In the limiting case of , the input and output sampling rates are equal, and all sidelobes of the frequency response (partially shown in Fig.4.9) alias into the main lobe.

If the output is sampled at the same exact time instants as the input
signal, the input and output are identical. In terms of the aliasing
picture of the previous section, the frequency response aliases to a
perfect flat response over
, with all spectral images
combining coherently under the flat gain. It is important in this
reconstruction that, while the frequency response of the underlying
continuous interpolating filter is aliased by sampling, the signal
spectrum is only imaged--not aliased; this is true for all positive
*integers*
and
in Fig.4.7.

More typically, when linear interpolation is used to provide
*fractional delay*, identity is not obtained. Referring again to
Fig.4.7, with
considered to be so large that it is
effectively infinite, fractional-delay by
can be modeled as
convolving the samples
with
followed by sampling
at
. In this case, a linear phase term has been introduced in
the interpolator frequency response, giving,

so that now downsampling to the original sampling rate does

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University