LTI system

A system is anything that takes an input signal and produces an output signal — an amplifier, a guitar pedal, a room that adds echo. An LTI system is the especially well-behaved kind that is both Linear and Time-Invariant, and it is the single most important idea in the whole subject because nearly every analysis tool (convolution, transfer functions, frequency response) only works for LTI systems. Think of a perfect, neutral hi-fi: it never invents new pitches and behaves identically whether you play your song now or tomorrow.

Linear means it obeys superposition: scale the input by 2 and the output scales by 2; add two inputs and the outputs add (no clipping, no new frequencies appearing). Time-invariant means delaying the input simply delays the output by the same amount — the system's character doesn't drift over time. The magic payoff is that an LTI system is fully described by ONE measurement, its impulse response h(t): once you know how it reacts to a single sharp tap, you can predict its response to any input at all by convolution.