Denoising ECG Signals using Weighted Iterative UFIR Filtering
CARLOS LASTRE-DOMINGUEZ1, VICTOR JÍMENEZ-RAMOS1,
HECTOR AZCARAY-RIVERA1, EDUARDO PÉREZ-CAMPOS2,
JORGE MUNOZ–MINJARES3, YURIY SHMALIY4
1Department of Electronic,
National Technology of Mexico/IT Oaxaca,
MEXICO
2Division of Graduate Studies and Research,
National Technology of Mexico/IT Oaxaca,
MEXICO
3Department of Electronic,
Universidad de Zacatecas,
MEXICO
4Department of Electronic,
University of Guanajuato,
MEXICO
Abstract: - The electrocardiogram (ECG) holds paramount importance in diagnosing heart disease, and as it
persists leading cause of global mortality. Over the past decades, diverse techniques have emerged for
processing ECG signals, with denoising taking a prominent role in enhancing feature extraction. Nonetheless,
achieving heightened accuracy remains an enduring challenge. In this study, we introduce an innovative
approach involving the application of a weighted unbiased finite impulse response (UFIR) filter. Under the
same noise conditions and in terms of the root mean square error (RMSE) and signal-to-noise ratio (SNR), our
proposed method showcases worthy performance in comparison to the weighted Savitzky-Golay (SG) filter.
This research contributes to the progressive evolution of ECG signal processing, offering the potential for more
precise and dependable detection of cardiac diseases.
Key-Words: - weighted UFIR, Savitzky-Golay filter, ECG signals, root mean square error (RMSE), Denoising
ECG Signals, Signal-Noise to Ratio (SNR).
Received: June 26, 2022. Revised: September 12, 2023. Accepted: October 19, 2023. Published: December 7, 2023.
1 Introduction
An electrocardiogram (ECG) is a recording that
represents the electrical activity of the heart and is a
vital diagnostic tool for detecting cardiac pathology.
The P-QRS-T waves that make up the ECG signal
provide valuable information, with the (QRS)
complex playing a particularly important role in
identifying cardiac arrhythmias, [1], [2]. Early
detection of arrhythmia is crucial for predicting and
preventing heart attacks, making the ECG a critical
tool in saving lives. However, the accuracy of
arrhythmia detection can be compromised by noise
and artifacts, which can result in incorrect
diagnoses. To address this issue, a preprocessing
step is essential. Preprocessing is a widely used and
indispensable process for ECG signal analysis,
aimed at reducing noise and improving the quality
of the ECG signal to ensure accurate feature
extraction and diagnosis. Hence, it is necessary to
continuously monitor ECG signals over extended
periods to enable precise diagnoses using electronic
analog and digital devices for data acquisition and
processing. Several techniques have been proposed
to remove noise and artifacts from ECG signals,
with smoothing techniques of special interest.
Recent studies have presented wavelet-based
digital filters and conventional filters as effective
techniques for reducing noise in biomedical signals
that have been digitized using embedded systems,
[3], [4], [5], [6], [7], [8], [9]. In one study, a unique
methodology was proposed for processing ECG
signals by utilizing wavelet-based transform
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DOI: 10.37394/232014.2023.19.16
Carlos Lastre-Dominguez, Victor Jímenez-Ramos,
Hector Azcaray-Rivera, Eduardo Pérez-Campos,
Jorge Munoz–Minjares, Yuriy Shmaliy
E-ISSN: 2224-3488
148
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techniques and wireless IoT devices to monitor the
behavior of the heart, [10]. Another study proposed
the use of the adaptive Fourier-Bessel domain
wavelet transform (FBDAWT) for the automatic
detection of anxiety stages, utilizing the signal from
a single-channel portable electrocardiogram (ECG)
sensor, [11]. Additionally, a study evaluated the
performance of Butterworth-type low-pass filters
configured with fourth and eighth order, compared
to other filters like Chebyshev-type, [12]. Other
approaches proposed a deep learning-based artificial
intelligence technique to classify and reduce the
noise associated with ECG signals, [13], [14], [15],
[16]. Moreover, the use of generative adversarial
neural networks (GANs) for the blind restoration of
ECG signals was also suggested, [17]. It is worth
noting that GANs have been utilized for generating
and classifying ECG signals, [18], [19], [20], [21],
[22], [23], [24], [25].
Finally, a study provided a general overview of
the stages of ECG signal processing and the
application of machine learning techniques, [26],
[27]. Overall, these studies highlight the
effectiveness of wavelet-based digital filters and
conventional filters in reducing noise in biomedical
signals, particularly those that have been digitized
with embedded systems. The presented techniques,
including deep learning-based artificial intelligence
and generative adversarial neural networks (GANs),
demonstrate the potential for advanced signal
processing in the biomedical field. The studies also
showcase the importance of monitoring the behavior
of the heart, detecting anxiety stages, and utilizing
machine learning techniques in ECG signal
processing.
