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Delay Lines

The delay line is an elementary functional unit which models acoustic propagation delay. It is a fundamental building block of both delay-effects processors and digital-waveguide synthesis models. The function of a delay line is to introduce a time delay between its input and output, as shown in Fig.2.1.

Figure 2.1: The $ M$-sample delay line.
\includegraphics{eps/delay}

Let the input signal be denoted $ x(n),\, n=0,1,2,\ldots$, and let the delay-line length be $ M$ samples. Then the output signal $ y(n)$ is specified by the relation

$\displaystyle y(n) = x(n-M),\quad n=0,1,2,\ldots \protect$ (3.1)

where $ x(n)\isdef 0$ for $ n<0$.

Before the digital era, delay lines were expensive and imprecise in ``analog'' form. For example, ``spring reverberators'' (common in guitar amplifiers) use metal springs as analog delay lines; while adequate for that purpose, they are highly dispersive and prone to noise pick-up. Large delays require prohibitively long springs or coils in analog implementations. In the digital domain, on the other hand, delay by $ N$ samples is trivially implemented, and non-integer delays can be implemented using interpolation techniques, as discussed later in §4.1.



Subsections
Previous: Acoustic Modeling with Digital Delay
Next: A Software Delay Line

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.


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