5Wavelets and Fourier Transforms
5.1 Introduction
In this chapter we continue studying transformation methods. The main idea behind the techniques presented is to transform data from the spatial domain to a frequency domain. We start by introducing the Fourier transform since it is simpler and historically older.
5.2 Dynamic Fourier Analysis
A physical process can be described either in the time domain, by the values of some quantity 
as a function of time 
, for example, 
, or in the frequency domain, where the process is specified by giving its amplitude 
(generally a complex number) as a function of frequency 
, that is, 
, with 
. For many applications, it is useful to think of 
and as being ...
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