Дослідження й оброблення ЕКГ-сигналів за допомогою дискретного та безперервного вейвлет-аналізу
The publication is devoted to analyzing electrocardiogram signals of artificial origin of realistic form with the possibility of controlling the duration, sampling frequency, noise level and pulse rate using Ingrid Daubechies wavelets. The synthesized signals were investigated using discrete wavelet...
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System research and information technologies| _version_ | 1869472190651432960 |
|---|---|
| author | Taranenko, Yurii Oliynyk, Olha Moroz, Borys Moroz, Dmytro Lopatin, Valerii |
| author_facet | Taranenko, Yurii Oliynyk, Olha Moroz, Borys Moroz, Dmytro Lopatin, Valerii |
| author_institution_txt_mv | [
{
"author": "Yurii Taranenko",
"institution": "Private Enterprise “Likopak”, Dnipro"
},
{
"author": "Olha Oliynyk",
"institution": "Dnipro Applied College of Radio Electronics, Dnipro"
},
{
"author": "Borys Moroz",
"institution": "Dnipro University of Technology, Dnipro"
},
{
"author": "Dmytro Moroz",
"institution": "Dnipro University of Technology, Dnipro"
},
{
"author": "Valerii Lopatin",
"institution": "M.S. Poliakov Institute of Geotechnical Mechanics of the National Academy of Sciences of Ukraine, Dnipro"
}
] |
| author_sort | Taranenko, Yurii |
| baseUrl_str | http://journal.iasa.kpi.ua/oai |
| collection | OJS |
| datestamp_date | 2026-06-30T06:14:59Z |
| description | The publication is devoted to analyzing electrocardiogram signals of artificial origin of realistic form with the possibility of controlling the duration, sampling frequency, noise level and pulse rate using Ingrid Daubechies wavelets. The synthesized signals were investigated using discrete wavelet analysis to study the influence of these parameters on the approximation and detail coefficients. The priority influence of noise on the detail coefficients and the dependence of the number of signal peaks on the given parameters were established. The article uses for the first time the method of packet discrete wavelet filtering of detail coefficients and approximation coefficients. This allowed to provide a high degree of signal restoration to the original form. Similar studies were conducted for continuous wavelet transformation with the generation of wavelet scalogram images, which provide additional diagnostically significant information. The results obtained in the form of an algorithm are promising for use in analyzing signals from radar systems. The developed model for generating realistic-shaped signals is more efficient and exceeds the average accuracy (96.2 %) compared to analogues (88.03 %). The effectiveness of the developed method is fully confirmed by the correlation matrix of functions of discrete spectra of arti-ficial ECG signals. |
| doi_str_mv | 10.20535/SRIT.2308-8893.2026.2.02 |
| first_indexed | 2026-07-01T01:00:13Z |
| format | Article |
| fulltext |
Yu. К. Taranenko, O. Yu.Oliinyk, B. I. Moroz, D. M. Moroz, V. V. Lopatin, 2026
20 ISSN 1681–6048 System Research & Information Technologies, 2026, № 2
UDC 004.925+ 004.382:577.3+ 519.6:004.93
DOI: 10.20535/SRIT.2308-8893.2026.2.02
RESEARCH AND PROCESSING OF ECG SIGNALS USING
DISCRETE AND CONTINUOUS WAVELET ANALYSIS
YU.К. TARANENKO, O.YU. OLIINYK, B.I. MOROZ,
D.M. MOROZ, V.V. LOPATIN
Abstract. The publication is devoted to analyzing electrocardiogram signals of artifi-
cial origin of realistic form with the possibility of controlling the duration, sampling
frequency, noise level and pulse rate using Ingrid Daubechies wavelets. The synthe-
sized signals were investigated using discrete wavelet analysis to study the influence
of these parameters on the approximation and detail coefficients. The priority influ-
ence of noise on the detail coefficients and the dependence of the number of signal
peaks on the given parameters were established. The article uses for the first time the
method of packet discrete wavelet filtering of detail coefficients and approximation
coefficients. This allowed to provide a high degree of signal restoration to the original
form. Similar studies were conducted for continuous wavelet transformation with the
generation of wavelet scalogram images, which provide additional diagnostically sig-
nificant information. The results obtained in the form of an algorithm are promising
for use in analyzing signals from radar systems. The developed model for generating
realistic-shaped signals is more efficient and exceeds the average accuracy (96.2 %)
compared to analogues (88.03 %). The effectiveness of the developed method is fully
confirmed by the correlation matrix of functions of discrete spectra of artificial ECG
signals.
Keywords: Electrocardiogram (ECG), wavelet transform, packet wavelet filtering,
approximation coefficients, detail coefficients, packet filtering, classification.
INTRODUCTION
The principles of filtering and processing an electrocardiogram (ECG) signal are
similar to those used in radio engineering (noise removal, spectral analysis, etc.)
