Delay-Line Interpolation

When delay lines need to vary smoothly over time, some form of interpolation between samples is usually required to avoid ``zipper noise'' in the output signal as the delay length changes. There is a hefty literature on ``fractional delay'' in discrete-time systems, and the survey in [272] is highly recommended.

This section will describe the most commonly used cases. Linear interpolation is perhaps most commonly used because it is very straightforward and inexpensive, and because it sounds very good when the signal bandwidth is small compared with half the sampling rate. For a delay line in a nearly lossless feedback loop, such as in a vibrating string simulation, allpass interpolation is usually a better choice since it costs the same as linear interpolation in the first-order case and has no gain distortion. (Feedback loops can be very sensitive to gain distortions.) Finally, in Appendix K, some higher order interpolation schemes are outlined.

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Subsections

• Linear Interpolation
• First-Order Allpass Interpolation
  • Minimizing the Transient Response of First-Order Allpass Interpolation

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Order a Hardcopy of Physical Audio Signal Processing

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written by 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.