However, despite the notable benefits of these
works, they have limitations associated with their
structure. In the case of the wavelet transform,
finding a mother wavelet function and its optimal
parameters is a process that takes computational
time. In the case of the conventional filters
mentioned, the filtered signal tends to produce
delays in the time domain, which is an inherent
characteristic of these types of filters. Although
deep learning-based approaches can help reduce
signal noise, their computational efficiency still lags
other filtering techniques. Additionally, the ECG
signal filtering process cannot be easily understood
using deep learning techniques.
Various techniques can be used to process ECG
signals, including the Kalman filter. The extended
Kalman filter (EKF) is the most popular among
these methods due to its compatibility with dynamic
models. Some studies have utilized adaptive filter
banks with EKF to denoise ECG signals, [28], while
others have concentrated on analyzing
morphological features by segmenting the ECG
signal, [29]. Additionally, some researchers have
estimated the breathing rate by smoothing ECG and
photoplethysmogram (PPG) signals using the
Kalman filter, [30], [31], [32], [33]. Other research
was conducted to evaluate the effectiveness of the
Kalman filter in reducing noise in telehealth
systems, [34]. Although the filter showed
impressive results, it has limitations when the model
is unknown. The success of this filter depends on
the formulation of the ECG signal model, which can
vary over time. As a result, establishing the
appropriate parameters of the model can be difficult.
There are several techniques available for
smoothing ECG signals and achieving promising
results, [35], [36], [37]. In one approach presented
in, [38], a smoothing filter was designed based on
the delay differential equation (DDE), which
requires the regularization parameter and the delay.
The regularization parameter is related to the cutoff
frequency, while the delay is related to the tuning
provided by the user. Another technique proposed
in, [39], is the quantum smoothing filter (QSF),
which is advantageous in terms of runtime
complexity compared to other methods like discrete
wavelet transform (DWT) and Empirical Mode
Decomposition (EMD). However, the QSF method
requires quantum computers to work. In, [40], the
Complete Ensemble Empirical Mode
Decomposition with Adaptive Noise (CEEMDAN)
was used to reduce noise in ECG signals. The
sample entropy was then utilized to identify the
noisy intrinsic mode functions (IMFs) and
subsequently apply the non-local mean smoothing
technique. However, this method is only suitable for
ECG signals with low Signal Noise to Ratio (SNR).
When studying cardiac pathologies, decomposition
methods are often more suitable, such as dynamic
mode decomposition (DMD), [41].
The Savitzky-Golay (SG) smoothing filter, [42],
on the other hand, is a widely used filter in ECG
analysis. It is known for yielding significant
insights, [43], [44]. However, it has certain
limitations concerning its parameters. For instance,
the length N of the horizon parameter must be odd,
otherwise, fractional values arise at the boundaries
of the summation. Additionally, the fixed delay is
positioned at the center of the horizon, which may
not align with the needs of certain applications
where optimal delays may vary. Despite the
limitations, the SG filter is still one of the standard
methods for denoising ECG signals, [45], [46].
Once the frequency bands in the ECG are
removed, a proper smoothing technique can
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DOI: 10.37394/232014.2023.19.16
Carlos Lastre-Dominguez, Victor Jímenez-Ramos,
Hector Azcaray-Rivera, Eduardo Pérez-Campos,
Jorge Munoz–Minjares, Yuriy Shmaliy
E-ISSN: 2224-3488
149
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improve the quality of an ECG signal. A p−shift
finite–length Unbiased Finite Impulse Response
filter (p−shift UFIR) has been widely used for
denoising ECG, [47]. The p-shift UFIR filter was
used in, [48], to achieve an adaptive averaging
horizon: optimal for slow ECG behaviors and
minimal for fast excursions. Additionally, in, [49],
the p-shift UFIR filter was employed to estimate the
QRS interval based on the information provided by
its second state. The p-shift UFIR filter has been
applied to denoise ECG signals, aiming to extract
ECG signal features, [50].
In this paper, we present a robust weighted
iterative UFIR filter designed for enhancing ECG
signals and compare it to the weighted SG filter.
This work is organized into the following sections:
Section II outlines different methods utilized in this
study. In Section III, we delve into the key findings,
as assessed through RMSE and SNR metrics, with
an additional focus on the practical implementation
of real ECG signals. Finally, the last section
describes the conclusions of the work.
2 Preliminaries
2.1 ECG Signal State Space Model
The discrete-time model for representing ECG
signals is given in, [51], where the signal is
represented on a horizon of length , where
. The degree polynomial used in
the representation is determined in space-state,
providing a precise representation of the ECG signal
within the specified time frame. The ECG signal is
time-invariant and deterministic. It is supposed that
measurement of the ECG signal is corrupted by
zero-mean noise with an unknown, standard
deviation and not necessary Gaussian distribution.
