biomedical signal processing and its analysis

Introduction
Quantum computing is a theoretical computation system that performs operations on data by using quantum-mechanical
phenomena(such as superposition, teleportation, and entanglement). Quantum computation and quantum information is
the study of the information processing tasks that can be accomplished using quantum mechanical systems. Quantum
computing executes some exciting behaviour for some non-polynomial complex problems. Analogous to a classical bit, the
quantum system uses quantum bit or qubit as an elementary unit of information. Qubit consists of two possible states |0 >
and |1 > and also form a linear combination of states, often called superposition [10]. So, unlike classical bit, a qubit can take
any quantum linear superposition of |0 > and |1 >, i.e., it can exist in any of uncountably many states [10]. The general state
of an electron can be represented by the superposition (|ψ) of the above two-qubit states, |ψ = α(0) + β(1), 2n−1 i=0 ci.

CVDs
• Cardiovascular disease (CVDs) refers to various problems with heart
or blood vessels, including heart attacks, heart failure, and stroke.
According to the world health organization survey, nearly eighteen
million human beings lose their lives each year [1]. Initial symptoms
such as unexplained chest pain or exhaustion after moderate physical
activity are frequently ignored.
• Thus, many patients are treated only after suffering from a heart
attack or stroke. CVDs mainly occur because of the accumulation of
plaque inside arteries, making the walls thicken and reducing the
arteries’ available cross-section area. As a result, the blood flow to
organs and tissues reduces. As a result, to bring the blood flow to
typical rates, the heart needs to pump more blood per unit time. Thus,
the pressure on the heart increases.
• This inadequate blood supply rate sometimes ruptures heart muscles,
which leads to myocardial infarction.

Cause of cardiovascular diseases
• In many cases, CVDs are also due to the chronic inflammatory condition. Atherosclerosis is due to
unhealthy eating habits, lack of exercise, a deposit of fats, cholesterol, and other substances present in
the blood building up over many years inside the arteries. The primary investigation and diagnosis of
CVDs are generally made with an ECG monitor.
• The heart’s conduction system controls the generation and propagation of electrical signals that cause
the heart muscle to contract and the heart to pump blood. This electrical activity is measured by placing
electrodes at specific points on the human body. The measured electrical activity from electrodes forms
a composite recording in the form of a graph famously known as ECG [2]. Tracing the heart’s resultant
electrical activity consists of propagating many action potentials, . ECG is the most recognized tool for
various biomedical applications, such as measuring heart rate, examining arrhythmia, diagnosing heart
abnormalities, emotion recognition, and biometric identification [3]. For proper diagnostics of heart
abnormalities, an ECG signal must be clean.
• In most cases, ECG signals are not clean as noises and artifacts corrupt these signals. The primary
sources of noise are poor contact between electrodes and skin, incorrect positioning of electrodes,
activities of various muscles in the body, respiration, surrounding electrical equipment, and electronic
devices used by the machine itself. Therefore, it is necessary to remove noises and artifacts so that
ECG features can be examined efficiently and correctly. Some common noises are listed below.

Types of noises in signals
• 1.Baseline wandering: It is a low-frequency noise from 0.15–
0.3 Hz and is generally created by the patient’s respiration or
movements [3].
• 2.Powerline interference: It is a high-frequency noise in the
frequency range of 50 Hz to 60 Hz, which is generally due to the
power supply lines.
• 3.Motion artifacts: They are low-frequency noises that result from
the displacement of electrodes placed on the skin and subject
movement.
• 4.Electromyogram Noise (created by muscles): Electromyogram
noise generally occurs due to muscle contraction and relaxation
other than cardiac muscles and lies typically in the frequency
range of 5–500 Hz.

Noises
• Out of the noises given above, baseline wandering, and powerline interference are the most
prominent noises because baseline wandering occurs in the low-frequency region. In contrast,
powerline interference occurs in the high-frequency region.
• These noises change some characteristics of the signal, which hinders proper diagnosis.
Baseline wandering disturbs the ST segment period, one of the crucial parameters used in
diagnosing CVDs .
• Similarly, powerline interference completely overlaps the ECG signal’s P and T waves, making
the signal useless . Thus, it is necessary to eliminate these noises without removing the
features of the ECG signal.
• The proposed study aims to provide a comparative analysis of the most used ECG denoising
techniques.

