Summary: An Introduction to Wavelet Transforms and Data Compression Using Mathematica.
Alkiviadis G. Akritas
University of Thessaly
Department of Computer and Communication Engineering
Wavelet Transforms trace their origin both to Signal Processing and Theoretical Mathematics.
Since their introduction they have found applications in many areas -- most notably in finger-
printing by the FBI, where they are used to compress fingerprint data before storing it. Using
Mathematica as a paradigm we present an introduction to these transforms and their applica-
tion and demonstrate the main ideas with a picture of Pedro. The book by George Nakos and
the papers by Colm Mulcahy and Gilbert Strang were inspirational.
Uniform and Adaptive Plotting of Functions
Plotting various functions with a computer algebra system like Mathematica is an activity quite similar to
signal processing; to wit, in both cases we take samples. In this section we review standard ways of plotting
discrete data sets and two dimensional digital images. The inherent difficulties of plotting functions by
uniform sampling will lead us to adoptive plotting techniques (the main idea of which is at the heart of
wavelet transforms) and to techniques based on wavelets (see the section on Image Compression with the
Haar Transform). We also indicate the need for data compression.
à Uniformly distributed sample points