Activity 1

In the figure below, we discussed the circular shifts by $3$ and $1$, respectively.

Now draw the following two signals:

• $x[(n+7) \:\textmd{mod}\: 8]$
• $x[(n-5) \:\textmd{mod}\: 8]$

You will find that these shifts are actually the same as $x[(n-1) \:\textmd{mod}\: 8]$ and $x[(n+3) \:\textmd{mod}\: 8]$, respectively!