There are two types of sampling to obtain fiber Fourier transform spectrometer (FFTS) interferogram, single-sided sampling and double-sided. The techniques for obtaining recovered spectrum from the two types of interferogram sampling are discussed in detail. The mathematical expressions and calculation procedures are proposed. The advantages and shortcomings of each technique are compared. The single-sided recovery algorithm is ameliorated and the phase correction efficiency is improved. The research results are proved through the experiment. The recovered spectra by two algorithms agree well with the standard spectrum, which proves the methods are effective.