[1]. The accuracy of ECG signal analysis determines the correct diagnosis [2]. Dur-
ing ECG signal acquisition, various noises such as transmission line interference,
baseline deviation, motion, and noise distort the ECG signal [3]. Since the ECG
signal is non-stationary, it is pretty challenging to remove these noises from the
recorded ECG signal [4].
Algorithms for processing cardiac signals are very diverse. Among the well-
known methods of ECG processing, wavelet analysis can be distinguished. Unlike
processing cardiograms using bandpass filters, wavelet transforms can accurately
record both time and information about the frequency of the cardiac signal. The
essence of the wavelet analysis method is that the cardiac signal using the wavelet
transform is decomposed into approximating and detailing coefficients [5]. They
are responsible for the low-frequency and high-frequency components of the signal,
respectively [6]. After processing, the signal is a reconstruction of the signal using
approximation and detail coefficients [6].
Research and processing of ECG signals using discrete and continuous wavelet analysis
Системні дослідження та інформаційні технології, 2026, № 2 21
The study’s authors [3] conducted a comparative analysis of noise reduction
using discrete wavelet transform and various noise reduction methods (low-pass
filtering, high-pass filtering, empirical mode decomposition, Fourier decom-posi-
tion method of ECG signal distorted by noise). The signal-to-noise ratio, root-
mean-square difference, and root-mean-square error were used as evaluation crite-
ria. The experiment result showed [3] that the proposed ECG denoising method
based on discrete wavelet transform outperformed other electrocardiogram signal
denoising methods because more components of the ECG signal are preserved than
other de-noising algorithms.
The development of the wavelet analysis theory of electrocardiogram (ECG)
signals is a promising research direction. The existing theory needs further
development to simplify the processing of ECG signals. The research results can
be applied to the analysis of radar system signals.
ANALYSIS OF AREAS OF RESEARCH AND STATEMENT OF THE
PROBLEM
Classification of ECG signals is a challenging task due to a number of technical,
medical, and practical challenges. ECG signals have high variability between dif-
ferent patients, which makes it difficult to create universal recognition algorithms.
A model for generating artificial electrocardiogram (ECG) signals of realistic shape
is important for training artificial intelligence models, as it allows expanding the
volume and variety of training data under controlled conditions.
The second significant problem is the presence of noise and artifacts in the
recordings [3]. The ECG signal is very sensitive to body movements, problems with
electrode contacts, or electrical interference. Such distortions can affect the accu-
racy of classification, so the signals need filtering and preprocessing before analy-
sis [2]. Artificially generated ECG signals allow for precise control of heart rhythm
parameters, arrhythmia types, heart rate, etc., which enables AI training on a wide
range of clinical scenarios, including rare pathologies that are difficult to collect in
real data. This is especially important for building diagnostic systems with high
sensitivity and specificity.
Many machine learning methods require a uniform length of input data, but
when trimming or scaling ECG signals, important information can be lost. Many open
databases are created in conditions far from real clinical practice and do not take into
account many of the variations that doctors encounter in their daily work [4]. The use
of real medical data is associated with ethical and legal restrictions.
Using a model to generate artificial electrocardiogram signals is similar to the
image augmentation method widely used in computer vision. In the case of image
recognition, in order to increase the accuracy and robustness of the neural network,
modified versions of real images are added to the training set – they are changed in
brightness, rotated, scaled, mirrored, etc. [7]. This allows the model to better gen-
eralize information and cope with new input variants. Similarly, in the case of ECG,
artificially generated signals are “augmented” variants of cardiac activity that allow
the AI model to “see” more examples, including those that are rare or have unclear
manifestations in real patients. This is especially important in medicine, where
a diagnostic error can have critical consequences. Thus, the generation of synthetic
ECGs is a form of data augmentation that increases the quality and reliability of
Yu. К. Taranenko, O. Yu.Oliinyk, B. I. Moroz, D. M. Moroz, V. V. Lopatin
ISSN 1681–6048 System Research & Information Technologies, 2026, № 2 22
AI-based systems. The use of artificially generated signals in combination with real
data provides a more balanced, complete and scalable training of artificial intelli-
gence models in medicine.
The use of wavelet transforms in the analysis and processing of electrocardi-
ogram (ECG) signals is considered one of the most effective methods due to its
unique properties that prevail over traditional approaches such as fast Fourier trans-
form (FFT), filtering or principal component analysis (PCA).
The most comprehensive review of publications for the period 2011–2020
devoted to ECG signal processing algorithms using wavelet transforms is given in
the work of researchers D. Darwan and H. Mustafidah [4]. The authors note that
the most important aspect of ECG research in the future may be the use of datasets,
as well as feature extraction and classifications taking into account the level of
accuracy [8].
Wavelet transform has the ability to simultaneously analyze signals in both
the time and frequency domains. This is especially important for ECG signals that
are non-stationary, that is, they contain important information in individual short-
term signal sections (e.g., P, QRS, T waves). Traditional methods, such as FFT,
provide only the frequency spectrum and lose time localization, which critically
reduces the accuracy of diagnosis. Studies [9, 10] contain data confirming the ef-
fectiveness of using wavelet transform to extract features of ECG signals with an
accuracy of about 95.5 %−98.38 %.
