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A First Course in Wavelets with Fourier Analysis, Second Edition offers a comprehensive and accessible treatment of Fourier analysis and wavelets. In this self-contained text, Albert Boggess presents fundamental concepts and techniques with clarity, ensuring that both mathematical theory and signal processing applications are approachable. The book opens with essential topics such as vector spaces and inner product spaces before developing the Fourier series, Fourier transform, and discrete Fourier analysis. The text further explores continuous wavelets, two-dimensional wavelets, and analyzes Haar, Shannon, and linear spline wavelets, along with the general framework of multi-resolution analysis. Enhanced with updated MATLAB code and expanded examples, the book guides the reader through the construction, smoothness, and computation of Daubechies' wavelets as well as advanced topics including wavelet decomposition and reconstruction. With its rigorous proofs, illustrative exercises, and detailed applications—often in the area of audio and video signal filtering and compression—this edition is particularly well-suited for upper-undergraduate and graduate courses in mathematics and engineering, as well as for professionals seeking a solid introduction to wavelet theory alongside Fourier analysis.
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