An Introduction to Wavelets Through Linear Algebra - Michael Frazier [Seduction28]

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Fourier Analysis: An Introduction (Princeton Lectures in Analysis) - Elias Stein

An Introduction to Wavelet Analysis - David Walnut


Wavelet theory is one of the newest branches of mathematics, originally emerged from the broader harmonic analysis, but now making its own way because of its multiple applications.

There are several possible approaches to the subject, but maybe this one is both the easiest and the best one. Modern analysis relies more and more on operator theory (linear algebra in infinite-dimensional spaces) so this approach fits nicely in the overall framework of modern mathematics.

This kind of introductory expositions are essential for a subject to get widespread, and this one really deserves full attention because by using these kind of techniques we are now able to solve better a lot of problems involving pulses, signals, oscillations, etc. Wavelet analysis provides a means for constructing a specific Fourier-like method to solve our problem according to its intrinsic nature.