Abstract: Based on rigious signal analysis,some spectrum expressions of direct digital synthesizer (DDS) are presented by employing discrete Fourier transform (DFT) and Fourier transform (FT) in this paper.First,the output characteristics of DDS with ideal parameters are discussed.Then,the distribution and amplitude of output spectrum of DDS are provided in the presence of phase accumulator truncation in details.The deduced results are quite in agreement with general-recognized ones.The conclusion is useful for real DDS System design.