filtering
• A high pass filter is used to remove baseline wandering
noises, while the lowpass filter is used to remove
powerline interference noises. While eliminating these
noises, some critical features of the signal get
eliminated.
• A notch filter effectively removes powerline interference
noise. The notch filter’s main disadvantage is its low-
speed of computation and ringing due to the extended
response. Zero-phase bi-directional filters compensate
for the drawbacks of a notch filter.
• Since notch filters are employed to remove a particular
noise, adaptive filters are preferred over notch filters.
Adaptive filters remove noise using a reference signal,
which is highly correlated with the original signal

EMD and
independent
component analysis
• Another technique suitable to denoise an ECG signal in
real-time is EMD. In EMD, a signal is decomposed into a
set of amplitude and frequency modulated components
commonly known as intrinsic mode functions (IMFs). IMFs
denoise the signals. Using EMD, some low-frequency
signals are discarded during the ECG signal’s
reconstruction, which leads to loss of valuable information.
• The loss of some prominent features and the extraction of
noise from corrupted ECG signals can be minimized using
the Independent Component Analysis, an extensively used
algorithm in the blind source separation method. Blind
source separation methods generally operate on multiple
ECG leads and are a very acclaimed technique for
denoising biomedical signals. However, their high
computational complexity leads to high power
consumption and processing cost. Therefore, it is not a
suitable algorithm for real-time monitoring in Holter ECG
devices .

SNR and RMSE of
SWT
• the proposed SWT method is quantitatively compared with
existing methods by evaluating signal to noise ratio (SNR),
the percentage-root-mean-square difference (PRD), and
root-mean-square-error (RMSE). A clean ECG signal taken
from the MIT-BIH Arrhythmia database is corrupted by
adding noise. Then the denoising algorithm is applied to the
corrupted ECG signal to get a denoised signal. The output
PRD and RMSE values are calculated to depict the
reconstructed and the reference signal’s congruency in the
subsequent stage. The robustness of the noise of an
algorithm is investigated by checking out the improvement in
SNR value.
• A comparison between the reference signal and the
reconstructed signal obtained using SWT showed that the
reconstructed signal entirely coincides with the reference or
clean ECG signal, reflecting maximum output SNR and
minimum PRD and RMSE values.
• Hence denoising using SWT achieved a reconstructed signal
with high visual quality and increased preservation of ECG
signal components compared to other denoising algorithms.
Further, the proposed denoising technique implemented
using SWT retains the QRS complex’s amplitude, while the
existing denoising algorithms reduce the QRS complex’s
amplitude.

Result of SWT
These remarkable results achieved by using the
SWT algorithm makes it more suitable for
hardware implementation with low computational
complexity as denoising followed by detection of
R-peaks becomes simple.
R peak detection becomes a tedious job in other
detection techniques as output alteration requires
other techniques like derivative followed by
thresholding to enhance and detect QRS Complex.
As a result, computational complexity increases
significantly. Further, SWT based denoising
techniques can enable the ECG recording in noisy
environments where the amplitude of the noise is
high.

DENOISING BY SWT
• Thus, denoising techniques using SWT outperform the
existing denoising techniques in terms of all three
parameters: Robustness to noise, denoising performance,
and computational complexity. SWT is generally a redundant
transform where the output samples after decomposition by
each level remain equal to the input.
• Correspondingly it is also a translation-invariant transform
where down-sampling does not occur at each level. Hence,
the SWT provides high efficiency as change detection and
pattern recognition is generally not affected by transformed
output, as in DWT.
• It is possible to analyze ECG signals in both the time and
frequency domain using SWT as it is simple to analyze a
non-stationary signal. In contrast, algorithms like high pass
filter, lowpass filter, EMD, and FDM, it is not at all possible to
analyze the ECG signal in both the time and frequency
domain.

