Phasor measurement units (PMUs) are fundamental tools in the applications of modern power systems, where synchronized phasor estimations are needed. The accuracy and dynamic performance requirements for phasor, frequency, and rate of change of frequency (ROCOF) estimations are established in the IEEE Std. C37.118.1-2011 along with the IEEE Std. C37.118.1a-2014, where two PMU performances are suggested: P class filters for applications requiring fast response and M class filters for applications requiring high rejection to aliased signals. In this paper, a methodology to design new phasor estimators that satisfy the P class and M class requirements in PMUs is presented. The proposed methodology is based on finite impulse response filters, brick-wall filters, and complex filter design concepts, where frequency range, time performance, harmonic rejection and out-of-band interference requirements are considered in its design. A comparative analysis using the reference model given by the IEEE Std. C37.118.1 is presented. The results show the effectiveness of the phasor estimators under steady-state and dynamic conditions according to the PMU standard, making them suitable tools for applications in power systems.