I'm implementing a digital audio delay effect using a simple circular delay line. Changing the delay time by making the delay line longer or shorter introduces discontinuities in the audio signal, resulting in clicks.
What would be the best (most pleasing for the ears) strategy to avoid such clicks when changing delay time?
If you are not changing the delay length very often, and you don't want to have a Doppler effect that comes from continuously changing the delay length, then try a cross-fade. Both delay lengths should be running simultaneously for a moment, and you would fade the old one out while fading the new one in.
The problem here is a discontinuity in the signal, which results in the click you're hearing. A possible solution is to make the delay variation as smooth as possible so that step-like discontinuities are avoided. If $x(n)$ represents the signal associated to the delay-line control (e.g. a knob) and $y(n)$ represents the signal associated to the effective change in delay that you allow, a possible relationship between the two could be: $$ y(n) = \alpha x(n) + (1 - \alpha) x(n-1) $$ with $0<\alpha<1$. This is a computationally inexpensive way of low-pass filtering $x(n)$.
If you have a continuously varying delay like, for example, a chorus or flanger, you need a to implement a time varying fractional delay in addition to your regular (integer) delay line.
If you only need to change the delay occasionally in discrete steps, a cross fade will work fine.