Under such conditions, an ECG signal can be
represented as follows:
(1)
where is the process vector of the ECG signal,
is the measurement observation of the ECG signal,
is the zero mean measurement noise with
unknown distribution, is the observation matrix
and, the matrix defined as:
(3)
2.2 The p-shift UFIR Filter with Weights
The UFIR approach assumes that a shift to the past
can be achieved at point k using data taken from
with a positive smoother lag
, a shift to the future at point k using data taken
from with a positive prediction
step p > 0, and that p = 0 means filtering. Thus, the
-shift UFIR filtering estimate can be defined as:
(4)
(5)
where the components of the gain
are formed
by
each
matrix is a diagonal matrix specified by
whose components, in turn, are the values of the
function
. The function
. is
called the th degree polynomial impulse response
and can be calculated by the following equation:
(6)
where and
and finally, the term is determined by:
(7)
where is a matrix defined as:
(8)
The determinant of matrix is . The
th component , , of is
calculated using a power series based on the minor
of ,
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Carlos Lastre-Dominguez, Victor Jímenez-Ramos,
Hector Azcaray-Rivera, Eduardo Pérez-Campos,
Jorge Munoz–Minjares, Yuriy Shmaliy
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, (9)
this expression can also be expressed differently,
(10)
where the term is called Bernoulli
polynomial.
The UFIR theory suggests that the process can
be estimated on in the following batch state-
space form,
(11)
As has been shown in, [52], [53], the UFIR filtering
estimate is is the extended
observation vector and is the augmented
measurement matrix. The p-shift estimate is given
by:
(12)
where
is known as the digital optimal lag 2
which is also used in SG smoothing. Unlike the SG,
the UFIR Smoother can minimize the MSE with an
optimum horizon . Specifically, without the
reference signal (ground truth), by minimizing the
trace of mean square value (MSV) derivative of the
residual matrix , the optimum horizon is
calculated as:
(13)
Moreover, an iterative UFIR smoothing
algorithm akin to the Kalman filter is presented in,
[54], recursively in two distinct phases: prediction
and update. This algorithm re-calibrates the
generalized noise power gain (GNPG), with its
adjustment reliant on a gain derived from batch
processing. In contrast to the Kalman filter, the
UFIR algorithm outlined in algorithm 1 presents a
significant advantage in that it does not necessitate
any prior knowledge regarding measurement noise.
This feature endows the UFIR algorithm with a
superior level of robustness and reliability. In, [55],
[56], it was shown an improvement of the
robustness of the UFIR filter with the weight γ,
defined by:
=
(14)
where and K are
the iintegerpart of and the numbers of states.
The root mean square (RMS) deviation of the
estimate is calculated using the innovation residual
as:
(15)
where k is the dimension of the target motion.
Algorithm 1: Iterative UFIR Filtering
Algorithm
1: Data:
2: Begin
3: for … do
4: ;
5: (
)(
);
6:
)(
);
7: for do
8:
9:
10
11:
=
12: end for
13: end for
14: Result:
2.3 Savitzky-Golay Filter for ECG Signals
The SG filter can be considered as a special case of
the UFIR smoothing filter as shown in, [57]. The
convolution-based smoothed estimate with a lag
in the middle of the averaging horizon is
given by
(16)
where represents the convolution coefficients
determined by the linear least square (LS) method to
configure with commonly low-degree polynomials
systems. The coefficients can be extracted from
the FIR function
The SG filter has the
following restrictions to ensure accurate
calculations, the horizon length must always be
an odd number. If an even number is used, the sum
limits would include fractional values, which is not
desirable.
While the fixed lag is typically set as
, it is important to note that different
applications may require alternative lag values. The
optimal lag might not necessarily be equal to this
default value. It is also worth mentioning that the
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DOI: 10.37394/232014.2023.19.16
Carlos Lastre-Dominguez, Victor Jímenez-Ramos,
Hector Azcaray-Rivera, Eduardo Pérez-Campos,
Jorge Munoz–Minjares, Yuriy Shmaliy
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UFIR smoothing filter explained by, [53], extends
the functionality of the SG filter for arbitrary
and lags . However, in the
specific case of an odd and , the
UFIR filter corresponds to the SG filter. Also note
that the -lag can be optimized for even-degree
polynomials.
3 Main Findings
3.1 ECG Signals Denoising by Different
Filters
Displayed in Figure 1 are the effects of various
estimators on filtering results. To conduct our
experiment, we utilized a simulated ECG signal
with Gaussian white noise that possessed a standard
deviatiequal .0316. This ECG signal was generated
using the model introduced by, [58], which can be
readily executed on platforms like MATLAB or
Octave. The SG filters, labeled as SGK-1 and SGK-
2, use the Kaiser window-like weights vector with
values of and , respectively. The
WUFIR q -lag 2 is the UFIR filter with GPNG
weight and lag determined by the
following expression:
(17)
Fig. 1: Synthetic ECG estimations from filters
based on weighted SG and UFIR filters.
Upon examining Figure 2, it is evident that the
proposed UFIRW method provides greater
variability compared to the SG estimator. Notably,
the estimation provided by UFIRW is closer to the
reference ECG signal.
