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  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.