Detection of atrial fibrillation (AF) from a wrist watch photoplethysmogram (PPG) signal is important because the wrist watch form factor enables long term continuous monitoring of arrhythmia in an easy and non-invasive manner. We have developed a novel method not only to detect AF from a smart wrist watch PPG signal, but also to determine whether the recorded PPG signal is corrupted by motion artifacts or not. We detect motion and noise artifacts based on the accelerometer signal and variable frequency complex demodulation based time-frequency analysis of the PPG signal. After that, we use the root mean square of successive differences and sample entropy, calculated from the beat-to-beat intervals of the PPG signal, to distinguish AF from normal rhythm. We then use a premature atrial contraction detection algorithm to have more accurate AF identification and to reduce false alarms. Two separate datasets have been used in this study to test the efficacy of the proposed method, which shows a combined sensitivity, specificity and accuracy of 98.18%, 97.43% and 97.54% across the datasets.