Fig. 2: A detailed visualization of the filtering
process of the T wave in synthetic ECG signals
Fig. 3: Performance of mean square error calculated
from estimations.
3.2 RMSE Analysis
Given the filtering estimate, to find the better
estimator, we calculate the root mean square error
(RMSE) determined by
(18)
where L is the sample length of and .
Individually, and are the samples associated
with the ECG synthetic signal and estimation of the
filter. Under the same noise conditions, we
conducted an experiment, where we tested the
performance of several filters by iterating the
process 100 times. The results are presented in
500 600 700 800 900 1000 1100 1200 1300 1400
Samples
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
Amplitude
Noisy Signal
UFIRW q-lag 2
SGK-1
SGk-2
ECG Signal
565 570 575
-0.2
-0.18
-0.16
-0.14
P
Q
R
T
S
1220 1240 1260 1280 1300 1320 1340 1360 1380 1400
Samples
0
0.05
0.1
0.15
0.2
0.25
Amplitude
Noisy Signal
UFIRW q-lag 2
SGK-1
SGk-2
ECG Signal
T
020 40 60 80 100
Iterations
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0.11
RMSE
UFIRW q-lag 2
SGK-1
SGK-2
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Carlos Lastre-Dominguez, Victor Jímenez-Ramos,
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Figure 3, where we can see the performance of each
filter. The filters based on Savitzky-Golay (SGK-1
and SGK-2) showed an RMSE between 0.04 and
0.1, which was lower than the RMSE provided by
the proposed UFIRW method, which showed an
RMSE value between 0.02 and 0.03. It is well-
known that the UFIR method provides good
stability, while methods based on SG exhibit high
variability, which indicates susceptibility to noise.
Fig. 4: Signal-to-Noise Ratio (SNR) obtained from
varying levels of noise in decibels (dB).
3.3 Signal-to-Noise Ratio (SNR) Analysis
A recent study was conducted to examine how
different levels of noise affect ECG signals. The
study used Gaussian noise ranging from -50 to 50
dB and analyzed the signal-to-noise ratio provided
by two filters shown in Figure 4 - the UFIR
weighted estimator and the SG filter. The results
showed that the UFIR weighted estimator
outperformed the SG filter in producing a clearer
ECG signal with less random noise. This study
helps in understanding the response of each filter to
noise and highlights the superiority of the proposed
UFIR method over SG estimators in terms of SNR
output.
3.4 Applications to Real ECG Signals
Following a rigorous analysis of the Root Mean
Square Error (RMSE) and Signal-to-Noise Ratio
(SNR), this study has identified the Unbiased Finite
Impulse Response (UFIR) filter with weights as the
most appropriate option for accurately estimating
real Electrocardiogram (ECG) signals. The analysis
has confirmed the filter’s superior performance over
other filters under consideration. The study focuses
on two types of pathologies, namely normal sinus
rhythm and premature ventricular complex (PVC),
and the ECG signal estimates are showcased
visually in Figures 5 and Figure 6. The UFIRW-
qlag2 filter provides a precise fit to the ECG real
signal, as attested by our analysis.
Fig. 5: Estimation of real ECG signal with normal
sinus rhythm, [59].
Fig. 6: Estimation of real ECG signal with
premature ventricular complex (PVC), [60].
Our study has demonstrated that the UFIR filter
with weights is a reliable method for estimating
ECG signals, and its application can significantly
improve the accuracy of ECG signal estimation,
particularly in the context of the two pathologies
analyzed. As such, the UFIR filter with weights is
highly recommended for accurately estimating real
ECG signals.
4 Conclusions
We evaluated the effectiveness of our UFIR filter in
comparison to the SG filter using Root Mean Square
Error (RMSE) and Signal-to-Noise Ratio (SNR)
-50 050
dB
6.5
7
7.5
8
8.5
9
9.5
10
10.5
11
SNR
UFIRW q-lag 2
SGK-1
SGk-2
600 650 700 750 800 850
Samples
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Amplitude
Real Signal
UFIRW q-lag 2
740 750 760 770
-0.45
-0.4
-0.35
-0.3
5.466 5.4665 5.467 5.4675 5.468 5.4685 5.469 5.4695
Samples 105
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
Amplitude
Real Signal
UFIRW q-lag 2
5.4669 5.467 5.4671
105
-0.5
-0.45
-0.4
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Carlos Lastre-Dominguez, Victor Jímenez-Ramos,
Hector Azcaray-Rivera, Eduardo Pérez-Campos,
Jorge Munoz–Minjares, Yuriy Shmaliy
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metrics. Our results showed that the UFIR filter
outperformed the SG filter, demonstrating its
adaptability and effectiveness in various ECG signal
pathologies. The UFIRW method displayed
superior error stability compared to the SG methods.
However, the weighted SG method showed high
variance and was easily affected by random noise.
The UFIR filter performance remained consistent
despite cardiac variability, and we could adjust the
horizon parameter, N, to obtain optimal results for
different noise levels.
