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Fourier transform has abundant applications in the field of power systems. One of the chief uses of this technique is differentiating between power swings and the faults occurring simultaneously with these swings in the power system. Despite many efforts to use Fourier transform for this purpose, the available methods have significant restrictions that affect their applicability. This paper introduces a new method based on Fourier transform for detecting power swings and various types of simultaneous faults that occur during the power swings. The strength of the proposed method in comparison with currently used schemes is the capability of detecting the unstable and multi-mode power swings and also detection of high-impedance faults. Since the performance of the proposed method depends on defining a threshold value, this paper also provides a quick and simple way to determine this threshold value for various power networks. DIgSILENT and MATLAB softwares have been used to test the proposed method on the standard IEEE 39-bus test system for different scenarios of power swing and simultaneous fault conditions.