Why the sampling theorem is wrong. (Part 1).
Why the sampling theorem is wrong. (Part 1). (This is on-line translate of a part of an article published in Dec-1999 in largest Russian computer magazine “Computerra”) The mathematician Jean-Baptiste-Joseph Fourier (not the utopian who is the source and integral part of Marxism, that one, Charles Fourier) invented a simple method (based on the work of the semi-Russian mathematician Leonhard Euler) for representing periodic processes of various natures by expressing them as the sum of sines and cosines of multiple frequencies. Only for periodic processes. For no other. It must be known in advance that the process is 100% periodic. An example is the bending vibrations of rotating helicopter blades (I took this from Nosach's book on interpolation). Later, mathematicians managed to adapt this method to non-periodic processes, or rather, to parts of non-periodic processes. In this case, the sum of the sines and cosines necessarily becomes infinite, and therefore th...