Wavelets allow for multi-level decomposition of the signal, dividing it into
different scale components. This allows you to accurately isolate noise, artifacts or
interference without distorting the most important elements of the ECG. For exam-
ple, high-frequency noise can be effectively filtered at the appropriate decomposi-
tion level, while maintaining the clarity of the QRS complex [11].
Many studies and practical implementations of artificial intelligence systems
based on ECG signals show that wavelet features provide higher accuracy in clas-
sifying heart pathologies compared to features obtained using other methods
[11–13]. Machine learning algorithms trained on wavelet representation of the
signal demonstrate better results in the detection of arrhythmias, ischemia, atrial
fibrillation, etc.
The authors of the study [14] used a semi-synthetic ECG dataset with artificial
baseline deviations superimposed. The authors generated twelve baseline devia-
tions, including sinusoids, peaks, and step functions. The authors implemented and
evaluated 14 common wavelets up to 12 levels. The evaluation criterion was the
mean square error (MSE) between the original ECG fragment and the processed
signal with the artificial deviation removed [14].
In the work [15], the authors proposed a model based on ECG signal pro-
cessing using the discrete wavelet transform (DWT). The decomposition first
removes noise in the signal, then extracts statistical features from the noise approx-
imation coefficients of the signal, and finally classifies the data using cross-valida-
tion for greater confidence.
The analysis result is affected by the type of wavelet chosen for analysis.
In the research paper [16], noise removal using different levels of wavelet transfor-
mation (DWT) decomposition based on different types of mother wavelets, such as
orthogonal (Haar, Daubéchy, Coiflet, Simmle) and biorthogonal, is analyzed and
compared. The studies used cardiac signals cleaned of low-frequency noise, so we
Research and processing of ECG signals using discrete and continuous wavelet analysis
Системні дослідження та інформаційні технології, 2026, № 2 23
cannot speak about the full applicability of the method to the processing of real
cardiograms.
In [17], a wavelet packet filtering algorithm was developed, which included
moving along the branches of the wavelet packet tree with a restriction on each
branch of approximation and detailing the coefficients at the time of achieving the
minimum mean square error. The possibility of applying the method to the 20 most
frequently used signals was investigated, but data on the application of this ap-
proach to ECG processing are missing.
Effective wavelet filtering of real signals is impossible without determining
their shape. The shape of a real signal is related to its wavelet spectrum. In [18] it
was proposed to use continuous color wavelet scalograms for analyzing the wave-
form. The disadvantage of a continuous wavelet spectrogram is the complexity of
analyzing a blurred color image. To eliminate this disadvantage, we used a tech-
nique based on the comparative analysis of signal spectrograms and correlation
matrices, which are calculated by the formula using mathematical functions of the
coefficients of discrete wavelet spectra [18]. This method was tested on 20 of the
most common signals. The method has proven its effectiveness and efficiency, but
electrocardiogram signals have not been studied.
Modern evidence-based medicine allows the use of non-trivial algorithms for
analyzing and interpreting ECGs only after thorough testing on test signals that
adequately reflect the entire spectrum of signals possible in reality [19]. The prob-
lem of generating test signals that simulate real electrocardiogram signals is no less
significant than the choice of wavelet analysis parameters [20].
One of the well-known methods of such verification is testing algorithms us-
ing artificial signals that simulate a variety of real ECGs of normal and pathological
form [21]. Today, there are many models for generating synthetic ECG data for use
as test sets.
Examples of such generative ECG signal models are presented in [22–24].
Most of the methods for generating test signals initially used transformations such
as dithering and warping [22]. However, these methods simply modify the original
signal, which leads to poor diversity in the generated samples.
Recently, the synthesis of artificial ECGs based on deep learning models has
become widespread. The authors of [23] use generative adversarial networks
(GANs) to obtain synthetic ECG data that are difficult for humans to distinguish
from experimental data. The resulting dataset was used to train and evaluate a de-
noising autoencoder that achieves state-of-the-art filtering quality of ECG signals.
In [24], it is shown that the generated data improves the performance of the model
compared to a model trained only on experimental data.
Previous studies have shown that the performance of recent computerized
ECG interpretations is comparable to that of expert physicians, with correct classi-
fication rates of 91.3 % for the computer program and 96.0 % for cardiologists,
respectively [25].
An example of one model for generating synthetic ECG data is the project
[26]. This program for generating artificial cardiac signals has a significant draw-
back due to the limited variability of the input parameters (noise characteristics and
a limited wavelet base). However, the main drawback that prevents the use of the
model for signal generation is the lack of a function that limits the wavelet coeffi-
cients by the level of decomposition and reconstruction.
