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.