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As mentioned above, cyclic convolution can be written as
where
and
. It is instructive to interpret this
expression 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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