A typical signal in communication theory is the varying voltage measured across two nodes of an electric system. Another typical example of a signal would be a black-and-white photograph, where the information is represented as the varying lightness of the photographic paper. We can make a crude division of signal processing tasks into the following three categories: removal of interference, transformation of signals into some other form more suitable for particular purposes, and analysis and extraction of some characteristics of the signal. The chapter illustrates the fundamental problems related to noise models and filtering methods by means of illustrative examples. They are simple examples but still reveal the main difficulties that we face in the search for better methods in signal and image processing. One should keep in mind that we were addressing a very specific filtering problem where the goal is to remove noise; the noise is impulsive; and the signal and the noise occupy the same frequency band.