# Biometric-Based Human Identification Using Ensemble-Based Technique and ECG Signals
## 3 Materials and Methods
### ECG Signal Preprocessing  
To preprocess the ECG signals, the following subsections present the preprocessing steps, which are data normalization and noise removal.  
Data Normalization: The signals were normalized in the range of 0 and 1. This work adapted min-max normalization, which can be seen in Equation (1) as:  
\[x=\frac{x-x_{min}}{x_{max}-x_{min}} \tag{1}\]  
where \(x\) is the original signal and \(x_{min}\), respectively, represent the minimum and maximum values of the original signal.  
The Discrete Wavelet Transform (DWT) is employed in ECG signal preprocessing for baseline correction and noise removal. This technique involves breaking down the ECG signal into different frequency scales, or subbands, using wavelet functions. By analyzing these subbands, baseline wandering and noise components can be identified in higher frequency ranges. Applying a thresholding operation to coefficients in these subbands reduces or eliminates these unwanted components, resulting in a denoised and baseline-corrected ECG signal. This processed signal retains essential features while removing distortions caused by baseline variations and noise. The denoised signal can then be used for subsequent tasks, such as feature extraction for biometric identification, where accurate ECG pattern recognition is critical for reliable authentication.  
Noise Removal: The ECG signals are affected by different noises like muscle artifacts, baseline wander, and power line interference [54]. Many approaches have been used to remove the noise from the ECG signal. A discrete wavelet transform (DWT) method is utilized in this paper to remove noise from the ECG signal. The Daubechies wavelet of order 1 (dB1) was selected for denoising. We used the DWT technique compared to other methods  
Figure 3: Random samples from ECG-ID database before.  
because the Discrete Wavelet Transform is a non-parametric feature extraction method for noisy signals. It is a good technique for detailed feature extraction and approximation of signals because it is a joint time-frequency resolution analysis. Figure 4 compares an ECG signal from the ECG-ID before and after applying DWT. After the EEG signal is filtered, the DWT acquires both the approximate and detailed coefficients from the ECG signal. Then, the approximate coefficient is iteratively divided into new approximate and exact coefficients, providing a set of complex and approximate coefficients [55].  
The mathematical equation for \(DWT\) is given in Equation (2) [56].  
\[DWT(s,l)=2^{-s}\sum_{n}x[n]\big{(}2^{-s}n-1\big{)} \tag{2}\]  
where \(l\) represents the location parameter, and s represents the dilation parameter, \(n=1\), 2, and the total number of samples \(N\) and Complex Conjugate of analyzing wavelet function \(\psi^{*}\). DWT decomposes the signal into low-frequency elements as Approximation Coefficients \(A_{\emptyset}\) that given by Equation (3), and high-frequency elements as detailed coefficients \(D\psi\) that is given by Equation (4).  
\[A_{\emptyset_{(S_{0})}}=\frac{1}{\sqrt{N}}{\sum_{n}x[n]\varnothing_{S_{0}}l[n]} \tag{3}\]  
\[D_{\psi_{(S)}}=\frac{1}{\sqrt{N}}{\sum_{n}x[n]\psi_{s,l}[n]} \tag{4}\]  
where \(S_{0}=0\), \(N=2^{s}\), \(s=1\), 2, 3, \(\ldots\), \(S\); \(n=1\), 2, 3\(\ldots\)\(N\); \(l=1\), 2, 3, \(\ldots\)\(2^{s-1}\), \(n=\) Number of samples, \(S\) determines the width of \(D_{\psi_{(S)}}[n]\), \(2^{s/2}\) is the amplitude of the function, \(l\) is the position vector of \(\psi(s,l)\)\([n]\), and \(\psi\) is the wavelet coefficient.  
Figure 4: A comparison between an ECG signal from the ECG-ID database before and after applying DWT.