Fourier transform spectrometry is an important device in spectral testing and analysis, which reconstructs a spectrum from a captured interference spectral signal. Invalid data points of the interference spectral signal, such as missing sampling points, oversaturation points, and noise points, arise from the photoelectric detection circuit’s instability and inadequate installation of interference module, and the recovery spectrum from an interference spectral signal containing such invalid data points causes distortion. Hence, a method for testing interference spectral signals is proposed using wavelet transforms, wherein invalid data points are quickly and effectively located, and a method for revising the interference spectral signal is researched based on interference signal characteristics of the interval where invalid data points are located. Spline interpolation is used for data fitting, and the interference spectral signal is revised accordingly. The feasibilities of both proposed methods are verified via simulation, and they are validated using a near-infrared Fourier transform spectrometer prototype. Thus, interference signals of the prototype are tested and revised to improve the accuracy of the recovery spectral signal.