Signal Digitizing – Sampling and Coding

The conversion of an analog signal to digital form involves a twofold approximation. Firstly, in the time domain, the signal function s(t) is replaced by its values at integral time increments T and is thus converted to s(nT). This process is called sampling. Secondly, in the amplitude domain, each value of s(nT) is approximated by a whole multiple of an elementary quantity. This chapter analyzes the effect of these two approximations on the signal. To achieve this, two basic tools will be used: Fourier analysis and distribution theory. The type of sampling is carried out on a temporal basis. Nevertheless, the general characteristics are also applicable to frequency sampling. Sampling theorem establishes the conditions under which the set of samples of a signal correctly represents that signal. The properties can be clearly illustrated by sampling sinusoidal signals, whose features are of use in numerous applications.