Health monitoring is increasingly moving to continuous, home-based applications with real time analytics. Fetal monitoring has been traditionally carried out in the hospital during checkups. While newly developed wearable systems offer home monitoring capabilities, rigorous real-time analytics require mobile or cloud connections for complex computation. However, these architectures result in higher energy output from the sensors and devices, reliance on a steady Bluetooth or WiFi signal, potential latency and synchronization variables, and data privacy issues. Furthermore, it is impossible to achieve telemedicine in resource-poor locations where mobile phone and internet are not accessible. To address these problems, we develop an edge computing paradigm for future integration in a compact abdominal patch to monitor the fetus remotely in the home. The energy saving and cost-effective algorithm, namely Lullaby, is developed to extract the fetal heartrate from a pregnant mother's abdominal electrocardiography (ECG) signal. The algorithm was validated using the Physionet 2013 Challenge Dataset and achieved an average F1-score of 90%. Our experiments have shown that the proposed approach is deployable in a multitude of physical systems, either as a standalone fetal ECG monitoring patch or integrated into a more complex architecture. Additionally, evaluation on real hardware shows that our methodology is suitable for devices having a minimum RAM of 64KB which can be implemented on low-cost MCUs and designed to be energy saving for longer, continuous monitoring.