Telecardiology systems, involving remote diagnosis of cardiac anomaly based on ECG signals, generally acquire such signals at the Nyquist rate, and transmits the data to diagnostic facilities. Such systems are not designed under either power or bandwidth constraints. However, in certain scenarios involving remote communities in developing and underdeveloped world, both the above constraints could be acute. The present paper takes a first step towards a constrained design keeping such scenarios in view. Specifically, we propose a system where automated classification is performed on the ECG signals, and only anomalous signals are transmitted for further diagnosis and intervention, thereby saving bandwidth. Additionally, we propose compressive sampling as a low-power alternative to traditional Nyquist sampling method, which also lowers bandwidth requirement. Finally, we illustrate our method by designing such a compressive classifier using ECG signals from the widely used PhysioNet database. Specifically, we demonstrate that an average down sampling factor of three leads to desirable classification performance in terms of both sensitivity and specificity while substantially saving both power and bandwidth. © 2013 IEEE.