This textbook for undergraduate mathematics, science, and engineering students introduces the theory and applications of discrete Fourier and wavelet transforms using elementary linear algebra, without assuming prior knowledge of signal processing or advanced analysis.It explains how to use the Fourier matrix to extract frequency information from a digital signal and how to use circulant matrices to emphasize selected frequency ranges. It introduces discrete wavelet transforms for digital signals through the lifting method and illustrates through examples and computer explorations how these transforms are used in signal and image processing. Then the general theory of discrete wavelet transforms is developed via the matrix algebra of two-channel filter banks. Finally, wavelet transforms for analog signals are constructed based on filter bank results already presented, and the mathematical framework of multiresolution analysis is examined.

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Roe W Goodman received his PhD in Mathematics from MIT in 1963, where he was a member of the mathematics faculty from 1964 1971. Since 1971, he has been on the faculty of the Department of Mathematics of Rutgers University and is now Distinguished Professor Emeritus. He is author or coauthor of more than 40 published articles on differential operators, representation theory, and harmonic analysis on Lie groups. He has published a research monograph on analysis on Lie groups and an undergraduate textbook on stochastic models, and he is coauthor of two advanced graduate textbooks on Lie groups and representation theory. He received two outstanding teacher awards from Rutgers University during more than four decades of teaching a wide range of undergraduate and graduate mathematics courses.

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Discrete Fourier and Wavelet Transforms : An Introduction Through Linear Algebra With Applications to Signal Processing

Goodman, Roe W.

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