Circular Shift

Time shifting a signal is one of the most fundamental ideas of digital signal processing. Circular shift is very similar to time shift with the following difference:

• In a regular time shift, the available axis is from $-\infty$ to $+\infty$.
• In circular shift, we only focus on a segment of $N$ samples.

Let us discuss how this is done.

• If a signal $x[n]$ is circularly right shifted by $m$, the samples of the signal $x[n]$ that fall off to the right of length-$N$ segment reappear at the start.
• Similarly, if $x[n]$ is circularly left shifted by $m$, the samples of the signal $x[n]$ that fall off to the left of length-$N$ segment reappear from the end.

This is just like the video game character Pac-Man who disappears at one end of the screen then emerges from the other.