Mathematical Preliminaries for Transforms, Subbands, and Wavelets

In this chapter we will review some of the mathematical background necessary for the study of transforms, subbands, and wavelets. The topics include Fourier series, Fourier transforms, and their discrete counterparts. We will also look at sampling and briefly review some linear system concepts.

The roots of many of the techniques we will study can be found in the mathematical literature. Therefore, in order to understand the techniques, we will need some mathematical background. Our approach in general will be to introduce the mathematical tools just prior to when they are needed. However, there is a certain amount of background that is required for ...

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