Yu. К. Taranenko, O. Yu.Oliinyk, B. I. Moroz, D. M. Moroz, V. V. Lopatin
ISSN 1681–6048 System Research & Information Technologies, 2026, № 2 24
Also, wavelet transform scales well and is suitable for both offline and real-time
analysis, which makes it an ideal tool for embedded cardiac monitoring systems. Thus,
wavelet transform provides high accuracy, flexibility, and efficiency in processing
complex medical signals, especially ECG, and is therefore rightfully considered one of
the best methods in modern biomedical engineering and diagnostics.
The purpose of this article is to further develop the theory of wavelet analysis
of ECG signals to improve the quality of signal analysis in medical information
systems for the detection of cardiac pathologies at early stages.
MATHEMATICAL MODEL OF DISCRETE WAVELET TRANSFORMATION
AND FILTERING OF ARTIFICIAL ELECTROCARDIOGRAM SIGNAL
FROM NOISE
For research and analysis, the article uses a generative model of electrocardiogram
signals of artificial origin of a realistic form. The difference between the created
model and that considered in the literature review [26] is the ability to control the
duration, sampling frequency, noise level, and pulse rate using Ingrid Daubechies
wavelets to simulate (Fig. 1).
A signal with additive Gaussian noise can be described by the relation:
( ) ( )i if t f t , (1)
where ( )if t – is the signal function; ( )if t – function of signal with noise;
– white normally distributed noise.
Wavelet decomposition of the signal f ti into levels for the approximation
and detail coefficients is determined by a system of equations [27]. For signals
without the influence of noise, can use a system of equations that has the form:
0 0
0 0
, ,
, ,
( ) ( )
( ) ( )
j j k i j j kR
j j k i j j kR
a f t t dt
d f t t dt
(2)
Fig. 1. Possibilities of a generative model of artificially generated electrocardiograms of
realistic shape compared to the model [26]
Research and processing of ECG signals using discrete and continuous wavelet analysis
Системні дослідження та інформаційні технології, 2026, № 2 25
For signals with additively added noise, the system of equations for the ap-
proximation and detail coefficients is as follows:
0 0
0 0
, ,
, ,
( ) ( )
( ) ( )
j j k i j j kR
j j k i j j kR
a f t t dt
d f t t dt
(3)
In expressions (2), (3) R – domain of definition ( ), ( )i if t f t ;
0 0, ,,j j k j j ka d ,
0 0, ,,j j k j j ka d – coefficients of approximation and detail under the influence of
noise, respectively;
0 0, ,( ), ( )J J k J J kt t – “maternal” and “paternal” wavelets, re-
spectively; 0 , ,j j k – initial, flow and serial number of wavelet coefficients.
Using a generative model of electrocardiogram signals, we synthesize an arti-
ficial electrocardiogram signal with a minimum noise level 𝑛𝑜𝑖𝑠𝑒 0.001, the dis-
crete wavelet decomposition of which is shown in Fig. 2. Let us change the level
of superimposed noise (𝑛𝑜𝑖𝑠𝑒 0.5), a discrete wavelet decomposition of such an
electrocardiogram is shown in Fig. 3.
Fig. 2. Discrete wavelet decomposition of an artificial electrocardiogram signal with
a minimum noise level noise 0.001
Signal reconstruction function using wavelet decomposition coefficients:
0 0 0 0, , , ,
1
( ,) )( ) ( ( )
J
i j j k j j k j j k j j k
k j k
f t a t d tF
(4)
where ( )if t – is the function of the noise-free signal; ( )jF – threshold function
j ;
0 0, , ( )( ), ( ),j j k j j k jt Ft – parameters of discrete wavelet-filtering to en-
sure minimal error [11]:
Yu. К. Taranenko, O. Yu.Oliinyk, B. I. Moroz, D. M. Moroz, V. V. Lopatin
ISSN 1681–6048 System Research & Information Technologies, 2026, № 2 26
2
1
1 ( ( ) ( )) ,
N
i i
i
Е f t f t
N
(5)
where Е – the minimum mean square filtering error or MSE model.
Fig. 3. Discrete wavelet decomposition of an artificial electrocardiogram signal with noise
level noise 0.5
For analysis, we compare the amplitudes of the discrete wavelet decomposi-
tion of the cardiogram with minimal noise (0.001) and a noise level of 0.5 (Fig. 4).
It is noteworthy that the increase in noise level is characterized by an increase in
the number of peaks (from 11 to 14 peaks).
Fig. 4. Comparison of amplitudes and number of peaks of signals, the discrete wavelet
decomposition of which is shown in Figs. 2 and 3
Research and processing of ECG signals using discrete and continuous wavelet analysis
Системні дослідження та інформаційні технології, 2026, № 2 27
FIRST ALGORITHM FOR PACKET WAVELET FILTERING OF ARTIFICIAL
ELECTROCARDIOGRAM SIGNAL
It should be noted that noise affects both the detailing and approximation coeffi-
cients (Fig. 3), and dramatically distorts the informative signal peaks (Fig. 4).
