Mobile health is gradually taking more importance in our society and the need of new power efficient devices acquiring biosignals for long periods of time is becoming substantial. In this thesis, we study the power reduction we could achieve on ECG sensing devices. Emphasis is made on reducing the number of samples both during the sensing phase and the compression phase. To that end, a new scheme called variable pulse width finite rate of innovation (VPW-FRI) is investigated. This new technique relies on the classical finite rate of innovation (FRI) theory and enables the use of a sum of asymmetric Cauchy-based pulses to model ECG signals. Research is done in order to implement VPW in practice and its performance are carefully analysed. Among others, we consider the potential instability of the method, we study its compression effectiveness and compare it with compression schemes widespread in the literature. We also evaluate the spectrum extrapolation performance of VPW when fed with signals sampled at sub-Nyquist rates and propose a modification that improves it. Furthermore, we introduce a method based on the similarities between different heart beats that reduces the computational costs of VPW. The parametric nature of VPW finally allows us to use it as a noise reduction algorithm. In parallel, we review and test a non-uniform sensing technique that adapts the sampling rate to the slope of the signal.