Atrial fibrillation (AF) is the most common type of cardiac arrhythmia and is characterized by the heart's beating in an uncoordinated manner. In clinical studies, patients often do not have visible symptoms during AF, and hence it is harder to detect this cardiac ailment. Therefore, automated detection of AF using the electrocardiogram (ECG) signals can reduce the risk of stroke, coronary artery disease, and other cardiovascular complications. In this paper, a novel time-frequency domain deep learning-based approach is proposed to detect AF and classify terminating and non-terminating AF episodes using ECG signals. This approach involves evaluating the time-frequency representation (TFR) of ECG signals using the chirplet transform. The two-dimensional (2D) deep convolutional bidirectional long short-term memory (BLSTM) neural network model is used to detect and classify AF episodes using the time-frequency images of ECG signals. The proposed TFR based 2D deep learning approach is evaluated using the ECG signals from three public databases. Our developed approach has obtained an accuracy, sensitivity, and specificity of 99.18% (Confidence interval (CI) as [98.86, 99.49]), 99.17% (CI as [98.85 99.49]), and 99.18% (CI as [98.86 99.49]), respectively, with 10-fold cross-validation (CV) technique to detect AF automatically. The proposed approach also classified terminating and non-terminating AF episodes with an average accuracy of 75.86%. The average accuracy value obtained using the proposed approach is higher than the short-time Fourier transform (STFT), discrete-time continuous wavelet transform (DT-CWT), and Stockwell transform (ST) based time-frequency analysis methods with deep convolutional BLSTM models to detect AF. The proposed approach has better AF detection performance than the existing deep learning-based techniques using ECG signals from the MIT-BIH database.