1. Digital sampling and filtering of 2D signals

The problems involved in sampling two-dimensional signals are similar to those for one-dimensional signals. Nyquist-Shannon theory applies in the same way. However, an interpretation in two-dimensional space is needed to better understand the phenomena associated with sampling in the spatial domain, such as the effects of the geometry of the sampling pattern.

Let's start by mentioning the necessary compromises between theoretical rigor and the specificities of certain applications in digital image processing.

Digital image processing specialists are accustomed to representing a sampled image as "pixels", squares where the image intensity is constant. This is not the interpretation compatible with sampling theory. Furthermore, the stroboscopic effect of cinema and the moiré effects that can be observed when digitizing clothing textures, for...