A digital delay line is a discrete element in digital filter 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 buffers. This means that integer delays can be computed very efficiently. An FIR filter In electronics,nirali a digital filter is any electronic filter that works by performing digital mathematical operations on an intermediate form of a signal. ... A circular buffer is a method of using memory within a computer program. ...

The delay by one sample is notated z ^{− 1} and delays of l samples is notated as z ^{− l} motivated by the role the z-transform plays in describing digital filter structures. In mathematics and signal processing, the Z-transform converts a discrete time domain signal, which is a sequence of real numbers, into a complex frequency domain representation. ... An FIR filter In electronics,nirali a digital filter is any electronic filter that works by performing digital mathematical operations on an intermediate form of a signal. ...

If a delay is not an integer of a sample additional filters are applied to account for the fraction of delay different to an integer. Hence delay lines with non-integer delay are called fractional delay lines (Laakso Välimäki Karjalainen Laine & 1996 30 - 60)

Digital delay lines are widely used building blocks in methods to simulate room acoustics, musical instruments and digital audio effects (Smith Lee 2007). Digital waveguide synthesis shows how digital delay lines can be used as sound synthesis methods for various musical instruments such as string instruments and wind instruments. Room acoustics describes how sound behaves in an enclosed space. ... A musical instrument is a device that has been constructed or modified with the purpose of making music. ... Digital waveguide synthesis is the synthesis of audio using a digital waveguide. ... The term synthesiser is also used to mean frequency synthesiser, an electronic system found in communications. ... A string instrument (also stringed instrument) is a musical instrument that produces sound by means of vibrating strings. ... A wind instrument consists of a tube containing a column of air which is set into vibration by the player blowing into (or over) a mouthpiece set into the end of the tube. ...

Sources

Smith, Julius O. & Nelson Lee (August 2007), Computational Acoustic Modeling with Digital Delay (published August 12 2007), <http://ccrma.stanford.edu/realsimple/Delay/Delay_lines.html>. Retrieved on August 21 2007.

Laakso, Timo I.; Vesa Välimäki & Matti Karjalainen et al. (January 1996), "Splitting the unit delay - tools for fractional delay filter design", IEEE Signal Processing Magazine 13 (1): 30-60, January 1996 This article or section does not cite its references or sources. ... Year 1996 (MCMXCVI) was a leap year starting on Monday (link will display full 1996 Gregorian calendar). ...