A delay line feeding back into itself creates a comb filter with resonant peaks at integer multiples of 1/delay

A delay line stores previous samples and outputs them after a fixed or variable number of samples. When the delayed output is added back to the input (feedback), the result is a comb filter: resonant peaks appear at the fundamental frequency 1/delay_time and its harmonics, while cancellations occur at odd multiples. Comb filters can be used for flanging (modulated short delay), chorus (multiple slightly detuned delays), echoes (long delays), and as the core of the Karplus-Strong plucked string algorithm. The ratio of feedback gain to 1 determines whether the filter is stable (below 1), neutral (exactly 1, infinite ringing), or unstable (above 1, growing oscillation). Circular ring buffers implement delay lines efficiently in memory.

Examples

A delay of 1/440 second (approximately 2.27 ms) with feedback creates a 440 Hz resonance. The flanger effect modulates the delay time to sweep comb notches through the spectrum.

Assessment

At what frequencies do the resonant peaks of a comb filter appear if the delay time is 5 ms? What determines whether a feedback delay line is stable?