Beamforming-based algorithms for recovering information from fetal ECG sensors


ACTA IMEKO 
ISSN: 2221-870X 
June 2023, Volume 12, Number 2, 1 - 8 

 

ACTA IMEKO | www.imeko.org June 2023 | Volume 12 | Number 2 | 1 

Beamforming-based algorithms for recovering information 
from fetal electrocardiographic sensors 

John P. Djungha Okitadiowo1, A. Lay-Ekuakille1, T. Isernia2, V. Bhateja3, S. P. Singh4 

1 DIEIS, University Mediterranea of Reggio Calabria, 89124 Reggio Calabria, Italy  
2 Department of innovation Engineering of Salento, Lecce 73100, Italy  
3 Department of Electrical and Computer Engineering, SRMCEM, 226028 Luckow (UP), India  
4 Department of Eletronics and communication Engineering, Netaji Subhas University of Technology, 110078 New Delhi, India  

 

 

Section: RESEARCH PAPER  

Keywords: Beamforming; array of sensors; ECG; fetal signals; adaptive filtering; MUSIC technique; apnea; applied mathematics 

Citation: John P. Djungha Okitadiowo, A. Lay-Ekuakille, T. Isernia, V. Bhateja, S.P. Singh, Beamforming-based algorithms for recovering information from fetal 
ECG sensors, Acta IMEKO, vol. 12, no. 2, article 20, June 2023, identifier: IMEKO-ACTA-12 (2023)-02-20 

Section Editor: Laura Fabbiano, Politecnico di Bari, Italy  

Received February 1, 2023; In final form April 19, 2023; Published June 2023 

Copyright: This is an open-access article distributed under the terms of the Creative Commons Attribution 3.0 License, which permits unrestricted use, 
distribution, and reproduction in any medium, provided the original author and source are credited. 

Corresponding author: John P. Djungha Okitadiowo, e-mail: johnpdjungha@unicr.it  

 

1. INTRODUCTION  

Eminent researchers in the scientific world are in the process 
of or have studied the separation or extraction of signals 
contained in an original envelope. The medicine applied in the 
field of paediatrics, more precisely in the branch of cardiology, 
encounters certain difficulties, to extract the fetal component of 
the electrocardiography (ECG) signal from the mother’s ECG 
signal to acknowledge problems of congenital diseases of the 
fetal/infant; in order to allow doctors to treat this as soon as 
possible, and to prevent the infant from being born with 
deformities or other problems that may complicate his/her life 

in the period of growth. The objective of this paper is to separate, 
by extracting from the raw ECG of the mother, the ECG of the 
fetal by preserving information content using Beamforming [1], 
[2], [3], [4], [5]. Currently, there are many methods for processing 
ECG signals, among which the transient electromagnetic 
method, short-time Fourier transform, de-shape short-time 
Fourier transform, and nonlocal median become the preferred 
method of researchers in ECG signal processing due to its fast 
signal extraction and decomposition, high efficiency, and great 
depth of exploration [6], [7], [8], [9]. The authors used the 
support vector machine to classify the electroencephalography 
signals of focal and non-focal electroencephalography using 
entropies [10]. Experimental results showed that the proposed 

ABSTRACT 
We deal with the extraction of the fetal electrocardiography (ECG) signal from the raw ECG signals of the mother by the beamforming- 
based algorithms. The foetal ECG sensors bring out signals containing information from the pregnant mother and the infant. Detailed 
and separate signals are already provided by the foetal ECG instruments; but for some specific studies related to the infant conditions, 
it is necessary to improve the quality of the signal with a dedicated processing. In this paper, four techniques, with some enhancements, 
are proposed to perform the processing; we have applied the following techniques: Least Mean Square (LMS) with adaptive noise 
cancellation technique, Discrete Wavelet Transform (DWT)-based technique, Empirical Wavelet Transform (EWT) technique, and 
Multiple Signal Classification (MUSIC). The LMS and the MUSIC pertain to beamforming approach. The techniques were used to 
decompose and identify the different elements constituting the source signal (mother's signal) and noise cancellation by Multivariate 
Empirical Mode Decomposition (MEMD) technique. The signal was adaptively decomposed by LMS, DWT and MUSIC according to 
optimised parameters to extract some hidden components of the source signal, such as the foetal features, QRS, heartbeat etc. The 
results have showed that LMS, with enhancements, is more effective in identifying and removing useless noise. The techniques were 
applied to the ECG signal of a 30-year-old healthy pregnant woman, which allowed to verify their applicability. 
The present research leads to the below main contributions among others: separation of the ECG signal of the foetus from the mother, 
highlighting the functional state of the foetal heart rhythm (heart rate and heartbeat,) and this can show us if the foetal ECG has 
malfunctions. 

