Many voice disorders induce subharmonic phonation, but voice signal analysis is currently lacking a technique to detect the presence of subharmonics reliably. Distinguishing subharmonic phonation from normal phonation is a challenging task as both are nearly periodic phenomena. Subharmonic phonation adds cyclical variations to the normal glottal cycles. Hence, the estimation of subharmonic period requires a wholistic analysis of the signals. Deep learning is an effective solution to this type of complex problem. This paper describes fully convolutional neural networks which are trained with synthesized subharmonic voice signals to classify the subharmonic periods. Synthetic evaluation shows over 98% classification accuracy, and assessment of sustained vowel recordings demonstrates encouraging outcomes as well as the areas for future improvements.