Cardiac arrhythmia diagnosis and early detection are essential practices in the classification of the electrocardiogram (ECG) signal. This paper introduces a successful deep learning framework which combines hierarchical Kalman filtering to denoise the signal with a lightweight convolutional neural network (CNN) trained by knowledge distillation. The suggested approach is tested on a well-known MIT-BIH Arrhythmia Database and it is aimed at classifying five types of arrhythmias: normal beat, left bundle branch block, right bundle branch block, atrial premature contraction, and premature ventricular contraction. These ECG signals use multi-level preprocessing using Kalman filtering (adaptive hierarchical), beat segmentation using R-peaks, z-score normalization, and class balancing. A teacher model with deeper CNN is nurtured to a high level of accuracy by training the model on high categorical cross-entropy loss, as a student model with a compressed CNN is trained through soft label supervision and minimization of the Kullback-Leibler divergence. Experimental testing indicates that both the models attain 99.94 accuracy, precision, and recall, and they converge smoothly with minimum training loss. The presented technique not only shows competitive results but also high-performance efficiency, being appropriate to real-time and mobile medical usage. In this paper, it has been demonstrated that ECG signal classification in the real-world setting with limitations on the available resources can be solved effectively using the combination of methods of advanced signal denoising and deep knowledge distillation.