mailto:johnpdjungha@unicr.it


 

ACTA IMEKO | www.imeko.org June 2023 | Volume 12 | Number 2 | 2 

approach distinguishes between seizure and non-seizure 
electroencephalography signals using performance measures 
such as sensitivity, accuracy, specificity, score, and Matthew 
Correlation Coefficient (MCC) to study the single-channel ECG 
to reconstruct the waveform of the respiratory signal, using the 
Discrete Wavelet Transform (DWT) [11]. The author applied 
Multivariate Empirical Mode Decomposition (MEMD) 
technique to separate maternal ECG from the abdomen ECG, 
and wavelet-based technique is employed to find fetal R-peaks. 
The performance was analysed by calculating cross correlation 
between the true and detected fetal heart rate signals [12]. The 
author applied an adaptive noise cancellation technique followed 
by the Stationary Wavelet Transform (SWT) in extracting fetal 
ECG from composite signal using Identification of Systems 
(DaISy) and PhysioNet database. Also, the fetal heart rate and 
Heart Rate Variability have been determined to identify fetal 
suffering [13]. In relation to all the techniques previously used, 
we have applied Beamforming with a combination of its two 
techniques (LMS and MUSIC) to perform decomposition to 
accurately extract the fetal electrocardiogram (fECG) 
components from the mother's ECG: The techniques of 
decomposition (MUSIC - Multiple Signal Classification, MEMD 
- Multivariate Empirical Mode Decomposition, LMS - Least 
Mean Square, and EWT - Empirical Wavelet Transform) it is 
obvious that the application of this combination has allowed to 
obtain one of the best results on the processing of the ECG the 
result obtained that we had implemented in this study is to have 
applied some enhanced techniques for the decomposition and 
extraction of the hidden components in the source signal. 

2.  ELECTROCARDIOGRAM  

The data quantity in the medical field is rapidly increasing, 
thus obliging scientists to find effective and adequate techniques 
and means for their rapid treatments to save human lives. From 
this need a series of methods have emerged, however 
electrocardiogram (ECG) occupies the best place in the field of 
measuring cardiac activities. ECG is a test that studies the 
functioning of the heart by measuring its electrical activity. With 
each heartbeat, an electrical impulse (or 'wave') passes through 
the heart. This wave causes the heart muscle to contract so that 
it expels blood from the heart. An ECG measures and records 
the electrical activity that passes through the heart. A doctor can 
determine whether the electrical activity seen is normal or 
irregular. An ECG may be recommended if one has arrhythmia, 
chest pain or palpitations. Abnormal ECG results can be used to 
detect various heart problems [13]. 

The ECG is used to detect arrhythmias that can lead to blood 
clots; that is to detect heart problems such as recent or ongoing 
heart attacks, arrhythmias (irregular heartbeats), blockages in the 
coronary arteries, damaged areas of the heart muscle (caused by 
a previous heart attack), enlargement of the heart and 
inflammation of the heart wall (pericarditis). In the case of a 
pregnant woman, it is mandatory to monitor the heart rate of the 
fetal to take appropriate precautions for treatment before and 
after birth if the baby has heart problems. 

