Wearable sensors are increasingly used for continuous health monitoring, but their small size limits battery capacity, affecting user experience and monitoring capabilities. To overcome this, we introduce an ultra-low power analog Folded Neural Network (FNN) for physiological signal processing in a batteryless fashion. Our proposed FNN, by serializing computation, provides several benefits over traditional analog implementations, such as lower space, lower power consumption, and lower peak-to-average power ratio. We evaluate our method extensively using a dataset designed for ECG-based screening and diagnosis. Our analysis considers factors such as thermal noise, spatial requirements, and power consumption. Additionally, we evaluate detection performance, investigating various parameters of the proposed FNN. This evaluation provides insights into the optimal configuration for accurate anomaly detection. We observe a good trade-off for accuracy around 6 layers and a hidden size of 30 and further demonstrate that such architecture could be implemented in a wearable device and executed in a batteryless fashion.