ABSTRACT
Wavelets are the latest tool in constructing function spaces. The spaces which can be constructed are more localized than that can be built with Fourier theory. The goal of Fourier and wavelet analysis is to represent functions in terms of “simpler” functions. These simple functions can be considered to be the building blocks of a set of functions. The idea of representation of a function via the use of a dictionary of functions is analogous to the idea of representing human thoughts via the proper use of vocabulary. The richer the vocabulary, the more precise is the representation of an idea. Fourier analysis involves the study of expansion of arbitrary functions in terms of trigonometric functions. Fourier methods transform the original signal into a function in the transform domain. Wavelet analysis is based upon the concept of scale, rather than frequency. Wavelets have found applications in astronomy, econometrics, geophysics, medicine, numerical analysis, signal processing, statistics, and many other diverse fields.
