Finite Signals

Abstract

In the previous chapters we have only briefly, and in a casual way, considered the problems arising from having a finite signal. In the case of the Haar transform there are no problems, since it transforms a signal of even length to two parts, each of half the original length. In the case of infinite length signals there are obviously no problems either. But in other cases we may need for instance sample s[−1], and our given signal starts with sample s[0]. We will consider solutions to this problem, which we call the boundary problem. Theoretical aspects are considered in this chapter. It is important to understand that there is no universal solution to the boundary problem. The preferred solution depends on the kind of application one has in mind The implementations are discussed in Chap. 11. The reader mainly interested in implementations and applications can skip ahead to this chapter.