Convolution applies an impulse response to a signal, enabling realistic room reverb simulation

Convolution is the mathematical operation that computes the output of a linear time-invariant (LTI) system for any input, given the system impulse response. The impulse response (IR) fully characterises a linear system: it is the output when an instantaneous click (Dirac delta) is the input. To apply a room acoustics to a dry signal, measure the room IR (shoot a starting pistol) and convolve it with the dry audio. The Fast Fourier Transform speeds up convolution from O(N squared) to O(N log N) by converting to the frequency domain, multiplying the spectra, and converting back. This is the basis of convolution reverb plug-ins.

Examples

Altiverb, Logic Space Designer, and Ableton Convolution Reverb all use real-world impulse responses captured in halls, cathedrals, and hardware units.

Assessment

Why is FFT-based convolution faster than direct time-domain convolution for long impulse responses? What makes an IIR filter potentially unstable?