Figure 11.1 shows the graphical symbol for a digital upsampler
by the factor
. To upsample by the integer factor
, we simply
insert
zeros between
and
for all
. In other
words, the upsampler implements the stretch operator defined
in §2.3.9:
In the frequency domain, we have, by the stretch (repeat) theorem for DTFTs:
Plugging in
, we see that the spectrum on
contracts by the factor
, and
images appear around the
unit circle. For
, this is depicted in Fig.11.2.