Bandlimited Functions Sampling and the Discrete Fourier Transform
In the preceding chapters we have dealt exclusively with signals and their transformations defined on a continuous time interval. Such signals can be referred to as analogue signals. In this chapter we introduce the important topic of discrete signals, i.e., signals that are represented by sequences of numbers. Sometimes these numbers can be interpreted as samples of a continuous signal taken at discrete time intervals. Such an interpretation is, however, not always possible or for that matter even necessary. Nevertheless, the subject is best introduced by starting with the idea of sampling. For this purpose we shall initially restrict the class of analogue signals which we propose to sample to so-called bandlimited functions.