Module 3.2: Periodic Sampling

Comparison of Rectangular and Hexagonal Sampling (contd)

We are interested in the hexagonal region with parameters as shown in Figure below.

Figure(3.2.7)

We have,

and

Let us compare the relative efficiencies of rectangular and hexagonal schemes when they are used to sample a 2-D continuous signal which is circularly bandlimited.

i.e.    

or   

Figure(3.2.8)

The circular baseband shown above, can be inscribed in a square with sides of length 2W or a hexagon with sides of length . Consequently this signal can be embedded via square or a hexagon base-band. Periodic replication of the square baseband corresponds to sampling continuous signal on a rectangular raster.

This is shown in Figure below.

Figure(3.2.9)

ontinued in the next slide)