Spectrum of the Sampled Signal: (contd:)

Note that is periodic with the fundamental period given by the region,

and

Letting and and using equ (3.1.2), we obtain the discrete space Fourier transform relation, in terms of unitless frequency variables and as,

	(3.1.7)

The 2D discrete-space inverse Fourier Transform is given by

	(3.1.8)

Note that the discrete-space Fourier transform is periodic with the fundamental period and .

The standard approach to relate FT or of the sampled signal to the continuous is to start with equ (3.1.3) and express as the 2D convolution of Fourier transforms of the continuous signal and the 2D impulse train (also called comb function) using the modulation property of the FT:

	(3.1.9)

where FT denotes 2D FT.

The FT