A new method combining the Fourier self-deconvolution(FSD),autoregressive model(AR)and truncated singular value decomposition (TSVD) forsuperresolution estimating of Fourier transform spectra is discussed. Comparing to theother methods for the purpose of resolution enhancement, the method proposed in thispaper (as is called the FAT method) has the advantages of higher resolution, narrowerline shape, no spurious peaks and insensitive to noise.