In this Topic, the shift-in-frequency theorem is investigated, and its importance in communication theory as well as sampling theory is highlighted. The duality between the shift-in-time and shift-in-frequency property is emphasised. The Topic considers the spectrum of a signal that is multiplied by a cosine wave, in terms of the spectrum of the original signal. Finally, the Topic highlights how this theorem is used in amplitude modulation, as the simplest communication system that enables multiple users to communicate simultaneously.