ECG signal is an important physiological signal mainly used for the diagnosis of abnormalities in the heart functioning. There are limitations in detecting the nonlinearities 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 optimized for reducing the error and redundancy, which are then classified as normal or abnormal signals. The ECG signal is obtained from the MIT-BIH arrhythmia database and the PhysioBank dataset. The two methods used are the Discrete Wavelet Transform (DWT), Stationary Wavelet Transform (SWT). The optimization is done using Cuckoo Search (CS) algorithm and the classification is performed by Feed Forward Neural Network using back propagation (FFBP). The performances are evaluated in terms of standard metrics namely, Signal to Noise Ratio (SNR) and Mean Square Error(MSE). The results suggest that although SWT performs better than other de-noising techniques, the two methods correctly classify the given ECG signal of a monitored patient as a normal or abnormal signal.