ADAPTIVE FILTERING
• A highpass filter is an electronic/digital filter that passes signals with a frequency higher than a specific cutoff frequency and
attenuates signals with frequencies lower than the cutoff frequency. Similarly, a lowpass filter allows low-frequency signals and
impedes high-frequency signals. The amount of attenuation for each frequency depends on the filter design. A lowpass filter
mainly affects the amplitude of the QRS complex, and while a high pass filter changes the phase shift of the signal,
hence bandpass filters are preferred.
• Notch filter uses the properties of the high pass filter and lowpass filter, which was conceptualized by Weaver et al. [29]. High
pass and lowpass filters are used as components to implement notch filters in SWT and DWT. The notch filter is designed in
such a way to reject a specific frequency band and to allow the remaining frequencies. Eq. (1) gives the transfer function of a
notch filter
h(s) = s2 + ω2 / s2+ 2ωRs + ω2
• A notch filter’s properties were modified to realize an all-pass filter, named infinite impulse response multiple notch filter. In [32],
Kim deployed a novel idea for a notch filter by making a sharp notch filter using some unique coefficient equations, efficiently
removing noises like PLI from the ECG signal. As the notch filter is not a suitable technique to denoise a signal with different
noises; therefore, adaptive filters, EMD, and wavelet-based methods are preferred. Adaptive filtering is one of the most efficient
methods used in denoising. It tends to track non-stationary signals. In [33], Widrow et al. introduced adaptive noise
cancelation using primary input, which consists of a corrupted signal (clean signal ＋ noise) and reference input, containing only
an additional unknown noise. The unknown noise is treated so that the reconstructed signal is very similar to the primary input.
After that, a newly constructed signal is subtracted from the primary input signal.
• The noise is eliminated without distortion of signal by taking care that both reference and primary input must coincide. If the input
and reference signal does not match, combining two or more algorithms can result in phenomenal denoising results. In [34],
IMEC’s Cool Bio Digital Signal Processor was designed considering a wearable ECG for real-time monitoring. Here, two-
algorithms, namely, electrode–tissue impedance with adaptive filtering and independent component analysis, are used to
remove noises present in an ECG signal. Since adaptive algorithms mostly require an additional reference signal to denoise a
signal, new ECG denoising techniques such as wavelet transform, EMD, and FDM are developed.
• Wavelet transform is an alternative approach to Fourier transform and short-time Fourier transform as it can give both time–
frequency components at any instant. At high frequencies, wavelet transform provides better time resolution, while at low
frequencies, it provides better frequency resolution. Wavelet transform consists of a wavelet and a transform. In wavelet
transform, wavelet or mother wavelet is a small oscillating wave that can change its finite window length and location depending
upon translation parameter (b) and scaling parameters (k),

CWT
• In CWT, scaling and translation parameters are
continuous parameters, and due to which huge
amount of wavelet coefficients are generated. The
scales and positions of a CWT are chosen to be
discrete to reduce the amount of data.
The discretization simplifies the analysis and
reduces the data size [36]. In a discrete wavelet
transform, a mother wavelet function is selected to
decompose and reconstruct a signal. Examples of
some mother wavelets include Haar, Daubechies,
biorthogonal, Morlet. The selection of wavelet
transform is always highly correlated with the signal
to get appropriate coefficients. In [37], Seljuq et al.
compared and used the best-fitted mother wavelet to
ensure that the ECG signal’s critical information is
retained. In DWT, coefficients are calculated at
each decomposition level, which is equal to
coefficients in the original signal, then coefficient
thresholding is performed at each decomposition
level. However, due to subsampling at each
decomposition level, DWT is a translation variant,
affecting the output.
• Therefore, its extended version, known as the
stationary wavelet transform, is preferred. Stationary
wavelet transform is almost similar to DWT and
designed so that the output remains unaffected
because of translation invariance. This translation
invariance is achieved by avoiding the subsampling
process. Hence, the number of output samples at
each level is equal to the number of input samples .
Therefore, it is observed that SWT is more
appropriate than DWT. Strasser et al. used SWT to
remove the complete QRS complex with P and T
waves by applying thresholding at each SWT
decomposition level. Further, a clean ECG signal is
obtained by subtracting the difference between the
original ECG signal and the reconstructed ECG
signal from the noisy ECG signal.

FDM
After segmenting the given signal into various IMFs,
the next step is to extract the relevant features for
denoising the biomedical signals such as ECG and EEG
signals.
Fourier mode decomposition (FDM) is the recently
developed signal decomposition procedure derived by
Singh et al. in [41] to analyze non-stationary time-
series data such as biomedical signals and earthquake
data speech signals. By applying this technique, any
signal, , can be represented in terms of a set
of orthogonal basis functions , commonly known as
Fourier intrinsic band functions (FIBFs)

