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Fourier and Wavelet Analysis
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This book is intended as an introduction to classical Fourier analysis, Fourier series, the Fourier transform, and Fourier sine and cosine transforms. The topics are developed slowly for the reader who has never seen them before, with a preference for clarity of exposition over elegance in stating and proving results. More recent developments, such as the discrete and fast Fourier transforms and wavelets, are covered in the last two chapters, where the approach is elementary, intended for the novice reader. The first three, short, chapters present requisite background material, and these could be read as a short course in functional analysis. The text includes many historical notes to place the material in a cultural and mathematical context; from the fact that Jean Baptiste Joseph Fourier was the nineteenth, but not the last, child in his family to the impact that Fourier series have had on the evolution of the concept of the integral.
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