In environments with high levels of noise, it is
imperative to adopt pre-processing steps to achieve
optimal results. However, implementing the
recommended approach on low-power devices in
such settings may present some challenges. This is
due to the method requiring a significant number of
points, represented by horizon N, which could
potentially impact the memory capacity of the
device. This limitation creates a promising avenue
for future research that could lead to the
development of more efficient solutions for
applying the method in low-power and high-noise
scenarios.
We will continue to explore various pathologies
to identify patterns associated with significant
diseases. Ultimately, this project has the potential to
greatly enhance ECG signal denoising and advance
medical diagnostics.
References:
[1] M. Ingale, R. Cordeiro, S. Thentu, Y. Park and
N. Karimian, ECG Biometric Authentication:
A Comparative Analysis, in IEEE Access,
Vol. 8, 2020, pp. 117853-117866.
[2] A. Burguera,” Fast QRS Detection and ECG
Compression Based on Signal Structural
Analysis, in IEEE Journal of Biomedical and
Health Informatics, Vol. 23, No. 1, 2019, pp.
123-131
[3] Amri, M. F., Rizqyaan, M. I., and Turnip, A.
(2016). ECG signal processing using offline
wavelet transform method based on ECG-IoT
device. 3rd International Conference on
Information Technology, Computer, and
Electrical Engineering (ICITACEE), 1–6.
[4] P. Darsana and V. N. Kumar, Extracting Fetal
ECG Signals Through a Hybrid Technique
Utilizing Two Wavelet-Based Denoising
Algorithms, in IEEE Access, Vol. 11, 2023,
pp. 91696-91708.
[5] A. Kumar, R. Ranganathan, M. Kumar, and R.
Komaragiri, Hardware Emulation of a
Biorthogonal Wavelet Transform-Based Heart
Rate Monitoring Device, in IEEE Sensors
Journal, Vol. 21, No. 4, 2021, pp. 5271-5281.
[6] H. B. Seidel, M. M. A. da Rosa, G. Paim, E.
A. C. da Costa, S. J. M. Almeida, and S.
Bampi, Approximate Pruned and Truncated
Haar Discrete Wavelet Transform VLSI
Hardware for Energy-Efficient ECG Signal
Processing, in IEEE Transactions on Circuits
and Systems I: Regular Papers, Vol. 68, No. 5,
2021, pp. 1814-1826.
[7] S. Banerjee and G. K. Singh,” Quality
Guaranteed ECG Signal Compression Using
TunableQ Wavelet Transform and Möbius
Transform Based AFD,” in IEEE
Transactions on Instrumentation and
Measurement, Vol. 70, No. 4008211, 2021,
pp. 1-11.
[8] S. Shimauchi, K. Eguchi, R. Aoki, M. Fukui,
and N. Harada, R-R Interval Estimation for
Wearable Electrocardiogram Based on Single
Complex Wavelet Filtering and Morphology
Based Peak Selection, in IEEE Access, Vol. 9,
2021, pp. 60802-60827.
[9] B. Yuen, X. Dong, and T. Lu, Detecting Noisy
ECG QRS Complexes Using WaveletCNN
Autoencoder and ConvLSTM, in IEEE
Access, Vol. 8, 2020, pp. 143802-143817.
[10] D. Lee, S. Lee, S. Oh, and D. Park, Energy-
Efficient FPGA Accelerator with Fidelity
Controllable Sliding-Region Signal
Processing Unit for Abnormal ECG Diagnosis
on IoT Edge Devices, in IEEE Access, Vol. 9,
2021, pp. 122789-122800.
[11] Tripathy, R. K., Dash, D. K., Ghosh S. K. and
Pachori R. B., (2023) Detection of Different
Stages of Anxiety from Single-Channel
Wearable ECG Sensor Signal Using Fourier–
Bessel Domain Adaptive Wavelet Transform,
in IEEE Sensors Letters, Vol. 7, No. 5, no.
7002304., pp. 1-4.
[12] Basu, S., and Mamud, S. (2020). Comparative
Study on the Effect of Order and Cut-off
Frequency of Butterworth Low Pass Filter for
Removal of Noise in ECG Signal. 2020 IEEE
1st International Conference for Convergence
in Engineering (ICCE), pp. 156–160.
[13] Hou, Y., Liu, R., Shu, M., Xie, X., and Chen,
C. Deep Neural Network Denoising Model
Based on Sparse Representation Algorithm
for ECG Signal. IEEE Transactions on
Instrumentation and Measurement, Vol. 72,
2023, pp. 1–11.
[14] M. S. Islam, M. N. Islam, N. Hashim, M.
Rashid, B. S. Bari and F. A. Farid, New
Hybrid Deep Learning Approach Using
WSEAS TRANSACTIONS on SIGNAL PROCESSING
DOI: 10.37394/232014.2023.19.16
Carlos Lastre-Dominguez, Victor Jímenez-Ramos,
Hector Azcaray-Rivera, Eduardo Pérez-Campos,
Jorge Munoz–Minjares, Yuriy Shmaliy
E-ISSN: 2224-3488
154
Volume 19, 2023
BiGRU-BiLSTM and Multilayered Dilated
CNN to Detect Arrhythmia, in IEEE Access,
Vol. 10, 2022, pp. 58081-58096.
