Note that the cyclic convolution operation can be expressed in terms
of previously defined operators as

where
and
. It is instructive to interpret the
last expression above 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.