Spectrum of the Sampled Signal: (contd:)
Another change of variables
 and
 shifts all the squares
SQ  down to the fundamental period
 to yield
 |
(3.1.10) |
As
 for
 integers, the frequencies
 map on to .
 . Comparing the last expression with equ(3.1.8), we conclude that,
 |
(3.1.11) |
We see that as a result of sampling, the spectrum of the continuous signal replicates in 2D frequency plane according to equ (3.1.11). The case when the continuous signal is band limited with a circular support of radius
 is shown in figure (3.1.2).
Figure (3.1.2a): Support of FT of continuous image |
Figure (3.1.2b): Spectral support of the sampled image. |
|