Frequency filter and
wavelet transform
• Lowpass Filter and Highpass Filter: lowpass filter and highpass
filter with a cutoff frequency of 0.5 Hz–40 Hz are used in the
present work as the energy of the ECG signal (P-wave, QRS
complex, and T-wave) lie in 0.5 Hz–40 Hz frequency range.
•
Discrete Wavelet Transform: In DWT, the ECG signal is sub-
sampled at each level, and simultaneously, the detail
coefficients are subjected to denoising thresholds. Some
thresholding schemes are hard threshold, adaptive threshold,
soft threshold, sure shrink threshold, and universal threshold.
Among the above thresholding techniques, adaptive thresholding
is most suitable for ECG signal denoising [45]. After eliminating
noise, finally, the inverse of DWT is performed to reconstruct the
denoised ECG signal. In the present work, biorthogonal 3.1
wavelet transform with adaptive thresholding is used to
decompose the noisy ECG signal.

EMD,FDM and SWT
• Empirical Mode Decomposition Technique: EMD is employed on the noisy ECG signal. In the pre-
processing stage, the data is normalized. Then, EMD decomposes a non-stationary time series into a
finite number of intrinsic mode functions, which are mono component non-stationary signals. A total of
six IMFs and residue components are achieved by employing EMD which is shown in Fig. 6(e).
• 4.Fourier Decomposition Method: A noisy ECG signal is decomposed into a set of mono component
non-stationary signals by dividing the signal’s complete bandwidth into an equal number of frequency
bands. These mono component non-stationary signal frequency bands are known as Fourier intrinsic
band functions (FIBFs). The maximum frequency of an ECG signal is calculated by dividing the
sampling frequency by two. The maximum frequency is used to determine the cutoff frequency of each
FIBF. FIBF should have zero mean function, which means the segmented ECG signal provides a zero
DC level shift. The segmented ECG signal contains low and high-frequency components only. After
determining FIBFs, various parameters like SNR, PRD, and MSE of each FIBF are competed. Eight
FIBFs are extracted from the noisy ECG signal, and the output of the 8th FIBF is the denoised ECG
signal.
• 5.Stationary Wavelet Transform: After the pre-processing, the input ECG signal is subjected to a series
of a lowpass filter and high pass filter to reject the frequency band as per the Nyquist criterion. This
method does not perform any sub-sampling or decimation. Hence, the length of both the signals
produced from the lowpass filter and high pass filter remains the same. At each level, the signal is
decomposed into detailed coefficients and approximate coefficients. The approximate coefficients are
outputs of lowpass filters (ℎ[n]), and detail coefficients are the outputs of high pass filters (gi[n]). This
process continues up to “n” decomposition levels

Biorthogonal transform
• The present work uses a biorthogonal
3.1 wavelet transform to decompose the
input ECG signal using three
decomposition levels known as
wavelet filter banks. Detail coefficients,
as well as approximation coefficients ,
are calculated at each decomposition
level.

SNR ,RSME
AND PRD
• The denoising efficiency of the
proposed method with the five
other techniques is compared
with some parameters at both
the input stage (original ECG
signal) and the output stage
(denoised ECG signal). SNR,
PRD, and RMSE [18] are the
parameters used in this study.
Signal to noise ratio (SNR) is
the ratio of signal to noise and
given by Eq. (10). The
improvement in SNR, Improved
SNR is given by Eq. (11).

PRD
• A ten-second recording with a
sampling frequency of 360 Hz,
350 Hz, and 1000 Hz
represents sample sizes of
3600, 2500, and 10000,
respectively. The sample size
is denoted by N. PRD
percentage-root-mean-square
difference (PRD) is calculated
to check the distortion in the
denoised signal as compared
to the original signal, and is
given by Eq. (12).

1. Input and
output SNR of
different ECG signal
denoising techniques
— evaluated on
entire MIT-BIH
arrhythmia database

Table 2. Obtained input SNR and output PRD using different ECG signal denoising techniques —
evaluated on entire MIT-BIH arrhythmia database

RSME Minimum
As observed in Table 3, the lowest RMSE in the range of 0.0006–0.0060 is achieved using the SWT-based ECG signal denoising technique. Table 1, Table 2, Table 3 shows that the SWT technique provides maximum SNR and minimum PRD
and RMSE compared to the other techniques. The average computation time of different ECG signal denoising techniques is listed in Table 4. The algorithms are implemented and computed on a computer with Intel Core i5 (7th generation),
8 GB memory, and 1 TB hard disk drive.

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biomedical signal processing and its analysis

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