This paper proposes an accurate and computationally efficient implementation of the IEEE Standard 1459-2000 for power measurements. The algorithm has two stages. In the first algorithm stage, the voltage and current signals are processed in parallel, and their spectrums are estimated independently of each other. Signal harmonics are estimated in a wide range of frequency using an efficient algorithm with reduced complexity. The algorithm is based on a recently introduced common structure for recursive discrete transforms and consists of digital resonators embedded in a common negative feedback loop. In the second algorithm stage, the unknown power components and other power quality indices are calculated according to definitions in the IEEE Standard 1459-2000. To demonstrate the efficiency of the proposed algorithm, the results of computer simulations and laboratory testing are presented. The laboratory results show accurate input power component estimates for a nonlinear load with rapid input current amplitude changes. In addition, a simple LabView implementation, based on the point-by-point processing feature, demonstrates the technique's modest computation requirements and confirms that the proposed algorithm is suitable for real-time applications.