Summing a signal with a delayed copy creates a comb filter: evenly-spaced spectral peaks and nulls set by the delay time

A comb filter mixes a signal with a delayed copy of itself. Because the delay shifts phase by an amount that grows with frequency, the two copies alternately reinforce and cancel across the spectrum, producing a series of evenly-spaced peaks and nulls that look like the teeth of a comb. For a positive (summing) FIR comb the first peak sits at f = fs/D (sampling rate over delay in samples), with further peaks at 2f, 3f, 4f… and nulls halfway between — so it reinforces a fundamental and its harmonics. Shorter delays spread the teeth wider apart (a more striking, resonant effect); longer delays pack the teeth close together. Subtracting instead of adding shifts the pattern so the fundamental is removed. A recursive (IIR) comb feeds output back to the input, giving a stronger resonant ringing — the building block of delay effects, flanging, and reverberation.

Examples

At 48 kHz with a 12-sample (0.25 ms) delay, a summing comb peaks at 4 kHz, 8 kHz, 12 kHz… with nulls at 2 kHz, 6 kHz. Slowly modulating the delay time sweeps the teeth — this is flanging. In Strudel/Hydra rigs a short feedback delay produces the same combing.

Assessment

A summing FIR comb filter uses a 1 ms delay. Calculate the frequency of its first spectral peak and the spacing between successive peaks. Then explain what audibly changes if the delay is lengthened to 20 ms.