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This paper presents a method for introducing a soft source in the Fourier PSTD algorithm. The idea stems from the total field/scattered field (TFSF) approach used in the FDTD method. However if the TFSF approach is used in the PSTD method directly, the abrupt changes between TF and SF create a severe Gibbs phenomenon. Instead, we introduce a smooth connecting region between the TF and SF using a scalar weighting term. As a result, in our modified Maxwell's equations, soft sources can be introduced simply by adding incident terms in the 8-10-cell connecting region between the total field and the scattered field. Our numerical experiments show that incident waves can be created and cancelled inside the connecting region, depending on the direction of propagation. By using dispersion compensation and a smooth weighting function, very accurate results can be obtained. A general procedure for constructing the weighting function is also provided. The numerical examples of soft source generation and a 2D scattering study of a dielectric cylinder proved the validity and efficiency of our method.