An Introduction to Wavelet Analysis provides a comprehensive
presentation
of the conceptual basis of wavelet analysis, including the
construction
and application of wavelet bases. The book develops the basic theory
of wavelet bases and transforms without assuming any knowledge of
Lebesgue integration or the theory of abstract Hilbert spaces. The
book motivates the central ideas of wavelet theory by offering a
detailed exposition of the Haar series, and then shows how a more
abstract approach allows us to generalize and improve upon the Haar
series. Once these ideas have been established and explored,
variations and extensions of Haar construction are presented. The
mathematical pre-requisites for the book are a course in advanced
calculus, familiarity with the language of formal mathematical proofs,
and basic linear algebra concepts. Features: *Rigorous proofs with
consistent assumptions on the mathematical background of the reader;
does not assume familiarity with Hilbert spaces or Lebesgue measure *
Complete background material on (Fourier Analysis topics) Fourier
Analysis * Wavelets are presented first on the continuous domain and
later restricted to the discrete domain, for improved motivation and
understanding of discrete wavelet transforms and applications.
* Special appendix, "Excursions in Wavelet Theory " provides a guide
to
current literature on the topic
* Over 170 exercises guide the reader through the text. The book is
an ideal text/reference for a broad audience of advanced students and
researchers in applied mathematics, electrical engineering,
computational science, and physical sciences. It is also suitable as a
self-study reference guide for professionals. All readers will find