In the batch algorithm, both approximating
0 ,j ka and detailing
0 ,j kd coeffi-
cients are also calculated according to Mull’s algorithm (Fig. 5). The application of
packet wavelet filtering is described in detail in [27]. However, the studies were
carried out using relatively simple signals. The essence of the method is that when
decomposing the wavelet function of each subsequent level n, we obtain from the
wavelet functions of the previous level, forming a tree structure with nodes and
branches [27]:
φ φ( ), ψ ψ( ),n n
n n
h t n g t n (6)
where nh – are the low-pass filter coefficients for the current level of decomposition;
ng – high-pass filter coefficients for the current level of decomposition (Fig. 5).
Fig. 5. Wavelet-packet decomposition
This allows you to obtain narrow ranges in the high frequency region and con-
trol the high frequency region of the signal (Fig. 6). In case different types of signals
exhibit different frequency characteristics, this difference in behavior is reflected
in one of the frequency subbands. By generating a feature from each subband and
using the feature set as input to the classifier (random forest, gradient boosting,
logistic regression, etc.), the classifier distinguishes between different types of ECG
signals. Additional features can be obtained using special functions.
Fig. 6. A signal filtered by the wavelet packet filtering method, the decomposition of which
is shown in Fig. 3
Yu. К. Taranenko, O. Yu.Oliinyk, B. I. Moroz, D. M. Moroz, V. V. Lopatin
ISSN 1681–6048 System Research & Information Technologies, 2026, № 2 28
We rewrite relation (4) taking into account (6) in the form:
0 0 0 0, , , ,
1 1
ψλ λˆ φ ,
J J
j j k j j k j j k j j k
j k k
j j
j
F Ff t a t d t
(7)
It should be noted that the filtering error is extremely low, 0.06 %, which is
determined not by relation (3), but using the Euclidean norms of vectors of time
series of compared signals depending on the level of decomposition Level 6 and
wavelet coefficient coif17, obtained from the condition of minimum values in the
system:
0 0
0
0 0
0
, ,
,
, ,
,
|| ||
|| ||
|| ||
|| ||
o o
o
o o
o
J J
j j k j j k
j k j kd
j J
j j k
j k
J J
j j k j j k
j k j ka
j J
j j k
j k
d d
d
a a
a
(8)
where ,d a
j j – are the relative errors of the wavelet-coefficients; || ... || | – designa-
tion of the Euclidean norms of the corresponding vectors.
It should be noted that the use of packet wavelet filtering when processing
a noisy electrocardiogram allows one to isolate only significant peaks (Fig. 7).
Fig. 7. Peaks of the filtered signal shown in Fig. 6
It should be noted that the main difference between using packet wavelet fil-
tering of cardiogram signals and existing filtering methods is the possibility of iden-
tifying the most informative signal peaks in the time series of wavelet coefficients
with smoothing of bursts that do not carry information (Fig. 8).
Research and processing of ECG signals using discrete and continuous wavelet analysis
Системні дослідження та інформаційні технології, 2026, № 2 29
Fig. 8. Decomposition of a noisy artificial signal filtered by the wavelet packet method
MATHEMATICAL MODEL OF CONTINUOUS WAVELET TRANSFORM
CWT USING EXPERIMENTAL DATA
Wavelet-analysis should be carried out according to the well-known relationship
for a continuous local wavelet-spectrum [17, 28]:
,
1 ,a b
t bW x t dt
aa
(9)
where x(t) – is a signal with a random component; t b
a
– basic wavelet;
0a – scale parameter; 0b – shift parameter.
The data under study is discrete, so we write formula (9) in the form, selecting
two arrays for scales coeffs for shifts fred:
2
0
, .
N
i
i
i
t btcoeffs fred x t
aa
(10)
Since when analyzing artificial signals, the scale is of greater interest than the
shift, then to eliminate the dependence of the results on the shift 𝑏, use the repre-
sentative amplitude of scale inhomogeneity 𝑐𝑜𝑒𝑓𝑓𝑠 for shifts 𝑓𝑟𝑒𝑑. Obtaining the
energy spectrum using the wavelet transform involves using not the squared wave-
let coefficients, but their absolute values 𝑎𝑏𝑠 𝑐𝑜𝑒𝑓𝑓𝑠 .
For a cardiac signal with noise, visual changes in wavelet scalograms are
noticeable, which provide additional significant information for diagnosis and de-
tection of anomalies and can be used for training a neural network (Figs. 9 and 10).
Despite the fact that changes in wavelet scalograms are visually easily identi-
fied, evidence-based medicine gives preference to numerical evaluation indicators.
This is due to the fact that a significant share of expert subjectivity is present in
visual evaluation.
Yu. К. Taranenko, O. Yu.Oliinyk, B. I. Moroz, D. M. Moroz, V. V. Lopatin
ISSN 1681–6048 System Research & Information Technologies, 2026, № 2 30
To increase the efficiency of the method for analyzing artificial ECG signals,
we use the technique that was used to process the most common signals [18, 29].
