The paper proposes a simple phasor estimator by utilizing the dictionary-based sparse representation of signals for control and protection applications in power system. It is also observed that the proposed method is found to be suitable for extracting the fundamental component of the signal required for protective relays with few number of samples. The simulations have been carried out to test the performance of proposed phasor estimator as per the requirements provided in IEEE C37.118.1a-2014 standard and also on a modified two-area power system. To further validate the effectiveness of proposed algorithm, it has also been tested on an analog radial power system simulator with fault in the laboratory experimental setup. The measured voltage and current signals are fed to the developed prototype of phasor measurement unit (PMU) with the proposed algorithm running for phasor estimation of signals in the power system. The real-time hardware and IEEE standard test results reveal that the proposed phasor estimation algorithm is able to estimate the phasor accurately in the presence of harmonics, decaying dc components, amplitude, and phase modulation, which are typically involved during disturbances. Furthermore, the proposed algorithm is able to estimate the phasor of a signal accurately with few measured samples, thus an analog-to-digital converter with lower sampling rate is suitable for developing a prototype of low cost P-class PMU for several applications in smart grids.