Discrete Fourier and Wavelet Transforms (ePub)

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. Request Inspection CopyThis 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. Request Inspection CopyReadership: Undergraduate mathematics, science and engineering students interested in the theory and applications of discrete Fourier and wavelet transforms.Key Features:Accessible account of the theory and applications of discrete Fourier and wavelet transforms based on ten years of classroom useIntroduction of discrete wavelet transforms for digital signals via elementary lifting steps and filter banksInterweaving of mathematical theory with examples and applications to digital signal processing and image compressionComputer explorations of signal and image processing in each chapterMathematical concepts clarified by more than 90 figures and 75 exercises with detailed solutions