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Precise monitoring of respiratory rate in premature newborn infants is essential to initiating medical interventions as required. Wired technologies can be invasive and obtrusive to the patients. We propose a deep-learning-enabled wearable monitoring system for premature newborn infants, where respiratory cessation is predicted using signals that are collected wirelessly from a non-invasive wearable Bellypatch put on the infant’s body. We propose a five-stage design pipeline involving data collection and labeling, feature scaling, deep learning model selection with hyperparameter tuning, model training and validation, and model testing and deployment. The model used is a 1-D convolutional neural network (1DCNN) architecture with one convolution layer, one pooling layer, and three fully-connected layers, achieving 97.15% classification accuracy. To address the energy limitations of wearable processing, several quantization techniques are explored, and their performance and energy consumption are analyzed for the respiratory classification task. Results demonstrate a reduction of energy footprints and model storage overhead with a considerable degradation of the classification accuracy, meaning that quantization and other model compression techniques are not the best solution for respiratory classification problem on wearable devices. To improve accuracy while reducing the energy consumption, we propose a novel spiking neural network (SNN)-based respiratory classification solution, which can be implemented on event-driven neuromorphic hardware platforms. To this end, we propose an approach to convert the analog operations of our baseline trained 1DCNN to their spiking equivalent. We perform a design-space exploration using the parameters of the converted SNN to generate inference solutions having different accuracy and energy footprints. We select a solution that achieves an accuracy of 93.33% with 18x lower energy compared to the baseline 1DCNN model. Additionally, the proposed SNN solution achieves similar accuracy as the quantized model with a 4× lower energy.