We present a Fourier transform spectrometer that associates a compact interferometer without any moving parts and various signal processing methods. The interferometer is composed of a polarizer, two identical spar Wollaston prisms, an analyzer, and a CCD sensor. Data and signal processing methods are introduced to improve the resolution. Due to the nonlinear behavior of the optical path difference versus the position along the sensor, a data preprocessing step is required before reconstructing the spectrum. This preprocessing method is based on key properties of the optical path difference that are identified. Then various spectrum analysis methods such as autoregressive, multiple signal classification (MUSIC), and Cauchy methods are illustrated, discussed, and compared with the periodogram by using the real data obtained from the spectrometer illuminated by a HgZnCd spectral lamp. From the optical system associated with the data processing and spectral analysis methods, it is possible to split the two closest spectral lines.