signal

A signal is any quantity that carries information by changing over time (or space) — your voice as a wiggling air pressure, the voltage out of a microphone, the brightness along a row of camera pixels. Picture a heartbeat traced on paper: the squiggle IS the signal, and everything in this field is about reading, reshaping, and sending such squiggles. We usually write a signal as x(t), meaning 'the value x at each instant t.'

Signals split into families that decide which math tool you reach for. A continuous-time signal x(t) has a value at every instant (the smooth analog wiggle from a guitar string); a discrete-time signal x[n] only exists at integer steps n (the numbers a computer stores after sampling). They also split into periodic (repeats forever, like a 50 Hz mains hum) versus aperiodic, and deterministic (predictable by a formula) versus random (noise). Knowing the family tells you whether to use a Fourier series, a Fourier transform, or statistics.