The fractional open-circuit voltage (FOCV) method is extensively used in low-power energy harvesting (EH) sources to extract maximum power. For fast-varying EH sources, a fast sampling rate is required. This work theoretically analyzes the influence of the sampling time and period on the harvested power of sinusoidal EH sources. In addition, the circuit limitations to achieve a fast sampling rate are presented and circuits to deal with them proposed and implemented. Furthermore, one of the circuits is based on a novel pseudoFOCV method and achieves the fastest sampling rate. Experimental tests are performed with a 2 Hz, 1 to 3 V sinusoidal source having an output resistance of 127 Ω, and the results are shown to agree with theoretical predictions. It is shown that the harvested power increases with the sampling rate when the sampling time is negligible (sampling 15 times faster than the source frequency extracts around 99% of the maximum), and for fixed sampling times, there is an optimum sampling rate where the harvested power is maximum. The first result is generic and valid for methods other than the FOCV. Tests were also performed with a small-scale wave energy converter placed in a linear shaker emulating a sea environment. Harvested power increases by 25% with respect using a commercial FOCV unit with a low sampling rate.