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The shift theorem says that a delay of
samples
in the time domain corresponds to a multiplication by
in the frequency domain:
![$\displaystyle {\cal Z}_z\{$](img645.png)
S
HIFT
or, using more common notation,
Thus,
, which is the waveform
delayed by
samples, has the z transform
.
Proof:
where we used the causality assumption
for
.
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