In this paper, the O-mode ultrashort-pulse reflectometry (USPR) millimeter-wave signals that propagate into the plasma and cover a frequency bandwidth of 33-158 GHz are examined numerically using MATLAB. Two important processes are involved in the computation: the propagation of the USPR impulse signal through a waveguide and the frequency up-conversion using millimeter-wave mixers. These mixers are limited to intermediate frequency signals that are less than 500 mV; thus, it is necessary to disperse the impulse signal into a chirped waveform using the waveguide. The stationary phase method is utilized to derive a closed-form formula for a chirped waveform under the assumption that the USPR impulse is Gaussian. In the process of frequency up-conversion, the chirped waveform is mixed with the mixer LO signal, and the lower frequency components of the RF signal are removed using high pass filters.