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