Electrocardiogram (ECG) signals play a vital role in diagnosing and monitoring patients suffering from various cardiovascular diseases (CVDs). This research aims to develop a robust algorithm that can accurately classify the electrocardiogram signal even in the presence of environmental noise. A one-dimensional convolutional neural network (CNN) with two convolutional layers, two down-sampling layers, and a fully connected layer is proposed in this work. The same 1D data was transformed into two-dimensional (2D) images to improve the model's classification accuracy. Then, we applied the 2D CNN model consisting of input and output layers, three 2D-convolutional layers, three down-sampling layers, and a fully connected layer. The classification accuracy of 97.38% and 99.02% is achieved with the proposed 1D and 2D model when tested on the publicly available Massachusetts Institute of Technology-Beth Israel Hospital (MIT-BIH) arrhythmia database. Both proposed 1D and 2D CNN models outperformed the corresponding state-of-the-art classification algorithms for the same data, which validates the proposed models' effectiveness.