Comparison of Rectangular and Hexagonal Sampling
For any bandlimited waveform, there is an infinite number of possible choices for the periodicity matrix  and the sampling matrix  .
Among these numerous possibilities, two strategies are common. They are rectangular sampling and hexagonal sampling.
For the rectangular sampling case  is diagonal. Hexagonal sampling refers to sampling
matrices of the form  . A set of sample locations for hexagonal sampling matrix is shown below.
The alternate rows of this raster are identical and the odd-indexed rows are staggered one half sample interval w.r.t the even indexed rows. The term "hexagonal" is used since each sample location will have six nearest neighbors when
Figure(3.2.5)
The corresponding periodicity matrix  will be
or 
This implies,
i.e.,
i.e. the periodicity matrix has same form as sampling matrix  .
There are several regions which when periodically, extended according to  cover the entire plane with no overlap
They are: .
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Figure (3.2.6b) |
Figure(3.2.6c) |
(continued in the next slide)
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