[15] Y. Hou, R. Liu, M. Shu, X. Xie and C. Chen,
Deep Neural Network Denoising Model
Based on Sparse Representation Algorithm
for ECG Signal, in IEEE Transactions on
Instrumentation and Measurement, vol. 72,
No. 2507711, 2023, pp. 1-11.
[16] Xiao, Qiao, Khuan Lee, Siti Aisah Mokhtar,
Iskasymar Ismail, Ahmad Luqman bin Md
Pauzi, Qiuxia Zhang, and Poh Ying Lim.
"Deep Learning-Based ECG Arrhythmia
Classification: A Systematic Review" Applied
Sciences Vol. 13, No. 8, 2023, pp. 1-25.
[17] Kiranyaz S, Devecioglu OC, Ince T, Malik J,
Chowdhury M, Hamid T, Mazhar R,
Khandakar A, Tahir A, Rahman T, Gabbouj
M. Blind ECG Restoration by Operational
Cycle-GANs. IEEE Trans Biomed Eng. Vol.
69, No. 12, 2022, pp.3572-3581.
[18] A. M. Shaker, M. Tantawi, H. A. Shedeed and
M. F. Tolba, Generalization of Convolutional
Neural Networks for ECG Classification
Using Generative Adversarial Networks,” in
IEEE Access, vol. 8, 2020, pp. 35592-35605.
[19] D. Nankani and R. D. Baruah, Investigating
Deep Convolution Conditional GANs for
Electrocardiogram Generation, 2020
International Joint Conference on Neural
Networks (IJCNN), Glasgow, UK, 2020, pp.
1-8.
[20] S. Janbhasha, S. N. Bhavanam and K.
Harshita, GAN-Based Data Imbalance
Techniques for ECG Synthesis to Enhance
Classification Using Deep Learning
Techniques and Evaluation, 2023 Third
International Conference on Advances in
Electrical, Computing, Communication and
Sustainable Technologies (ICAECT), Bhilai,
India, 2023, pp. 1-8.
[21] Berger L, Haberbusch M, Moscato F.,
Generative adversarial networks in
electrocardiogram synthesis: Recent
developments and challenges, Artificial
Intelligence in Medicine, Vol. 143, No.
102632, 2023, pp. 1-13.
[22] Zhou X, Zhu X, Nakamura K, Noro M.
Electrocardiogram Quality Assessment with a
Generalized Deep Learning Model Assisted
by Conditional Generative Adversarial
Networks. Life. Vol. 11, No. 10, 2021, pp. 1-
25.
[23] Skandarani Youssef, Alain Lalande, Jonathan
Afilalo, and Pierre-Marc Jodoin. Generative
Adversarial Networks in Cardiology. The
Canadian Journal of Cardiology Vol. 38, No.
2, 2022, pp. 196–203.
[24] Delaney, A. M., Brophy, E., & Ward, T. E.
(2019). Synthesis of Realistic ECG using
Generative Adversarial Networks. ArXiv.
2019, pp. 1-19.
[25] Kim, Min-Gu, and Sung Bum Pan. A
Study on User Recognition Using the
Generated Synthetic Electrocardiogram
Signal. Sensors, Vol.21, no. 5, 2021, pp. 1-13.
[26] Mohamed Suhail, M., y T. Abdul Razak.
Cardiac Disease Detection from ECG Signal
Using Discrete Wavelet Transform with
Machine Learning Method. Diabetes
Research and Clinical Practice Vol.187,
2022, pp.1-9.
[27] Wasimuddin, M., Elleithy K., Abuzneid A. -
S., Faezipour M. and Abuzaghleh O., Stages-
Based ECG Signal Analysis from Traditional
Signal Processing to Machine Learning
Approaches: A Survey, in IEEE Access, Vol.
8, 2020, pp. 177782-177803.
[28] H. D. Hesar and M. Mohebbi, An Adaptive
Kalman Filter Bank for ECG Denoising, in
IEEE Journal of Biomedical and Health
Informatics, Vol. 25, No. 1, 2021, pp. 13-21.
[29] H. D. Hesar and M. Mohebbi, A Multi-Rate
Marginalized Particle Extended Kalman Filter
for P and T Wave Segmentation in ECG
Signals,” in IEEE Journal of Biomedical and
Health Informatics, Vol. 23, No. 1, 2019, pp.
112-122.
[30] S. Khreis, D. Ge, H. A. Rahman, and G.
Carrault, Breathing Rate Estimation Using
Kalman Smoother with Electrocardiogram
and Photoplethysmogram, in IEEE
Transactions on Biomedical Engineering, vol.
67, no. 3, 2020, pp. 893-904.
