Abstract: We describe the mathematical principle of a Digital Sideband-Separating Mixer (DSSM) to work with a wideband or ultra-wideband receiver based on modern digital signal-processing technologies. We also realize certain optimization of a DSSM. We present MATLAB simulations of an optimized DSSM in the L-band (1GHz to 2GHz). Sideband Rejection Ratios better than 300dB are achieved at all frequencies in a band of a width of 500MHz. Our work can improve computing speeds of future DSSMs, and it fits development trends of radio-astronomy receivers, i.e. those toward hardware integration and using wider bands.