IIR filter

An IIR filter computes each output from recent inputs and recent outputs — it feeds its own result back in. That feedback is like a swing you keep nudging: a single push can leave it oscillating for a long time, so a lone input spike produces a response that, in principle, rings on forever, dying away but never quite reaching zero. Hence 'infinite impulse response.' The recursion lets a handful of coefficients do work that would take an FIR filter hundreds of taps.

That efficiency is the whole appeal: IIR designs (Butterworth, Chebyshev, elliptic) deliver steep, selective frequency cutoffs with very little computation, and they directly mirror the classic analog filters engineers already understood. The price is real, though — feedback can make them unstable if a pole drifts outside the unit circle, their phase response is nonlinear (so waveform shapes get smeared), and fixed-point rounding errors can accumulate dangerously through the loop.