We propose the signal padding method to solve the problem of low spectral resolution in the spatially modulated Fourier transform spectrometer. The required number of sampling data for the given optical path difference was calculated and applied to the experimental data. The spatially modulated Fourier transform spectrometer based on the Sagnac interferometer was fabricated and its maximum optical path difference was 8 mm. A one-dimensional detector of 512 pixels was used to measure the spectrum of a LED light source of 6451 cm-1 center wavenumber. The obtained spectral resolution in an experiment for 1 mm optical path difference was 271 cm-1; however, it could be drastically improved to 31 cm-1 when the signal padding method was applied to the sidelobes of the measured interferogram.