We study the correlation of hourly series of discrete wavelet coefficients of a car-
diac signal using the example of a correlation matrix of time series compiled from
a complete filtered data set using the wavelet packet filtering method ECG signal
decomposition coefficients.
The open biosignal database PhysioNet [30] was used as the real medical data.
PhysioNet is an open scientific platform that provides free access to a large amount
of physiological and clinical data, tools for their analysis, and research resources.
The platform contains various types of patient medical records, including electro-
cardiograms (ECGs), the data are anonymized and presented in formats convenient
for processing. Among the most famous datasets hosted on PhysioNet is the
MIT-BIH Arrhythmia Database. This database represents one of the first and most
famous ECG datasets. Processing in accordance with the described methodology
was applied to each file of the PhysioNet database.
Fig. 9. Artificial ECG signal and signal spectrum with noise level 𝑛𝑜𝑖𝑠𝑒 0.001
Fig. 10. Artificial ECG signal and signal spectrum with noise level 𝑛𝑜𝑖𝑠𝑒 0.5
Research and processing of ECG signals using discrete and continuous wavelet analysis
Системні дослідження та інформаційні технології, 2026, № 2 31
A set of artificial cardiac signals is obtained by changing the parameters:
duration (int) – desired recording duration in seconds; sample_rate (int) – desired
sampling rate (in Hz, i.e. samples per second); length (int) – desired signal length
(in samples); noise (float) – noise level (Laplace noise amplitude); heart_rate (int) –
desired simulated heart rate (in beats per minute); heart_rate_std (int) – desired
standard deviation of heart rate (beats per minute); method (str) – the model used
to generate the signal. For a model based on Daubechies wavelets, this is “simple”.
(Fig. 11).
Fig. 11. Correlation matrix of functions from discrete spectra of artificial ECG signals
Using a correlation matrix makes it possible to identify groups of cardiac sig-
nals with similar influence of parameters. This significantly simplifies the task of
creating artificial ECG signals, which are used as a test base.
For the matrix above (Fig. 11), we study the nature of the dependence of the
entropy of signals on additively added noise (Fig. 12).
Fig. 12. Shannon entropy of artificial electrocardiogram signals
Yu. К. Taranenko, O. Yu.Oliinyk, B. I. Moroz, D. M. Moroz, V. V. Lopatin
ISSN 1681–6048 System Research & Information Technologies, 2026, № 2 32
To classify ECG signals, we use Shannon entropy as a criterion, similar to the
study [18]. In the study [18], signals are conventionally divided into simple and
complex by comparing the numerical values of entropy.
A feature of ECG signal processing (Fig. 12) is that for a group of cardiac
signals, as noise increases, their entropy remains constant. This feature is important
when building ultra-precise neural networks using signal images.
To demonstrate the effectiveness of the developed signal generation model,
a comparative analysis of the effectiveness of signal classification was performed
using the KURIAS-ECG database [30]. KURIAS-ECG is a standardized database
of 12-lead electrocardiograms with a common standard to facilitate cardiovascular
research [31]. KURIAS-ECG Database consists of a CSV file and 20.000 wave-
form database files. The database comprises 20.000 ECG data from 13.862 patients.
The average age of the patients is 58 years (±20), and the ratio of males to females
is 56% and 44%, respectively. The ECG data consists of 10 classifications based
on the Minnesota system, and each classification can be subdivided into statements
provided by the ECG device. [29, 30].
The deep learning model used in well-known studies to verify the signal qual-
ity of the electrocardiogram database [29, 32] showed an average accuracy of
88.03% in classification for seven categories. The developed model for generating
realistic shaped signals has the following accuracy indicators:
The Train Score is 1.0;
The Test Score is 0.9620253164556962.
The increase in the accuracy of the model classification is due to the fact that
the work uses denoising of electrocardiogram signals using the packet wavelet fil-
tering method (the approximation coefficients and detail coefficients are limited).
Therefore, data preparation for CNN using sets of wavelet decomposition of ECG
signals is more efficient (96.2%) compared to analogues.
CONCLUSIONS
A model has been developed for generating artificial electrocardiogram signals of
realistic shape to create test signals. The difference between the models is the ability
to control the duration, sampling frequency, noise level, and pulse rate using Ingrid
Daubechies wavelets to simulate. The presence of a large list of cardiac signal pa-
rameters allows the model to be used to generate a wide range of ECG test signals.
Using the parameters of artificial ECG signals, it is easy to prepare a DATASET
for CNN training.
The synthesized ECG signals were studied using discrete wavelet analysis to
study the influence of these parameters on the approximation and detail coeffi-
cients. It was found that the noise level has the most significant impact on detail
factors. The number of signal peaks increases with increasing noise level.