2.1. Heartbeat modelling 

Heartbeat modelling is an essential step to automatically 
identify characteristic waves. The aim is to find a mathematical 
representation, as simple and compact as possible, of the shape 
of each wave constituting the heartbeat. Thus, the most natural 
representation of waves is to describe the signal by its amplitude 
at each instant. Thus, a vector in a space whose dimension would 

be equal to a few hundred. The identification of the characteristic 
waves of the cardiac rhythm is carried out in two stages: 
segmentation and labelling. Segmentation corresponds to the 
division of the cardiac rhythm into zones likely to contain each 
cardiac wave. Labelling corresponds to the attribution of a 
medical label (P, Q, R, S or T) to each of the zones defined during 
segmentation. The signal to be decomposed is therefore an 
isolated heartbeat. 

For example, if we consider the signal 𝑆 of a beat to be 
modelled (Figure 1) sampled at 500 Hz, it is composed of 342 

points. The signal 𝑆0, used for the decomposition, is the vector 
composed of the signal 𝑆 preceded by 85 zeros and followed by 
84 zeros, which brings the dimension of this vector to 512, or 

29 ∙ 𝑆0 is therefore also a vector 𝑆0 of the 512-dimensional space 
whose 𝑖-th coordinate in the canonical base is the value of the 

signal at point 𝑖. In all that follows, the vectors of this space are 
noted in bold type.  

The first step in the decomposition is the construction of the 

wavelet basis. If 𝑆0 is the signal, to be decomposed, of length 𝑁𝑝 

(the number of points), the basis consists of 𝑁𝑝 orthogonal 

wavelets 𝑆 𝐼, all of which are deduced from the "mother" wavelet 
by translations and dilations. Let 𝜑 be the mother wavelet; the 
basis is constructed as follows: 

𝐵 = {𝜑(2𝑚 × ±𝑛), 𝑛 ∈ [1. . 2𝑚−2], 𝑚 ∈ [1. . log2( 𝑁𝑝)]}. (1) 

In (1) it is shown that, 𝑚 and 𝑛 are respectively the expansion 
and position coefficients of each wavelet, and 𝑁𝑝the length of 

the signal to be modelled wavelets, and 𝑁𝑝is the length of the 

signal. The 𝑁𝑝 − 𝑝 basic functions are denoted {𝜑1}𝑖=[1..𝑁𝑝−1] 

in the following. Such a library is shown in Figure 2; wavelets 

 

Figure 1. The orthogonal wavelet transforms.  

 

Figure 2. Wavelet family used for the decomposition of the 𝑆0 signal.  



 

ACTA IMEKO | www.imeko.org June 2023 | Volume 12 | Number 2 | 3 

(here Coiflets) that have the same expansion (constant 𝑚) are 
represented on the same line. The modelling of the signal is 
computationally inexpensive due to the orthogonality property 
of wavelets mentioned above. 

Once the basis is constructed, the decomposition of the signal 

𝑆0 is to apply to the vector 𝑆0 the matrix of passage from the 
canonical basis to the in other terms, to calculate the coordinates 

of the 𝑆0 vector in wavelet basis wavelet basis:  

𝑆0 = ∑ ⟨𝑆0|𝜑𝑖 ⟩𝜑𝑖

𝑁𝑝−1

𝑖=1

 . (2) 

Also, in (2) where ⟨𝑆0|𝜑𝑖 ⟩ represents the 𝑖-th coordinate of 
the signal in the wavelet base. Thus, if we decide to choose 

𝑁 <  𝑁𝑝 − 1 wavelets to model the signal 𝑆0, the best 𝑌 model 

will be obtained with the 𝑁 wavelets having the largest scalar 
product in value.  

The model 𝑌 demonstrated in [15] will be obtained with the 
wavelets having the largest absolute scalar product with the signal 

𝑌(𝑡) = ∑ ⟨𝑆|𝜑𝑖 ⟩𝜑𝑖 (𝑡)

𝑖={𝐴}

, (3) 

where 𝐴 represents the indices of the 𝑁 largest absolute scalar 
products between the 𝜑𝑖  and 𝑆0, the mean square modelling 
error is then written in (4) as  

𝐽 =
1

𝑁𝑝
∑((𝑆(𝑖) − 𝑌(𝑖))2

𝑁𝑝

𝑗=1

 . (4) 

The results of the decomposition the example of an 𝑁 = 10 
wavelet model of the previous beat is shown below in Figure 3. 

