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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 [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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