Delay-Lines and Digital Waveguides

Abstract

A digital delay line is a particular type of finite impulse response (FIRfinite impulse response (FIR)) filter that has many useful applications in audio signal processing. Simply put, signals that are input to a delay line reappear at the output after a specified time period (in samples). Delay lines are often implemented to support delay times that can vary dynamically. As well, delay times corresponding to noninteger sample lengths can be approximated. Time delay of signals is fundamental to signal processing systems. In this chapter, we focus on applications in digital audio signal processing and in particular, the modeling of wave propagation in air and in strings. The fundamentals of delay lines will be introduced and their implementation detailed, including common fractional-delay filtering techniques. Feedforward and feedback comb filters are simple signal processing structures built with delay lines and they exhibit characteristics that not only make them interesting for delay-based audio effects algorithms, but also as simple models of acoustic wave propagation. Finally, the use of delay lines to simulate wave propagation in one-dimensional waveguides will be introduced with a focus on the synthesis of plucked string instrument sounds.