Converting from a continuous image a(x,y) to its digital representation b[m,n] requires the process of sampling. In the ideal sampling system a(x,y) is multiplied by an ideal 2D impulse train:
where Xo and Yo are the sampling distances or intervals, d(*,*) is the ideal impulse function, and we have used eq. . (At some point, of course, the impulse function d(x,y) is converted to the discrete impulse function d[m,n].) Square sampling implies that Xo =Yo. Sampling with an impulse function corresponds to sampling with an infinitesimally small point. This, however, does not correspond to the usual situation as illustrated in Figure 1. To take the effects of a finite sampling aperture p(x,y) into account, we can modify the sampling model as follows:
The combined effect of the aperture and sampling are best understood by examining the Fourier domain representation.
where 
s = 2
/Xo is the sampling
frequency in the x direction and 
s =
2/Yo is the sampling frequency in the y direction.
The aperture p(x,y) is frequently square, circular, or
Gaussian with the associated P(,). (See
Table 4.) The periodic nature of the spectrum, described in eq. is clear from
eq. .