Spectrum of the Sampled Signal:

We now relate the Fourier transform or of the sampled signal to that of the continuous signal .

As given earlier, the 2D continuous space Fourier transform of a signal with continuous variables is given by,

	(3.1.4)

where  and the inverse Fourier transform is given by,

	(3.1.5)

Here the spatial frequency variables have the units in cycles/mm and are related to radian frequencies by a scale factor of .

In order to evaluate the 2D FT of we substitute equ (3.1.3) in to equ (3.1.4) and exchange the order of and summation to obtain,

which simplifies as,

	(3.1.6)

(continued)