ECG signal is an important physiological signal mainly used for diagnosis of abnormalities in the heart functioning. There are limitations in detecting the non-linearities due to the presence of different forms of noises in the ECG signal. In our work, the de-noised signal coefficients obtained from different de-noising methods are classified as normal or abnormal signals. The ECG signal is obtained from MIT-BIH arrhythmia database and the PhysioBank dataset. The method of denoising is by using Variational Mode Decomposition and Discrete Wavelet Transform (DWT). The classification is performed by Feed Forward Neural Network using back Propagation (FFBP). Signal to Noise Ratio (SNR) and Mean Square Error (MSE) are the two metrics used for performance evaluation. The results suggest that optimized DWT coefficients correctly classify the given ECG signal of a monitored patient as normal or abnormal signal.