[31] A. Adami, R. Boostani, F. Marzbanrad and P.
H. Charlton, ”A New Framework to Estimate
Breathing Rate From Electrocardiogram,
Photoplethysmogram, and Blood Pressure
Signals,” in IEEE Access, Vol. 9, 2021, pp.
45832-45844.
[32] Manju B. R., y Sneha M. R. ECG Denoising
Using Wiener Filter and Kalman
Filter. Procedia Computer Science Vol. 171,
2020, pp. 273–81.
[33] Akhbari M., Nasim Montazeri
Ghahjaverestan, Mohammad B. Shamsollahi,
and Christian Jutten. ECG Fiducial Point
Extraction Using Switching Kalman
Filter. Computer Methods and Programs in
Biomedicine Vol. 157., 2018, pp. 129–36.
WSEAS TRANSACTIONS on SIGNAL PROCESSING
DOI: 10.37394/232014.2023.19.16
Carlos Lastre-Dominguez, Victor Jímenez-Ramos,
Hector Azcaray-Rivera, Eduardo Pérez-Campos,
Jorge Munoz–Minjares, Yuriy Shmaliy
E-ISSN: 2224-3488
155
Volume 19, 2023
[34] A. Sulthana, M. Z. U. Rahman and S. S.
Mirza, An Efficient Kalman Noise Canceller
for Cardiac Signal Analysis in Modern
Telecardiology Systems, in IEEE Access, Vol.
6, 2018, pp. 34616-34630.
[35] A. Kheirati Roonizi, A New Approach to
Gaussian Signal Smoothing: Application to
ECG Components Separation, in IEEE Signal
Processing Letters, Vol. 27, 2020, pp. 1924-
1928.
[36] Z. Hao, X. Zhang, and Z. Lai, Adaptive R-
Peak Detection Algorithm Based on Brown
Exponential Smoothing Model, in IEEE
Access, Vol. 10, 2022, pp. 114355-114363.
[37] H. Liu, D. Chen, and G. Sun, Detection of
Fetal ECG R Wave from Single-Lead
Abdominal ECG Using a Combination of RR
Time-Series Smoothing and Template-
Matching Approach, in IEEE Access, Vol. 7,
2019, pp. 66633-66643.
[38] A. K. Roonizi and R. Sassi, A new DDE
Smoothing filter for ECG Signal Denoising,
2022 Computing in Cardiology (CinC), Vol.
498. IEEE, 2022, pp. 1–4.
[39] Laskar, M. R., Pratiher, S., Dutta, A. K.,
Ghosh, N. Patra, A., A Complexity Efficient
PentaDiagonal Quantum Smoothing Filter for
ECG Signal Denoising. TechRxiv, Preprint,
2023, pp. 113
[40] P. Bhavsar, Improved ECG Denoising Using
CEEMAN Based on Complexity Measure and
Nonlocal Mean Approach, IAENG
International Journal of Computer Science,
Vol. 49, No. 2, 2022, pp. 606-615.
[41] Niyigena Ingabire H, Wu K, Toluwani Amos
J, He S, Peng X, Wang W, Li M, Chen J,
Feng Y, Rao N, Ren P. Analysis of ECG
Signals by Dynamic Mode Decomposition.
IEEE J Biomed Health Inform. 2022 Vol. 26 ,
No. 5, 2022, pp. 2124-2135.
[42] R. Schafer, What is a Savitzky-Golay filter?
[lecture notes], IEEE Signal Processing
Magazine, Vol. 28, 2011. pp. 111-117.
[43] M. Krishna Chaitanya and L. D. Sharma,
Electrocardiogram signal filtering using
circulant singular spectrum analysis and
cascaded Savitzky Golay filter, Biomedical
Signal Processing and Control, Vol. 75, 2022,
pp. 1-15
[44] N. Raheja and A. K. Manoacha, Wavelet and
Savitzky–Golay filter based denoising of
electrocardiogram signal: An improved
approach, In Emergent Converging
Technologies and Biomedical Systems, Vol.
1040, 2023, pp. 317–326.
[45] H. S. H. Siew, Y. S. Alshebly, and M. Nafea,
Fetal ECG Extraction Using Savitzky-Golay
and Butterworth Filters, 2022 IEEE
International Conference on Automatic
Control and Intelligent Systems (I2CACIS),
2022, pp. 215–220.
[46] M. Chylinski, M. Szmajda, J. Sacha, and J.
Mroczka, The way of ECG signal obtaining
from the respiratory wave by Savitzky-Golay
Filtration, 2021 6th International Conference
on Nanotechnology for Instrumentation and
Measurement (NanofIM), 2021, pp. 1–4.
[47] S. Zhao, Y. S. Shmaliy, and F. Liu, Batch
optimal FIR smoothing increasing state
informativity in nonwhite measurement noise
environments, IEEE Transactions on
Industrial Informatics, Vol. 19, No. 5, 2022,
pp. 6993-7001.
