#### Graphical Convolution

As mentioned above, cyclic convolution can be written as

*graphically*, as depicted in Fig.7.5 above. The convolution result at time is the inner product of and , or . For the next time instant, , we shift one sample to the right and repeat the inner product operation to obtain , and so on. To capture the cyclic nature of the convolution, and can be imagined plotted on a

*cylinder*. Thus, Fig.7.5 shows the cylinder after being ``cut'' along the vertical line between and and ``unrolled'' to lay flat.

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Convolution Example 3: Matched Filtering