3. SIGNAL POST PROCESSING TECHNIQUES 

Broadly speaking, we have two procedures for extracting fetal 
ECG signal (fECG). The first is to attach an electrode directly to 
the fetal scalp (head), but this makes the mother too 
uncomfortable. The last and second one, for the one we used, 
consists in the extraction of the fECG using electrodes placed on 
the mother (Figure 4) to mean that here we will have in a single 
envelope carrying the signal both ECGs, which will carry out the 
objective of our study to carry out the extraction of the fECG 
from the ECG signal of the mother (MECG). The importance 

of this method is that it avoids any contact between the fetal and 
any external energy. 

It is very important to point out that the ECG technique is a 
painless, non-invasive procedure, which means that nothing is 
injected into the body. The technique is carried out by means of 
electrodes (Figure 4 and Figure 5), usually between 12 and 15, 
which are attached to various parts of the body such as the arm, 
leg, and chest, in a particular way its electrodes are attached with 
small suction cups or adhesive patches, which have sensors that 
detect the electrical activity of the heart. An ECG normally takes 
between 5 and 10 minutes [14].  

For the adaptive filter unit, the two main parts (blocks) are: 
first digital filter and last the adaptive algorithm; the filtering is 
performed by the digital filter and the adaptive algorithm 
performs a weight adjustment; the operation is carried out 
automatically, see Figure 6, and see also the adaptive filter with 

explanation: 𝑑(𝑛) desired signal, 𝑦(𝑛) output of a digital filter 
driven by input signal 𝑥(𝑛), and the error signal 𝑒(𝑛) is the 
difference between 𝑑(𝑛) and 𝑦(𝑛). A predetermined cost 
function that is related to 𝑒(𝑛) that the adaptive algorithm can 
minimize by updating the weights of the filters [15]. 

The adaptive filter is implemented with a different number of 
structures and realization: the calculation, the complexity and the 
level of performance are decided by the choice of the structure 
and the number of iterations. In its adaptive implementation: 
speed of learning or convergence, computational complexity 

 

Figure 3. The best 𝑌 model with N = 10 Coiflets for the signal S0 is shown on 
the left (a). The decomposition is the weighted sum of the 10 wavelets shown 
on the right (b).  

 

Figure 4. Acquisition of the maternal and fetal ECG signal, A1 … A4: abdominal 
leads, V0: reference electrode, N: active ground.  

 

Figure 5. ECG signal collection in a pregnant mother.  

 

Figure 6. Diagram of adaptative filter.  



 

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numerical precision and the stability of the algorithm are of the 
fundamental questions. LMS is a simple and stable algorithm but, 
its speed is slow. In the LMS algorithm, the weight update is 
written in the form below. The relationships of the filter 
algorithm are given in (5) and (6). 

𝑦(𝑛) = 𝑤 T(𝑛 − 1) 𝑢(𝑛) (5) 

𝑒(𝑛) = 𝑑(𝑛) − 𝑦(𝑛) (6) 

𝑤(𝑛) = 𝛼 𝑤(𝑛 − 1) + 𝑓(𝑢(𝑛), 𝑒(𝑛), 𝑢). (7) 

LMS filters allow us to find the filter coefficients, minimizing 
the difference between the desired signal and the error signal, 
which formulas are described in (8) to (10) 

𝑓(𝑢(𝑛), 𝑒(𝑛), 𝑢) = 𝑢(𝑛) 𝑢∗(𝑛) (8) 

𝑤(𝑖 − 1) + 𝑢 𝑒(𝑖) 𝑥(𝑖) (9) 

where 𝑒(𝑖) is the error signal, 𝑥(𝑖) is the input, 𝑢(𝑛) is step size 
parameter,  𝑢∗(𝑛) is the estimated filter; interpreted as the 
estimation of the filter coefficients after 𝑛 samples, and 𝑤(𝑖) is 
the weight function. The parameter 𝑢 satisfies the condition 

0 < 𝑢 <
1

𝜆max
. (10) 

Figure 7 shows detection and extraction of the fetal heartbeat 
from the mother's heartbeat (measured signal) by adaptive 
filtering technique; Figure 8 shows the cancellation and error 
detection also noise contained in the signal to output reference 
signal with MEMD. 

