Among the various logical components of a phasor measurement unit (PMU), the synchrophasor estimation (SE) algorithm definitely represents the core one. Its choice is driven by two main factors: its accuracy in steady state and dynamic conditions as well as its computational complexity. Most of the SE algorithms proposed in the literature are based on the direct implementation of the Discrete Fourier Transform (DFT). This is due to the relatively low computational complexity of such technique and to the inherent DFT capability to isolate and identify the main tone of a discrete sinusoidal signal and to reject closeby harmonics. Nevertheless, these qualities come with non-negligible drawbacks and limitations that typically characterize the DFT: mainly they refer to the fact that the DFT theory assumes a periodic signal with time-invariant parameters, at least along the observation window. The latter, from one side should be as short as possible to be closer to the above-mentioned quasi-steady-state hypothesis also during power system transient; on the other hand, longer windows are needed when interested in rejecting and isolating harmonic and inter-harmonic signals that are quite frequent in power systems. In this respect, this chapter first analyses the DFT with a particular focus on the origin of the well-known aliasing and spectral leakage effects. Then it formulates and validates in a simulation environment a novel SE algorithm, hereafter referred as iterative-Interpolated DFT (i-IpDFT), which considerably improves the accuracies of classical DFT- and IpDFT-based techniques and is capable of keeping the same static and dynamic performances independently of the adopted window length that can be reduced down to two cycles of signal at the nominal frequency of the power system. This chapter is organized as follows: Section 3.2 introduces the nomenclature and some basic concepts in the field of synchrophasors. Section 3.3 presents the theoretical background of the DFT, with a specific focus on the detrimental effects of aliasing and spectral leakage. Next, Section 3.4 discusses advantages and drawbacks of DFT-based SE algorithms and derives the analytical formulation of the i-IpDFT method. Finally, Section 3.5, after illustrating the procedure presented in Reference 1 to assess the performances of a PMU, analyses the performances of the i-IpDFT algorithm using two of the testing conditions presented in Reference 1 and compares them with those of the classical IpDFT technique.