Digital delay line
Encyclopedia
A digital delay line is a discrete element in digital filter
Digital filter
In electronics, computer science and mathematics, a digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal. This is in contrast to the other major type of electronic filter, the analog filter, which is...

theory, which allows a signal to be delayed by a number of samples. If the delay is an integer multiple of samples digital delay lines are often implemented as circular buffer
Circular buffer
A circular buffer, cyclic buffer or ring buffer is a data structure that uses a single, fixed-size buffer as if it were connected end-to-end.This structure lends itself easily to buffering data streams.-Uses:...

s. This means that integer delays can be computed very efficiently.

The delay by one sample is notated and delays of samples is notated as motivated by the role the z-transform
Z-transform
In mathematics and signal processing, the Z-transform converts a discrete time-domain signal, which is a sequence of real or complex numbers, into a complex frequency-domain representation....

plays in describing digital filter
Digital filter
In electronics, computer science and mathematics, a digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal. This is in contrast to the other major type of electronic filter, the analog filter, which is...

structures.

If a delay is not an integer of a sample additional filters are applied to account for the fraction of delay different from an integer. Hence delay lines with non-integer delay are called fractional delay lines.

Digital delay lines are widely used building blocks in methods to simulate room acoustics
Room acoustics
Room acoustics describes how sound behaves in an enclosed space.The way that sound behaves in a room can be broken up into roughly four different frequency zones:...

, musical instruments and digital audio effects. Digital waveguide synthesis
Digital waveguide synthesis
Digital waveguide synthesis is the synthesis of audio using a digital waveguide. Digital waveguides are efficient computational models for physical media through which acoustic waves propagate...

shows how digital delay lines can be used as sound synthesis methods for various musical instruments such as string instruments and wind instruments.