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

The *frequency response* [452] 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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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University