoising may create severs problems. For example, the EMD based noise reduction techniques
introduce QRS widening issue due to the big distortion effect at its beginning and end [15]. Hence, the noise
removal techniques might clearly vary the ECG segment waves by overlapping their spectrum with several
noise and artifacts especially in the frequency duration of 0.5 Hz to 100 Hz.
Unfortunately, all the presented methods such as SVD, DCT, DWT, EMD, and NBF are not suitable
for real-time processing since they take a very long time. This paper presents a new technique for ECG signal
denoising using a novel approach of adaptive filter. Up to our knowledge, no paper has presented such idea
for ECG signal denoising. The remaining structure of the paper are as follow: section 2 presents the proposed
filtering method, section 3 presents the obtained results as well as discussion, and finally section 4 is the
conclusions and recommendations for future work.
Figure 1. ECG signal
2. PROPOSED METHODOLOGY
The common way of removing noise from ECG signal is digital filters. Processing the recorded
ECG signal using digital filters most of the time has been done offline. When the noise change, one might
need to change the filters’ coefficients to deal with the new kinds of noise. To avoid this issue, adaptive
filters can be used to deal with the different kinds of noise. But adaptive filters need a reference noise that
should be close enough to the targeted noise, so it can be removed as shown in Figure 2. Based on Figure 2,
only specific type of noise can be removed.
In the proposed method, different kinds of noise can be removed using only one adaptive filter.
Besides that, there is no need to have a reference signal. The suggested method uses a delayed version of the
ECG signal itself as a reference, based on adaptive predictive filtering, which makes it more suitable for real-
time ECG signal denoising. Figure 3 explains the block diagram of the suggested method.
Adaptive filters are digital linear filter with frequent iterative weight changes capability to obtain the
best possible solution of the error or cost function as shown in Figure 2. The reference input signal is
considered as the main input to the adaptive filter, whereas its output will be added negatively (subtracted) to
the primary input signal and the result will be the error signal. The error signal controls the weights of the
filter taps. Several algorithms and different block diagram have been used to find the best possible solution of
the error function. Sayed [16] and Haykin [17] presents several methods for solving the optimization goals in
their textbooks. Least mean square (LMS), normalized least mean square (NLMS), and recursive least
squares (RLS) are the commonly used algorithms for reducing unwanted signal.

Int J Elec & Comp Eng ISSN: 2088-8708 
ECG signal denoising using a novel approach of adaptive filters for real-time processing (Amean Al-Safi)
1245
Adaptive
filter
+
_
/
/
/
,e
primary
reference
filtered
signal
error
signal
+
Figure 2. Block diagram of adaptive noise canceller
+_
+
/
/
primary
reference
error, e
Adaptive
filter
filtered
signal
Figure 3. Block diagram of adaptive predictive filter
2.1. LMS algorithm
LMS has been employed more often than other algorithms in removing noise and distortion in
different signal processing applications due to its distinguished properties. Simplicity, stability, and easier
implementation are among its features. The reputative procedure in LMS algorithm consists of: computing
the adaptive filter’s output, produced by a set of taps, generating an estimation for the error signal by subtracting
the filter’s output to the desired input, and using the obtained error to adjust the filter weights [18]. The length of
the adaptive filter as well as the step size have a direct impact on the stability and the speed of convergence
of LMS algorithm.
To derive the weight update equation in this algorithm, first the objective cost function must be
defined. It is usually known as the mean square error between the estimated filter’s output and the real or
actual output. Based on this definition, the filter’s weights, error, and the output equation of LMS algorithm
will be as follow [19, 20]:
For a given input signal

)
(k
x , which is an array of size M*M:
)]
1
(
.
.
)
1
(
)
(
[
)
( 




M
k
x
k
x
k
x
k
x (1)
where M refers to the filter taps, k refers to current input sample, and )
(k
x is the current input sample.
The adaptive filter’s output

)
(k
y is known as:
T
T
k
w
k
x
M
k
y
k
y
k
y
k
y )
(
)
(
)]
1
(
.
.
)
1
(
)
(
[
)
(







 (2)
where T
means the transpose of the matrix, and )
(k
y is the filter’s output at the current time instance k. The
weight matrix

)
(k
w is:
T
M
w
w
w
w
k
w ]
)
1
(
.
.
)
2
(
)
1
(
)
0
(
[
)
( 


(3)

 ISSN: 2088-8708
1246
LMS algorithm aims to find the best filter coefficients to minimize the cost signal )
(k
C which
directly depends on the error signal

)
(k
e . The error signal is nothing other than the difference between the
intended output

