# Circular Shift

Investigate the important property of circular shifts that helps in understanding the discrete Fourier transform (DFT).

## We'll cover the following

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.

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