As mentioned above, when an audio delay line needs to vary smoothly over time, some form of interpolation between samples is usually required to avoid ``zipper noise'' in the output signal as the delay length changes. There is a hefty literature on ``fractional delay'' in discrete-time systems, and the survey in [#!LaaksoB!#] is highly recommended.
This section will describe the most commonly used cases. Linear interpolation is perhaps most commonly used because it is very straightforward and inexpensive, and because it sounds very good when the signal bandwidth is small compared with half the sampling rate. For a delay line in a nearly lossless feedback loop, such as in a vibrating string simulation, allpass interpolation is sometimes a better choice since it costs the same as linear interpolation in the first-order case and has no gain distortion. (Feedback loops can be very sensitive to gain distortions.) Finally, in later sections, some higher-order interpolation methods are described.