Filters not only attenuate but phase-shift a waveform's individual harmonics, distorting its shape

A filter’s effect is not limited to turning harmonics down: filters not only change a waveform by attenuation, but distort it by individually phase-shifting the harmonics within it. Because each harmonic is delayed by a different amount as it passes through the filter, the summed time-domain waveform emerges with a visibly different shape even where the harmonic amplitudes are only mildly altered. This is why a filtered waveform can look quite unlike the original and why phase, not just amplitude, matters when reasoning about what a filter really does to a sound.

Examples

Passing a square wave through a low-pass filter yields a rounded, asymmetric shape because its harmonics are phase-shifted by differing amounts, not merely reduced.

Assessment

Explain the two things a filter does to the harmonics passing through it, and why a filtered waveform’s shape changes beyond simple attenuation.