)
(k
d and the actual one

)
(k
y :
T
M
k
e
k
e
k
e
k
e )]
1
(
.
.
)
1
(
)
(
[
)
( 




(4)
T
M
k
d
k
d
k
d
k
d )]
1
(
.
.
)
1
(
)
(
[
)
( 




(5)
From the cost signal definition,









 2
)
(
)
( k
e
E
k
C (6)
Where )
(k
e refers to the current sample’s error, whereas E is the expected function. Applying the steepest
decent technique by taking the partial derivatives with respect to the individual filter’s weights will lead to:
w
k
e
k
e
k
e
E
k
C w
w

















)
(
)
(
2
)
(
)
(
2
(7)
but
T
k
w
k
x
k
d
k
e )
(
)
(
)
(
)
(





 (8)
Hence






)
(
)
(
k
x
w
k
e (9)
To minimize the value of the cost signal, it is required to reverse the direction of )
(n
C
w
 which can be
expressed in math as:
)
(
2
)
(
)
1
( k
C
k
w
k
w w







(10)












 )
(
.
)
(
.
)
(
)
(
.
)
(
.
2
.
2
)
(
)
1
( k
e
k
x
k
w
k
x
k
e
k
w
k
w 

(11)
where  is known as the step size. In (11) represents the direct relation between the current and next
vectors weights.
2.2. NLMS algorithm
The convergence, stability, as well as the steady state behaviors of LMS algorithms depend heavily
on the length of the adaptive filter and the primary input’s strength. In order to deal with this issue, NLMS
might be a good choice to use. It normalizes the input power to reduce the effects of the above-mentioned
issues. All the equations listed before, remain as they are. Whereas the new weight update equation is as
follow [18]:








 )
(
*
)
(
*
)
(
)
(
)
1
( 2
k
e
k
x
k
x
k
w
k
w


(12)

1247
where



 )
(
*
)
(
)
(
2
k
x
k
x
k
x H
is the norm vector, H
refers to the complex conjugate transposed, and  is
known as the regularization size.
2.3. Leaky LMS algorithm
Sometimes LMS algorithm fails in reaching the stability goal. The use of learning rate or variable
step size might be a good solution to ensure the stability condition. Leaky LMS algorithm is an alternative
solution for this issue. It was proposed to avoid the LMS convergence’s slowness [21]. All the variables and
signals mentioned before (LMS and NLMS) remain as they are in this algorithm. The new equation for the
weight update in Leaky LMS is as follow:







 )
(
*
)
(
*
)
(
)
*
1
(
)
1
( k
x
k
e
k
w
k
w 

 (13)
where  ( positive and very small number) is known as the leaky factor.
3. SIMULATION AND RESULTS
To verify the operation of the proposed denoising method, an ECG signal with different type of
noise was used in MATLAB software. In (11)-(13) were used as the weight update equations for LMS,
NLMS, and Leaky LMS algorithms respectively. The length of the adaptive filter was M=20. The step size
was selected as in LMS, NLMS, and Leaky LMS. The leaky factor gamma=0.1 in Leaky LMS algorithm.
The noisy and clean ECG signals are shown in Figures 4-6 using LMS, NLMS, and leaky LMS algorithms
respectively. In each figure, there is the signal before processing which appears on the top, and the signal
after processing which appears on the bottom of the figures. It is obvious how the proposed method was able
to clean the signal under different noise scenarios. Besides that, the propsed method dosnt need any externel
signal source as other ones [22-25].
Figure 4. Noisy and filtered ECG when the setting; LMS, step size = 0.05, and M = 20
0 500 1000 1500 2000 2500
-1
-0.5
0
0.5
1
1.5
sample.no
Amplitude
noisy signal
500 1000 1500 2000 2500 3000
-1
-0.5
0
0.5
1
1.5
sample.no
Amplitude
cleaned signal

 ISSN: 2088-8708
1248
Figure 5. Noisy and filtered ECG when the setting; NLMS, step size=0.05, and M=20
Figure 6. Noisy and filtered ECG when the setting; Leaky LMS, step size=0.05, gamma=0.1 and M=20
4. CONCLUSION AND FUTURE WORK
The paper presents a novel method for ECG signal denoising using adaptive filters. The proposed
method works properly for real time application since it depends only on the upcoming ECG signal without
the need for a reference noise signal. The suggested method was tested and verified using LMS, NLMS, and
Leaky LMS algorithms. As a future work, the author will investigate the possibility of using the proposed
model or Kalman filter based on the proposed model in different biomedical signal processing applications.
0 500 1000 1500 2000 2500
-1
-0.5
0
0.5
1
1.5
sample.no
Amplitude
noisy signal
0 500 1000 1500 2000 2500 3000
-0.5
0
0.5
1
sample.no
Amplitude
cleaned signal
500 1000 1500 2000 2500 3000
-1
-0.5
0
0.5
1
1.5
sample.no
Amplitude
noisy signal
0 500 1000 1500 2000 2500 3000
-0.5
0
0.5
1
sample.no
Amplitude
cleaned signal

1249
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