The spectral resolution can be increased by detecting the optical signal in a narrowband spectrum for the Fourier transform spectrometer based on spatial modulated in our study. In this paper, to study the effect of the radiant source on the interference system, we regard the radiant noise as a narrowband stationary Gaussian random process. Using the linear system analysis method and the statistical theory, we deduce the input signal-to-noise ratio (SNR) and the output SNR after the optical signal and the radiant noise have passed through the interference system. Then we simulate the system and compare the obained result with a narrowband rectangle spectrum, and obtain the SNR gains along the optical path difference (OPD) in different autocorrelation degree and cross-correlation degree values. The simulation result indicates that the SNR gains at different OPDs in the correlation degree space each are a monotonic smooth surface. The SNR gain maximum moves along the radius and the contour of the correlation degree circle, and it returns to the initial position. after an OPD According to the analysis of the SNR gain, the autocorrelation degree and cross-correlation degree values can be controlled in a certain area, which can serve as a criterion for the design and the test of the radiant source.