Digital receiver is an important component in the radar analog array channel. Its influence on the slope, signal spectrum and noise spectrum of the linear Frequency Modulation(LFM) signal are modeled and simulated in the paper. Firstly, the time domain model of LFM signal in descending and ascending channels is introduced respectively, and the change pattern of the corresponding FM slope is given. Then, the signal spectrum and the noise spectrum in the frequency domain are derived and the frequency spectrum is simulated. Combined with the characterization of two scenarios such as uniform distribution and normal distribution, the conclusion that the phase noise between spectral lines and the FM bandwidth are almost irrelevant is validated. The correlation analysis in the paper gives the relatively clear signal and noise characteristics of narrowband LFM signals.