## 3 Materials and Method  
### Preliminaries  
ECG time series data:A sequence of data points taken in successive points of time by a time order is known as a time series. The most common form of time series is a sequence taken in successive, consistently spaced moments of time. In this paper, we follow the method proposed in signals with random sampling intervals [17]. The method is based on the concept that, in continuous domain discrete value, a function defines sampling interval. It is a technique where the algorithm tries to optimize the representation of the signal by changing the sampling intervals of a signal, also called time points. It is followed by gradient descent, which iteratively updates the initial time points created with a linear space to much more closely match the original signal [18; 19].  
_Non-uniform sampling_: Since the ECG signals are non-uniformly sampled, the time interval left between any two successive measurements is no longer constant. It may be due to level-crossing sampling, compression, or limitations of the hardware used for data capture. For example, non-uniform sampling presents many issues: special signal processing techniques have to be used; there is a possibility of losing diagnostic information; and lastly, many of the standard methods used for signal analysis are aimed at uniformly sampled data [20].  
_The ECG-ID database and preprocessing of signal_: In order to evaluate our proposed models, a synthetic ECG signal and real patient records from the ECG-ID database [21] downloaded from Physionet [22] were used. There are 310 ECG recordings from Lead-I in the ECG-ID database. The digital ECG records were taken in Lead-I for 20 s and digitized at a rate of 500 Hz with 12-bit precision. Lead I represent the possible distinction between the right and left hands (LA-RA). It is selected because it can be measured with ease and is insensitive to small differences in the positions of the electrodes. The records came from 90 volunteers aged 13 to 75 years (44 men and 46 women). This ECG-ID database consists of signals that are baseline drift corrected, frequency-selective filtered, and signal enhanced. Baseline drift correction was implemented using multilevel one-dimensional wavelet analysis (db8, N = 9). Frequency-selective signal filtering was implemented using a set of adaptive band stop (Ws = 50 Hz, dA = 1.5) and lowpass (Butterworth, Wp = 40 Hz, Ws = 60 Hz, Rp = 0.1 dB, Rs = 30 dB) filters followed by smoothing with N = 5 points averaging [21]. An adaptive band stop filter fairly suppresses power-line noise, and a lowpass filter is used to remove the remaining noise components caused by possible high-frequency distortions.  
As some baseline wanders were still observed while implementation, to refine further, the band-pass Butterworth filter (filter order of 4, f\({}_{\text{low}}\) = 0.5 Hz, f\({}_{\text{high}}\) = 60 Hz, and f\({}_{\text{s}}\) is from the ECG record) was used to remove low- and high-frequency noise components and baseline wander muscle noise and used as input to the models as a modified signal. The frequency range analyzed in the models is set at 0.5-60 Hz for 10 s, as shown in Figures 1 and 2[23; 24].  
The modified ECG signal, which has been subjected to preprocessing steps, is utilized as the input to the neural network models. These models then process the modified signal to capture the essential dependencies and features within the data.