From Fourier Analysis to Wavelets, Softcover reprint of the original 1st ed. 2015
IMPA Monographs Series, Vol. 3

This text introduces the basic concepts of function spaces and operators, both from the continuous and discrete viewpoints. Fourier and Window Fourier Transforms are introduced and used as a guide to arrive at the concept of Wavelet transform. The fundamental aspects of multiresolution representation, and its importance to function discretization and to the construction of wavelets is also discussed.

Emphasis is given on ideas and intuition, avoiding the heavy computations which are usually involved in the study of wavelets.  Readers should have a basic knowledge of linear algebra, calculus, and some familiarity with complex analysis. Basic knowledge of signal and image processing is desirable.

This text originated from a set of notes in Portuguese that the authors wrote for a wavelet course on the Brazilian Mathematical Colloquium in 1997 at IMPA, Rio de Janeiro.

Includes extensive appendices on Systems and Filters and the Z Transform

Emphasis is given on ideas and intuition rather than heavy computations

Provides great detail on different types of wavelets: Orthogonal Wavelets, Biorthogonal Wavelets, Wavelet Design, and Constructing Wavelets