4. PROPOSED APPROACH 

We have proposed four joint approaches, including wavelet 
transformation technique. The wavelet technique is essential in 
clinical studies to detect the different signals that make up a raw 
one; the wavelet transformation is a recent technique in non-

invasive electrocardiology. Details of the ECG signal are 
highlighted in time and frequency resolution using wavelet 
transformation [16]. During our study, we have opted for the 
wavelet technique to extract up to the minute information of the 
abdominal signal and knowing that this algorithm remains 
complex. The goodness of this set of algorithms is the following: 
the best representation of the signal missed by one member 
could necessarily be represented by another, to have the fECG 
(fetal ECG) signal. We have tried to apply the wavelet (dB10), 
with the regularity of the wavelet is dB10 (1.25) which is a little 
higher than that of dB4 (2.90). fECG signal is extracted from the 
original signal using a two-level wavelet transform. Wavelet 
transformation technique uses the convolution of the wavelet 

function 𝜓(𝑡) with the signal 𝑥(𝑡) is the wavelet transform. In 
this technique, the dyadic orthonormal discrete wavelets will be 

put together to scaling functions 𝜑(𝑡), the coefficient 
approximation is produced by convolving the scaling function 
and the signal. The DWT is written in Eq. (11), [17].  

To reconstruct the original signal, we have selected a wavelet 

base 𝜓𝑚,𝑛 (𝑡) of coefficient approximation, at the scale and in 

the location as represented by the 𝑚, 𝑛, is described in (11) and 
(12)  

𝑆𝑚,𝑛 = ∫ 𝑥(𝑡) 𝜑𝑚,𝑛(𝑡) d𝑡
∞

−∞

 (11) 

𝑥0(𝑡) = 𝑥𝑀 (𝑡) + ∑ 𝑑𝑚 (𝑡)

𝑀

𝑚=1

. (12) 

The least mean square is a search algorithm in which a 
simplification of the gradient vector computation is made 
possible by appropriately modifying the objective function. The 
LMS algorithm, as well as others related to it, is widely used in 
various applications of adaptive filtering due to its computational 
simplicity. The convergence characteristics of the LMS algorithm 
are studied in order to establish a range for the convergence 
factor that will guarantee stability; (difference between the 
desired and the actual signal), as shown from (13), up to (16). 

𝑊𝑘 (𝑛 + 1) = 𝑊𝑘 (𝑛) − 𝜇 ∇𝐽 , (13) 

where, ∇ is the gradient of MSE 𝐽, 𝜇 is the step size, 𝑊𝑘 (𝑛) is 
tap value of kth tap nth iteration. The step size can be variable or 
constant. In LMS algorithm, it is a constant positive number 
whose value ranges from 

0 < 𝜇 <
2

𝑌max
 , (14) 

where 𝑌max is maximum eigen value of R. If 𝜇 exceeds the limit, 
then the trajectory of 𝑊𝑘  becomes unstable. 

In (15) and (16) of steepest descend algorithm [18], [19]. Now 
LSM algorithm estimates the gradient as: 

𝑊𝑘 (𝑛 + 1) = 𝑊𝑘 (𝑛) + 𝜇 𝐸[𝑒(𝑛)
∗ 𝑋(𝑛)] (15) 

𝑊𝑘 (𝑛 + 1) = 𝑊𝑘 (𝑛) + 𝑢
∗𝑒𝑛 × 𝑋𝑛. (16) 

With this algorithm, calculating the value of the next catch 
becomes easier. Updating the kth value requires only 1 
multiplication and 1 addition. Therefore, for a filter of order 
P+1, P+1 multipliers and adders are needed. An adder is needed 

to find 𝑒(𝑛) and a multiplier for 𝑢∗ 𝑒(𝑛) [20], [21]. Finally, P 
adders and P+1 multipliers are needed to find the output 𝑦(𝑛). 

