The abnormal pause or rate reduction in breathing is known as the sleep-apnea hypopnea syndrome and affects the quality of sleep of an individual. A novel method for the detection of sleep apnea events (pause in breathing) from peripheral oxygen saturation (SpO2) signals obtained from wearable devices is discussed in this paper. The paper details an apnea detection algorithm of a very high resolution on a per-second basis for which a 1-dimensional convolutional neural network -- which we termed SomnNET -- is developed. This network exhibits an accuracy of 97.08% and outperforms several lower resolution state-of-the-art apnea detection methods. The feasibility of model pruning and binarization to reduce the computational complexity is explored. The pruned network with 80% sparsity exhibited an accuracy of 89.75%, and the binarized network exhibited an accuracy of 68.22%. The performance of the proposed networks is compared against several state-of-the-art algorithms.