(contd. )

In this case the sampling matrix is,

because

This is so because,

or

and

For hexagonal baseband case:

Periodicity matrix is :

Figure(3.2.10)

where and

Sampling matrix

and

Since sampling density is proportional to , we see that by taking the ratio of we get . This implies that the hexagonal sampling requires less samples than rectangular sampling to represent the same circulating bandlimited continuous signal . There is no other efficient sampling scheme for circularly bandlimited signals than hexagonal sampling.