 

Figure 7. Fetal ECG detection/extraction using the adaptative filtering 
technique.  

 

Figure 8. Adaptative noise cancellations. 



 

ACTA IMEKO | www.imeko.org June 2023 | Volume 12 | Number 2 | 5 

Thus, a total of 2 P+3 multipliers and 2 P+2 adders are needed. 
Flowchart of LMS algorithm, the flowchart of is based on the 
following three equations: 

𝑦(𝑛) = 𝑤(𝑛)∗ 𝑥(𝑛) (17) 

𝑤(𝑛 + 1) = 𝑤(𝑛) + 𝜇∗ 𝑒(𝑛)∗ ∙ 𝑥(𝑛). (18) 

Equation (17) calculates the output of filter by multiplying 
input with the filter weights, (6) calculates the error between 
desired signal and output. The equation (18) is of filter weight 
adaptation. It denotes the LMS algorithm. The weights are 
calculated by changing the previous weight and the converging 

factor. 𝜇∗ is the complex conjugate of the vector of input 
samples. We also used the MUSIC technique, the literature on 
the MUSIC algorithm is described in [20]. 

Pre-processing  

In the field of signal processing, it is obviously necessary to 
prepare the signal before processing; to improve the quality of 
the signal and the operation is called pre-processing. 

The objective is to remove all kinds of impurities and 
unwanted elements from the signal as shown in Figure 9. We 
have used the MEMD technique to pre-process the signal, which 
has allowed us to detect and remove the noise as shown in 
Figure 9. 

Segmentation 

The segmentation of components of the mother's ECG signal 
allows to point out them , at this stage also the components of 
our fetal ECG signal (peak, QRS, frequency, heartbeat, apnea 
peak etc.) will appear automatically, by means of the MUSIC 
algorithm (Figure 10 and Figure 11).  

The use of the algorithms saves time in the interpretation of 
the ECG signal and especially for a pregnant woman, which 
brings the fetal signal inside [21].  

Post-processing 

An ECG is a test that looks at how the heart works by 
measuring its electrical activity. With each heartbeat, an electrical 
impulse or wave passes through the heart. This wave causes the 
heart muscle to contract so that it expels blood from the heart, as 
discussed in Section II. Here we are not dealing with an ordinary 
ECG signal, but with an ECG signal from a pregnant woman, so 
by taking this ECG automatically we have a double ECG in its 
components (mother and fetus). The objective of this study is to 
separate all the components of the source signal to highlight the 

ECG of the fetal as well as its internal components, as shown by 
the different results. This is of paramount importance to provide 
information to the cardiologist or paediatrician to diagnose 
cardiological condition of the mother and much more so of the 
fetal, and to prepare for the different eventualities if the fetal heart 
has abnormalities. The algorithms allow to clearly separate the 
components of the two signals in terms of frequency, wave peaks, 
power spectrum, decimations, interpolations. 

5. RESULTS  

ECG, by its nature, is a non-invasive technique that provides 
electrical signals of the heart activity. In this paper, ECG signal 
processing with appropriate techniques (MUSIC, MEMD, LMS, 
EWT) have brought a significant improvement in the 
interpretation of an ECG signal, 

Especially in the interpretation of an ECG signal from a 
pregnant woman. The detection of the different components of 
the signal, the most innovative improvement is the separation the 
components of two ECG signals (mother and fetus), which were 
initially in one ECG signal, the mother's as we have mentioned 
at the beginning of our work, that is the framework in which we 
have worked, the results Figure 12–Figure 20 show how the two 
ECG signals are separated. 

