Communication signals, systems, and noise are all random processes. For carrier-modulated communication systems, they are bandpass random processes. The chapter begins with a mathematical framework for bandpass- modulated signals and presents various mathematical representations for bandpass signals. This is followed by a mathematical description of bandpass systems and their complex low-pass system equivalents. Wide-sense stationary bandpass random processes are considered along with their power spectrum. This is important for describing both bandpass random signals and bandpass random radio propagation channels. The chapter concludes with a discussion of thermal noise and filtered thermal noise that appears in all communication receivers.