Discrete Fourier Analysis and Wavelets

Maintaining a comprehensive and accessible treatment of the concepts, methods, and applications of signal and image data transformation, the Second Edition features updated and revised coverage throughout with an emphasis on key and recent developments in the field of signal and image processing.  The major motivating application continues to be signal and image compression.   The authors introduce a new chapter on frames that is appropriately implemented after...
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Maintaining a comprehensive and accessible treatment of the concepts, methods, and applications of signal and image data transformation, the Second Edition features updated and revised coverage throughout with an emphasis on key and recent developments in the field of signal and image processing.  The major motivating application continues to be signal and image compression.   The authors introduce a new chapter on frames that is appropriately implemented after the coverage on spectrograms.  Frames are a new technology in which signals, images, and other data are redundantly measured, and this redundancy allows for more sophisticated signal analysis.  This new coverage also expands upon the discussions on spectrograms using a frames approach.  In addition, this Second Edition includes a new chapter on lifting schemes for wavelets and provides a variation on the original low-pass/high-pass filter bank approach to the design and implementation of wavelets.  These new chapters also include appropriate exercises and MATLAB#65533; projects for further experimentation and practice.  The authors clearly explain terms that may be unfamiliar to readers, and they also detail mathematical concepts that are relevant to image compression and signal processing. Most of the existing related texts focus on the concepts of imaging science and algorithms while this book focuses more on the underlying mathematics, with image compression as a motivation.  A companion website features updated supplementary solution sets in addition to computer software support, including additional methods for applying the MATLAB routines as well SciPy (Scientific Python) support.  Topical coverage includes: vector spaces, signals, and images; the discrete Fourier transform; the discrete cosine transform; convolution and filtering; windowing and localization; frames; filter banks; lifting schemes; and wavelets.