In order to help the cardiologist in saving time in the 
interpretation of the ECG signal of a pregnant woman, which 
will allow him/her to have precise information on the cardiac 
activities of the fetus, to see if the heart of the fetus is in good 
health, on the contrary, to prepare an appropriate therapy 
immediately, because the algorithms will highlight the problems 
detected so the cardiologist can give a precise diagnosis.  

 

Figure 9. Fetal ECG detection/extraction using EWT technique.  

 

Figure 10. Detection and labelling of apnea components.  

 

Figure 11. Decimated and interpolated tremor suppression (left), 
Interpolated and Decimated and noise cancellation signal (right). 



 

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The plot of the Figure 13 shows a overlapping of the two 
signals (Power Spectrum of the ECG signal of (the red) mother 
and that of the fetal in blue); the plot indicates that the fetal heart 
is still dependent on that of its mother, since the peaks of the two 
signals are at the same rate with just a small difference because 
that of the fetal lives on the blood of its mother. This leads us to 
confirm that the algorithm has worked. 

Figure 15 shows a separation of the signals which were 
contained in a single envelope of origin or source (maternal ECG 
signal) with the different R peaks of each signal; the present result 
is obtained thanks to the Multiple Signal Classification algorithm 
(MUSIC), which allows to classify, to separate and to provide 

 

Figure 12. Abdominal ECG after suppressed power line interference noise at 
50 Hz and Abdominal ECG after removing interference from the power line, 
line based on the wandering and trembling.  

 

Figure 13. Power spectrum of simulated mother ECG signal and power 
spectrum extracted fetal ECG signal.  

 

Figure 14. Power Spectrum overlapping of the mother's ECG signal and her 
fetal component.  

 

Figure 15. Fetal QRS detection from mother's ECG signal.  

 

Figure 16. Power spectrum overlapping of the monther’s apnea and her fetal 
signal.  

 

Figure 17. Power spectrum overlapping of the mother’s apnea and her fetal 
signal on the left, Detection of maternal, fetus and airway pressure apnea 
peaks on the right.  

 

Figure 18. A comparison of the SNR of the EWT and LMS algorithm.  



 

ACTA IMEKO | www.imeko.org June 2023 | Volume 12 | Number 2 | 7 

unbiased estimates of the number of muniscule signals and also 
to discriminate the signals from the noise which was on board 
during transmission, recording or during its diffusion in different 
transmission channels and, sometimes with certain details as 
detected, see Figure 19. 

We have decided, given the objectives of the paper to 
introduce decimation and interpolation for a further 
interpretation. Decimation and interpolation are two operations 
that affect the timescale of a signal. For discrete signals, time 
scaling corresponds to increasing or decreasing the length of the 
signal. However, we must pay attention to how these operations 
are carried out. Decimation is the time compression of a signal. 
This corresponds to speeding up a signal or reducing its sampling 

rate. Suppose we have a signal 𝑥[𝑛] which corresponds to a 
continuous signal 𝑥(𝑡) samples at 𝑡𝑠 intervals. The signal 𝑦[𝑛] is 
then equivalent to the compressed signal which is sampled at and 

contains the samples 𝑥[0], 𝑥[2], 𝑥[4], . .. . 𝑦[𝑛] can also be 
obtained directly if the signal 𝑥(𝑡) is sampled at intervals of 2 𝑡𝑠. 
Decimating by a factor of N is equivalent to keeping all N 
samples of a signal. This can lead to information loss. Figure 10 
details the procedure for detecting the components of the apnoea 
signal and labelling them with the MUSIC algorithm, on a normal 
class of apnoea including hypopnoea which are shown here in 
bright colours: red, yellow, and green, as well as other lines 
labelled in this way, with this legend: AF: Airflow, AE: 
Abdominal Effort, TE: Thoracic Effort ST: Stage Label. 

