The human heart is a vital organ, and its proper functioning is essential for overall health. Electrocardiogram (ECG) analysis serves as a fundamental diagnostic tool for identifying cardiac abnormalities [1]. However, accurately interpreting ECG signals is challenging due to the presence of noise and artifacts [2,3]. Furthermore, with the emergence of machine learning, there is a growing interest in leveraging these technologies to enhance ECG analysis and automate diagnosis processes.

Recent research is focusing on the modeling of ECG signals because of several key factors. Firstly, accurate modeling of ECG signals is essential for understanding the underlying physiological processes of the heart and diagnosing cardiovascular diseases [[4], [5], [6]]. By accurately representing ECG waveforms, researchers can gain insights into the electrical activity of the heart and identify abnormalities or irregularities that may indicate cardiac disorders. Secondly, advancements in computational techniques and signal processing algorithms have enabled researchers to develop more sophisticated models for ECG signals. These models can capture complex features and patterns present in ECG recordings, allowing for more accurate analysis and interpretation [[7], [8], [9], [10]]. Various models have emerged for synthesizing Electrocardiogram (ECG) signals, with the Denoising diffusion probabilistic models offering a versatile approach capable of addressing different scenarios like heartbeat generation and signal imputation [11,12]. While advantageous for data augmentation and disease detection tasks, these models present challenges in computational complexity and interpretability. In this series, some neural network based ECG modeling approach are also proposed [1,[13], [14], [15], [16], [17]]. These models have an ability to learn complex patterns and capture intricate relationships in ECG data but drawbacks are also associated with them, like Complexity and computational requirements, Lack of interpretability, large data requirement and overfitting. Another approach generates synthetic P wave morphology sets but relies on regression modalities, introducing implementation complexities [18]. Despite computational efficiency, this method may still incur prohibitive costs. Overall, while these approaches offer advancements in ECG synthesis, challenges remain in achieving accuracy, interpretability, and computational efficiency.

The studies have also delved into the parametric representation of Electrocardiogram (ECG) signals. Dolinsky et al. introduced a model based on elementary trigonometric and linear functions, further implemented by Gerasimov et al. However, these methods have limitations such as potential discontinuities, lack of smooth transitions, and adaptability issues to different signal types [7,19]. In contrast, the work presented by Alka et al. offers several advantages in ECG signal analysis and classification. By employing parametric cubic splines for ECG signal modeling and subsequent classification using machine learning techniques, the proposed method demonstrates superior accuracy and fidelity [20,21]. Cubic splines, utilized in this approach, involve fitting piecewise cubic polynomials to the data, resulting in reduced computational complexity and robustness against overfitting. However, they may exhibit limitations in flexibility and produce less smooth curves, especially with complex data.

In this series, quartic splines are introduced as a novel method for ECG signal modeling, followed by classification using machine learning techniques. However, above existing methods fail to prioritize the vital preservation of feature points within the signal, a crucial aspect particularly significant in medical contexts. The quartic method offers higher flexibility through fourth-degree polynomials, enabling precise representation of intricate ECG waveforms with smoother curves and reduced artifacts. Leveraging higher-order polynomials enhances modeling accuracy and diagnostic insights, while providing greater control over the interpolation process enables customization to specific requirements, marking quartic splines as a promising advancement in ECG signal analysis and interpretation. Moreover, the machine learning methodologies presented in this study exhibit high classification accuracy and exceptional performance, providing invaluable support to healthcare professionals in achieving precise diagnoses. As machine learning techniques continue to advance, there has been a notable increase in interest surrounding the automation of ECG signal classification to expedite and enhance diagnostic processes. Through continuous analysis of ECG signals within clinical environments, machine learning models serve as vigilant monitors, promptly notifying healthcare practitioners of any deviations or anomalies in the patient's cardiac activity. This proactive approach enables timely interventions and treatments, contributing significantly to patient care and outcomes.