This chapter deals with the theory and simulations of continuous and burst-mode pseudo-random PAM signals (PRPS). The burst-mode operation modifies the spectral shape of the continuous pseudo-random PAM signal according to the duration and repetition rate of the burst signal. In LiDAR, the transmitted signal is properly modeled as a periodic burst-mode PRBS pattern. The spectral properties of the periodic burst-mode PRPS are determined by the period of the pattern and the shape of the pulse. Spectral shaping is very usual in optical communication, providing at the same time minimum signal bandwidth without intersymbol interference. This practice is needed for a more sophisticated digital signal processing (DSP) to synthetize the waveform. Spectral shaping allows designing the receiver with the minimum noise bandwidth, optimizing the signal-to-noise ratio and maximizing the LiDAR sensitivity. Despite a suboptimal LiDAR sensitivity design, the simpler square-wave like pulse shape is still a suitable candidate for LiDAR applications, requiring simpler DSP with cost and power reduction. Bessel–Thomson filters are suitable to model the linear phase transfer function of the optical receiver, including a different number of poles to tailor high frequency cutoff and linear phase profile. Sampled and filtered PRBS are extensively described with the intent to manage key parameters for a LiDAR optimum design approach.