Another needed operation is the interpolation. It is the stretch 
over time. This corresponds to slowing down the signal or 

increasing the sampling rate. Suppose we have a signal 𝑥[𝑛] 
which corresponds to a continuous signal 𝑥(𝑡) sampled at 

intervals 𝑡𝑠. The signal 𝑦[𝑛] = 𝑥 [
𝑛

2
] is then equivalent to the 

signal 𝑥(𝑡) which is sampled at intervals of 𝑥(𝑡) (or at a rate of 

𝑆 =
2

𝑡𝑠
). We therefore have twice as many samples: we have 

stretched the signal (8) in both directions. However, how do you 
calculate the value of the new samples? Three popular techniques 
exist for doing the interpolation: 1. Zero interpolation: Implies 
that each new sample is zero, 2. Step interpolation: We take the 
previous value for the new sample, and 3. Linear interpolation: 
The values on each side of the new sample are averaged, the 
figure: interpolation shows an example of three types of 
interpolation. Figure 11 is the original signal. The samples in red 
are the new samples. Decimation is the reverse of interpolation, 
but the inverse is not necessarily true. When we apply the 
decimation, we lose some information; so we are not able to 
reproduce the original signal correctly. As an example, we use the 

sequence.
{1,2,6,4,8}
  First, we apply the step 

interpolation to this sequence, and we get: 
{1,1,2,2,6,6,4,4,8,8}
  

However, if we inverse the order of operations, we will not 
find the original sequence. First, we apply the decimation on the 
sequence 𝑥[𝑛], and then we apply the step interpolation: 

{1,1,6,6,8,8}
  which is not the same sequence as the original. 

6. CONCLUSIONS 

Currently, considerable progress has been made with the 
advent of the beamforming technique. Beamforming, also called 
spatial filtering, or channel formation, is a signal processing 
technique used in antenna and sensor networks for the 
transmission or directional reception of signals. four approaches 
are used (LMS, MUSIC, MEMD, EWT) as shown in Figure 20 
during different experiments.  

The objective of this study is to decompose, visualize and 
highlight internal components of the ECG signal of a pregnant 
woman, as we are seeing in Figure 11 – Figure 20, the various 
techniques made it possible to carry out a normal decomposition 
and separation of the internal components of the initial signal 
(mother's ECG). referring to the previous paragraph, the goal is 
to save time for health professionals (cardiologist) in the 
interpretation of an ECG signal, especially the ECG of a 
pregnant woman including that of the fetus.  

The approach used in this paper remains mostly filtering to 
separate components of a signal by their frequencies and on their 
channels; the beamforming approach (adaptive filtering) is 
reliable in the processing of ECG signals; each component of the 
signal source has been filtered by its appropriate frequency. 

 

Figure 19. EWT Flowchart.  

 

Figure 20. A comparison of the SNR of the MUSIC, MEMD, LMS and EWT 
algorithms for ECG (a) and apneas (b) of the mother and the fetus.  



 

ACTA IMEKO | www.imeko.org June 2023 | Volume 12 | Number 2 | 8 

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https://doi.org/10.3389/fphys.2022.964755
https://doi.org/10.1515/jpm-2018-0221
https://doi.org/10.1088/1361-6579/ab3c96
https://doi.org/10.1016/j.earlhumdev.2014.04.009
https://doi.org/10.3389/fphys.2017.00277
https://doi.org/10.3389/fams.2017.00002
https://doi.org/10.1016/j.patrec.2017.05.007
https://doi.org/10.1016/j.bbe.2020.02.002
https://doi.org/10.1109/JSEN.2013.2257742
https://doi.org/10.1016/j.compbiomed.2015.11.007
https://doi.org/10.1109/ICEEE.2016.7751243
https://doi.org/10.3390/app9142921
https://doi.org/10.1016/j.jelectrocard.2020.10.006
https://doi.org/10.1109/PROC.1975.10036
https://doi.org/10.1016/j.sbsr.2022.100502
https://doi.org/10.1016/j.bbe.2017.06.001
https://doi.org/10.1016/jmeasen.2022.100389
https://doi.org/10.3390/s22082843
https://doi.org/10.1016/j.sigpro.2021.108344
https://doi.org/10.1016/S0167-6393(02)00087