A filter's frequency response describes its amplitude effect per frequency; its phase response describes the per-frequency time delay it introduces

A filter can be characterised fully by its complex frequency response, which has two components: the magnitude response (how much each frequency is amplified or attenuated) and the phase response (how much each frequency is delayed). Most filters introduce both. An all-pass filter has a flat magnitude response but a non-trivial phase response, adding frequency-dependent delays that alter transient shape without changing spectral energy distribution. FIR filters can have exactly linear phase (constant group delay across all frequencies), which is desirable for audio processing where transient integrity matters. IIR filters can achieve sharp cutoffs with fewer coefficients but at the cost of non-linear phase and potential instability.

Examples

The Linkwitz-Riley crossover filter has a flat summed response with phase-matched outputs. FIR linear-phase filters are standard in professional mastering equalizers.

Assessment

What is the difference between an all-pass filter and a low-pass filter in terms of their magnitude and phase responses? When is linear phase important in audio processing?