An Introduction to Wavelet Analysis

An Introduction to Wavelet Analysis by David F. Walnut offers a thorough exploration of the fundamental ideas behind wavelet theory. The book starts by carefully developing the building blocks of wavelet bases and transforms, using an accessible approach that does not require prior knowledge of Lebesgue integration or abstract Hilbert spaces. Beginning with a detailed discussion on the Haar series, the text gradually introduces more general frameworks that refine and extend these initial concepts. Emphasizing clarity and rigor, the book provides complete background material on Fourier analysis topics, paving the way for a smooth transition from the continuous to discrete domains. This progression not only deepens understanding of discrete wavelet transforms but also highlights their applications in various fields. With over 170 exercises integrated throughout the text, readers are invited to engage actively with the material, making it an ideal reference for advanced students, researchers in applied mathematics and engineering, and professionals seeking a self-study guide.