2. Sampling, z-transform and digital filtering

The precursors of the invention of sampling and the development of the corresponding theory are those who took an interest in motion analysis in the nineteenth century: the creators of the stroboscope (Plateau in Belgium and Von Stampfer in Austria in 1829); then those of the "chronoscope", a rapid-fire system for motion analysis (Muybridge in the USA and Marey in France, circa 1870). The first reconstructions of animated image sequences were based on retinal persistence (an image is preserved for about 1/10 of a second), discovered by Plateau and used in the stroboscope and then the cinematograph (Edison in 1891 and the Lumière brothers in 1895). The mathematical formulation of good sampling conditions was proposed by H. Nyquist in 1928 and then taken up by C. Shannon in 1948, specialists in communications at Bell's Labs.

The fundamental results on sampling are...