Fractional Delay Filters

In fractional-delay filtering applications, the interpolator typically slides forward through time to produce a time series of interpolated values, thereby implementing a non-integer signal delay:

where spans the central one-sample range of the interpolator. Equivalently, the interpolator may be viewed as an FIR filter having a linear phase response corresponding to a delay of samples. Such filters are often used in series with a delay line in order to implement an interpolated delay line (§4.1) that effectively provides a continuously variable delay for discrete-time signals.

The frequency response [449] of the fractional-delay FIR filter is

For an ideal fractional-delay filter, the frequency response should be equal to that of an ideal delay

where denotes the total desired delay of the filter. Thus, the ideal desired frequency response is a linear phase term corresponding to a delay of samples.

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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.