Condition for a perfect recovery (Nyquist criterion)
w_max < pi / T
A function f(x) that is bandlimited to w_max can be reconstructed exactly from its equidistant samples provided that the sampling step …
T < pi / w_max
Ideal sampling is modeled as a multiplication with
a sequence of Dirac impulses (ideal samplign function)
Sampling … the Fourier transform of the image
periodize
Perfect recovery is possible only if the image is sampled at or above the Nyquist pulsation …
w_max / 2
Undersampling produce …
Aliasing.
It can be prevented by ideal lowpass prefilter prior to sampling