For stream cipher to implement effective fast discrete Fourier spectra attack, it is necessary to find a low spectral weight relation or a low spectral weight annihilator. By using discrete Fourier transform of periodic sequences, a necessary and sufficient condition of the sequences which meet product relation was achieved. And on this basis, by defining spectral cycle difference, a kind of low spectral weight relation and annihilator was derived. At the same time, the spectral properties of m sequences was researched, a method to calculate the spectral space quickly was proposed and an example was given.