The Fourier transform spectrometer based on cascaded Fabry-Perot interferometers is analyzed, where one of the interferometers has a fixed length, while the other is scanning. We propose a method to reconstruct the spectrum correctly based on solving the integral equation of the overall response of the cascaded interferometers. The method is tested for different design parameters and noise conditions. Low reconstruction error below -80 dB is found to be achievable.