Ripples In Mathematics The Discrete Wavelet Transform
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Ripples in Mathematics
Author: A. Jensen
language: en
Publisher: Springer Science & Business Media
Release Date: 2001-06-06
This introduction to the discrete wavelet transform and its applications is based on a novel approach to discrete wavelets called lifting. After an elementary introduction, connections of filter theory are presented, and wavelet packet transforms are defined. The time-frequency plane is used for interpretation of signals, problems with finite length signals are detailed, and MATLAB is used for examples and implementation of transforms.
Ripples in Mathematics
Author: A. Jensen
language: en
Publisher: Springer Science & Business Media
Release Date: 2011-06-28
This introduction to the discrete wavelet transform and its applications is based on a novel approach to discrete wavelets called lifting. After an elementary introduction, connections of filter theory are presented, and wavelet packet transforms are defined. The time-frequency plane is used for interpretation of signals, problems with finite length signals are detailed, and MATLAB is used for examples and implementation of transforms.
Discrete Fourier And Wavelet Transforms: An Introduction Through Linear Algebra With Applications To Signal Processing
Author: Roe W Goodman
language: en
Publisher: World Scientific Publishing Company
Release Date: 2016-01-21
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.