This paper presents a novel numerical algorithm implemented in a unique methodology for the control of smart single-phase autoreclosure and comprehensive fault analysis for overhead lines using synchronized measurement technology. The algorithm improves on existing methodologies for adaptive single-phase autoreclosure, fault location, detailed disturbance records analysis, and fault data management. It is based on line current and voltage data sampled at both line terminals and synchronized sampling of all analogue input variables is assumed in this paper. The proposed algorithm is derived in the spectral domain and based on the application of the Discrete Fourier Transform. The electrical arc as a source of higher harmonics is included in the complete fault model and represents the starting point for the development of the new algorithm. The algorithm's distinctive feature is that it can determine both the fault arc and the fault resistance. The presence or absence of an arc resistance is used to determine the nature of the fault. The algorithm can be applied to both short and long lines. The algorithm is thoroughly tested using electromagnetic transient simulations of an overhead line connected between two active networks, as well as with field data.