For the first time, an optimal packet wavelet filtering algorithm for both detail
coefficients and approximation coefficients of ECG signals was used to analyze
ECG signals of artificial and natural origin. This approach made it possible to
ensure a high degree of restoration of the cardiac signal to its original form and the
lowest possible error in filtering ECG signals. Similar studies have been carried out
for continuous wavelet transform with the generation of wavelet scalogram images.
It has been shown that scalograms provide additional diagnostically significant
information and changes in noise levels are visualized using scalograms.
Research and processing of ECG signals using discrete and continuous wavelet analysis
Системні дослідження та інформаційні технології, 2026, № 2 33
Comparative analysis of the accuracy of the developed model for generating
realistic signals with the indicators of known models showed that the developed
model is more effective (96.2%) compared to analogues (88.03%). The increase in
the accuracy of the model is due to the denoising of electrocardiogram signals by
the method of packet wavelet filtering (limitation of approximation coefficients and
detail coefficients). The effectiveness of the developed method is fully correlated
with the correlation matrix of functions of discrete spectra of artificial ECG signals.
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Research and processing of ECG signals using discrete and continuous wavelet analysis
Системні дослідження та інформаційні технології, 2026, № 2 35
INFORMATION ON THE ARTICLE
Yurii K. Taranenko, ORCID: 0000-0003-2209-2244, Private Enterprise “Likopak”,
Ukraine, e mail: tatanen@ukr.net
Olha Yu. Oliynyk, ORCID: 0000-0003-2666-3825, Dnipro Applied College of Radio
Electronics, Ukraine, e mail: oleinik_o@ukr.net
Borys I. Moroz, ORCID: 0000-0002-5625-0864, Dnipro University of Technology,
Ukraine, e mail: moroz.b.i@nmu.one
Dmytro M. Moroz, ORCID: 0000-0003-2577-3352, Dnipro University of Technology,
Ukraine, e mail: moroz.d.m@nmu.one
Valerii V. Lopatin, ORCID: 0000-0003-2448-0857, M.S. Poliakov Institute of Geotech-
nical Mechanics of the National Academy of Sciences of Ukraine, Ukraine, e-mail:
vlop@ukr.net
ДОСЛІДЖЕННЯ Й ОБРОБЛЕННЯ ЕКГ-СИГНАЛІВ ЗА ДОПОМОГОЮ
ДИСКРЕТНОГО ТА БЕЗПЕРЕРВНОГО ВЕЙВЛЕТ-АНАЛІЗУ / Ю.К. Тараненко,
О.Ю. Олійник, Б.І. Мороз, Д.М. Moроз, В.В. Лопатін
Анотація. Присвячено аналізу сигналів електрокардіограм штучного похо-
дження реалістичної форми з можливістю керування тривалістю, частотою дис-
кретизації, рівнем шуму та частотою імпульсів за допомогою вейвлетів Інгрід
Добеші. Синтезовані сигнали досліджувалися за допомогою дискретного
вейвлет-аналізу для вивчення впливу цих параметрів на коефіцієнти апроксима-
ції та деталізації. Встановлено пріоритетний вплив шуму на коефіцієнти деталі-
зації та залежність кількості піків сигналу від заданих параметрів. Уперше ви-
користано метод пакетної дискретної вейвлет-фільтрації коефіцієнтів
деталізації та коефіцієнтів апроксимації. Це дозволило забезпечити високий
ступінь відновлення сигналу до початкової форми. Аналогічні дослідження про-
водилися для безперервного вейвлет-перетворення з генерацією вейвлет-скало-
грамних зображень, які надають додаткову діагностично значущу інформацію.
Результати, отримані у вигляді алгоритму, є перспективними для використання
у ході аналізу сигналів радіолокаційних систем. Розроблено модель генерації
сигналів реалістичної форми, яка є більш ефективною та перевищує середню
точність (96,2 %) порівняно з аналогами (88,03 %). Ефективність розробленого
методу повністю підтверджується кореляційною матрицею функцій дискретних
спектрів штучних ЕКГ-сигналів.
Ключові слова: електрокардіограма (ЕКГ), вейвлет-перетворення, пакетна
вейвлет-фільтрація, коефіцієнти апроксимації, коефіцієнти деталізації, пакетна
фільтрація, класифікація.