[48] C. Lastre-Domínguez, Y. S. Shmaliy, O.
Ibarra-Manzano, J. Munoz Minjares, L. J.
Morales Mendoza, ., ECG Signal Denoising
and Features Extraction Using Unbiased FIR
Smoothing, BioMed research international,
Vol. 2019, 2019, pp.1-16.
[49] O. R. Roberto, R. R. Claudia, M. M. Jorge, L.
D. Carlos, and L. R. Misael, ECG Waveform
Detection Based on Modified Iterative UFIR
Algorithm, Revista de Difusión Científica,
Ingeniería y Tecnologías, Vol. 16, No. 2,
2022, pp. 7-13.
[50] W. Wang, C. Zhao, X. Li, Z.-Q. Zhang, X.
Yuan, and H. Li, Research on Multimodal
fusion recognition method of upper limb
motion patterns, IEEE Transactions on
Instrumentation and Measurement, Vol. 72,
No. 4008312, 2023, pp. 1-12.
[51] C. Lastre-Dominguez, Y. S. Shmaliy, O.
IbarraManzano, and M. Vazquez-Olguin,
Denoising and Features Extraction of ECG
Signals in State Space Using Unbiased FIR
Smoothing, IEEE Access, Vol. 7, 2019, pp.
152166-152178.
[52] Y. Shmaliy and S. Zhao, Optimal and Robust
State Estimation: Finite Impulse Response
and Kalman Approaches. John Wiley and
Sons, Inc., 2022.
[53] Y. Shmaliy, Neuvo Y, Khan S Review of
Unbiased FIR Filters, Smoothers, and
Predictors for Polynomial Signals. Front Sign
Process, Vol. 2, No. 1, 2018, pp.1–29.
[54] Y. Shmaliy, S. Zhao, and C. K. I. Ahn,
Unbiased Finite Impulse Response Filtering:
An iterative alternative to Kalman filtering
ignoring noise and initial conditions, IEEE
WSEAS TRANSACTIONS on SIGNAL PROCESSING
DOI: 10.37394/232014.2023.19.16
Carlos Lastre-Dominguez, Victor Jímenez-Ramos,
Hector Azcaray-Rivera, Eduardo Pérez-Campos,
Jorge Munoz–Minjares, Yuriy Shmaliy
E-ISSN: 2224-3488
156
Volume 19, 2023
Control Systems, Vol. 37, No. 5, 2017, pp.
70–89.
[55] Sun J, Fu JB, Wang J, Improved Manoeuvring
Target Tracking Method Based on Unbiased
Finite Impulse Response (UFIR) filter, US
patent 103 500 455 A Jan. 8, 2014.
[56] J. B. Fu, J. Sun, G. Fei, and S. Lu,
Manoeuvring Target Tracking with Improved
Unbiased FIR Filter, 2014 International
Radar Conference, 2014, pp. 1–5.
[57] A. Savitzky and M. J. E. Golay, Smoothing
and Differentiation of Data by Simplified
Least Squares Procedures. Analytical
Chemistry, Vol. 36, 1964, pp. 1627–1639.
[58] P. E. McSharry, G. D. Clifford, L. Tarassenko
and L. A. Smith, A Dynamical Model for
Generating Synthetic Electrocardiogram
Signals, in IEEE Transactions on Biomedical
Engineering, Vol. 50, No. 3, 2003, pp. 289-
294.
[59] Moody and R. G. Mark, The impact of the
MIT-BIH Arrhythmia Database, in IEEE
Engineering in Medicine and Biology
Magazine, vol. 20, no. 3, 2001, pp. 45-50.
[60] Goldberger, A., Amaral, L., Glass, L.,
Hausdorff, J., Ivanov, P.C., Mark, R., Mietus,
J.E., Moody, G.B., Peng, C.K. and Stanley,
H.E. PhysioBank, PhysioToolkit, and
PhysioNet: Components of a new research
resource for complex physiologic signals.
Circulation [Online]. Vol. 101, No. 23, 2000,
pp. 215–220.
Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
- The research project was led by Carlos Lastre-
Dominguez, who supervised the simulation,
algorithm implementation, paper preparation and
review, and paper editing.
- Victor Jiménez-Ramos was responsible for project
administration and methodology of work.
- Hector Azcaray-Rivera and Eduardo Pérez-
Campos carried out the writing, reviewing, and
editing of the paper.
- Jorge Munoz-Minjares was responsible for the
simulation and paper preparation, review, and
editing.
- Yuriy S. Shmaliy carried out writing, reviewing,
and editing as well.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The authors have no conflicts of interest to declare.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
_US.
WSEAS TRANSACTIONS on SIGNAL PROCESSING
DOI: 10.37394/232014.2023.19.16
Carlos Lastre-Dominguez, Victor Jímenez-Ramos,
Hector Azcaray-Rivera, Eduardo Pérez-Campos,
Jorge Munoz–Minjares, Yuriy Shmaliy
E-ISSN: 2224-3488
157
Volume 19, 2023
