Example 1: (1's on diagonal of square)

Consider a spatial sequence of finite extent , as illustrated in the left-hand side of Figure (4.3).

Proceeding to take the DFT, we obtain for :

and, of course, elsewhere, as illustrated on the right-hand side of Figure (4.3 ). Note that this is analogous to the case of the continuous-parameter Fourier transform of an impulse line. This ideal result occurs only when the line is exactly at and the DFT size is square. For other angles, we get a in k type of approximation that tends to the impulse line solution more and more as N grows large without bound. Of course, as was true for the continuous-space (parameter) Fourier transform, the line of impulses in frequency is perpendicular or at 90⁰ to the impulse line in space.