Converting Propagation Distance to Delay Length

We may regard the delay-line memory itself as the fixed ``air'' which propagates sound samples at a fixed speed ( meters per second at degrees Celsius and 1 atmosphere). The input signal can be associated with a sound source, and the output signal (see Fig.2.1 on page ) can be associated with the listening point. If the listening point is meters away from the source, then the delay line length needs to be

where denotes the discrete-time sampling interval. In other words, the number of samples delay is the propagation distance divided by , the distance sound propagates in one sampling interval. In practice, rounding to the nearest integer causes no audible difference, unless the echo time is so short that the system is not really perceived as an echo (we'll learn about ``comb filters'' in §2.6 below).

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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.