It is challenging to visually detect heart disease from the electrocardiographic (ECG) signals. Implementing an automated ECG signal detection system can help diagnosis arrhythmia in order to improve the accuracy of diagnosis. In this paper, we proposed, implemented, and compared an automated system using two different frameworks of the combination of convolutional neural network (CNN) and long-short term memory (LSTM) for classifying normal sinus signals, atrial fibrillation, and other noisy signals. The dataset we used is from the MIT-BIT Arrhythmia Physionet. Our approach demonstrated that the cascade of two deep learning network has higher performance than the concatenation of them, achieving a weighted f1 score of 0.82. The experimental results have successfully validated that the cascade of CNN and LSTM can achieve satisfactory performance on discriminating ECG signals.