|
| id | journaliasakpiua-article-365248 |
| institution | System research and information technologies |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-07-01T01:00:13Z |
| publishDate | 2026 |
| publisher | The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" |
| record_format | ojs |
| resource_txt_mv | journaliasakpiua/23/f09a7b2fc7a6a1d45067541543349023.pdf |
| spelling | journaliasakpiua-article-3652482026-06-30T06:14:59Z Research and processing of ECG signals using discrete and continuous wavelet analysis Дослідження й оброблення ЕКГ-сигналів за допомогою дискретного та безперервного вейвлет-аналізу Taranenko, Yurii Oliynyk, Olha Moroz, Borys Moroz, Dmytro Lopatin, Valerii електрокардіограма вейвлет-перетворення пакетна вейвлет-фільтрація коефіцієнти апроксимації коефіцієнти деталізації пакетна фільтрація класифікація electrocardiogram wavelet transform packet wavelet filtering approximation coefficients detail coefficients packet filtering classification The publication is devoted to analyzing electrocardiogram signals of artificial origin of realistic form with the possibility of controlling the duration, sampling frequency, noise level and pulse rate using Ingrid Daubechies wavelets. The synthesized signals were investigated using discrete wavelet analysis to study the influence of these parameters on the approximation and detail coefficients. The priority influence of noise on the detail coefficients and the dependence of the number of signal peaks on the given parameters were established. The article uses for the first time the method of packet discrete wavelet filtering of detail coefficients and approximation coefficients. This allowed to provide a high degree of signal restoration to the original form. Similar studies were conducted for continuous wavelet transformation with the generation of wavelet scalogram images, which provide additional diagnostically significant information. The results obtained in the form of an algorithm are promising for use in analyzing signals from radar systems. The developed model for generating realistic-shaped signals is more efficient and exceeds the average accuracy (96.2 %) compared to analogues (88.03 %). The effectiveness of the developed method is fully confirmed by the correlation matrix of functions of discrete spectra of arti-ficial ECG signals. Присвячено аналізу сигналів електрокардіограм штучного походження реалістичної форми з можливістю керування тривалістю, частотою дискретизації, рівнем шуму та частотою імпульсів за допомогою вейвлетів Інгрід Добеші. Синтезовані сигнали досліджувалися за допомогою дискретного вейвлет-аналізу для вивчення впливу цих параметрів на коефіцієнти апроксимації та деталізації. Встановлено пріоритетний вплив шуму на коефіцієнти деталізації та залежність кількості піків сигналу від заданих параметрів. Уперше використано метод пакетної дискретної вейвлет-фільтрації коефіцієнтів деталізації та коефіцієнтів апроксимації. Це дозволило забезпечити високий ступінь відновлення сигналу до початкової форми. Аналогічні дослідження проводилися для безперервного вейвлет-перетворення з генерацією вейвлет-скалограмних зображень, які надають додаткову діагностично значущу інформацію. Результати, отримані у вигляді алгоритму, є перспективними для використання у ході аналізу сигналів радіолокаційних систем. Розроблено модель генерації сигналів реалістичної форми, яка є більш ефективною та перевищує середню точність (96,2 %) порівняно з аналогами (88,03 %). Ефективність розробленого методу повністю підтверджується кореляційною матрицею функцій дискретних спектрів штучних ЕКГ-сигналів. The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2026-06-30 Article Article application/pdf https://journal.iasa.kpi.ua/article/view/365248 10.20535/SRIT.2308-8893.2026.2.02 System research and information technologies; No. 2 (2026); 20-35 Системные исследования и информационные технологии; № 2 (2026); 20-35 Системні дослідження та інформаційні технології; № 2 (2026); 20-35 2308-8893 1681-6048 en https://journal.iasa.kpi.ua/article/view/365248/350702 |
| spellingShingle | електрокардіограма вейвлет-перетворення пакетна вейвлет-фільтрація коефіцієнти апроксимації коефіцієнти деталізації пакетна фільтрація класифікація Taranenko, Yurii Oliynyk, Olha Moroz, Borys Moroz, Dmytro Lopatin, Valerii Дослідження й оброблення ЕКГ-сигналів за допомогою дискретного та безперервного вейвлет-аналізу |
| title | Дослідження й оброблення ЕКГ-сигналів за допомогою дискретного та безперервного вейвлет-аналізу |
| title_alt | Research and processing of ECG signals using discrete and continuous wavelet analysis |
| title_full | Дослідження й оброблення ЕКГ-сигналів за допомогою дискретного та безперервного вейвлет-аналізу |
| title_fullStr | Дослідження й оброблення ЕКГ-сигналів за допомогою дискретного та безперервного вейвлет-аналізу |
| title_full_unstemmed | Дослідження й оброблення ЕКГ-сигналів за допомогою дискретного та безперервного вейвлет-аналізу |
| title_short | Дослідження й оброблення ЕКГ-сигналів за допомогою дискретного та безперервного вейвлет-аналізу |
| title_sort | дослідження й оброблення екг-сигналів за допомогою дискретного та безперервного вейвлет-аналізу |
| topic | електрокардіограма вейвлет-перетворення пакетна вейвлет-фільтрація коефіцієнти апроксимації коефіцієнти деталізації пакетна фільтрація класифікація |
| topic_facet | електрокардіограма вейвлет-перетворення пакетна вейвлет-фільтрація коефіцієнти апроксимації коефіцієнти деталізації пакетна фільтрація класифікація electrocardiogram wavelet transform packet wavelet filtering approximation coefficients detail coefficients packet filtering classification |
| url | https://journal.iasa.kpi.ua/article/view/365248 |
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