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Fourier Analysis and Applications: Filtering, Numerical Computation, Wavelets |  |
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Fourier Analysis and Applications: Filtering, Numerical Computation, Wavelets | |
For this reason, the object of this text, which focuses on Fourier analysis, signal analysis and filters, is two-fold. On the one hand it conveys to the mathematician a rigorous presentation illustrated with important practical applications of the theory, including a discussion of Fast Fourier Transform. On the other hand it imparts to the physicist and engineer a body of theory in which the `well-known' formulae find their justification.
There is a systematic development of fundamental concepts, such as the Lebesgue integration and theory of distribution, that allows one to establish precise relations among several domains: Fourier transform and convolution; filtering and sampling; time-frequency analysis (gabor transforms and wavelets).
Each of the 42 lectures provides an easily assimilated set of ideas and techniques, suitable for both classroom or self-study. Maneuvering through the book is facilitated by grouping the lectures into 12 chapters and by adding numerous summary tables. This latter feature makes the book a handy reference for the subjects covered.
Senior undergraduate and graduate students in engineering, physics and mathematics will find this book helpful. It will also serve as a useful reference for scientists and engineers who deal with modelling and signal processing.
媒体推荐 From the reviews: BULLETIN OF MATHEMATICS BOOKS "This book should have wide appeal, from those who are just getting into the area and wish to learn mathematical foundations and applications to those who are already experienced and wish to have a reference that provides a mathematically rigorous coverage of the state of the art…The coverage is thorough but not overwhelming, perhaps because the chapters are divided into lessons, allowing the reader a chance to pause and think. The authors work clearly to impart an understanding of the theory and applications, and not just offer an encyclopedic tome."
目录
Signals and Systems.- Periodic Signals.- The Discrete Fourier Transform and Numerical Computations.- The Lebesgue Integral.- Spaces.- Convolution and the Fourier Transform of Functions.- Analog Filters.- Distributions.- Convolution and the Fourier Transform of Distributions.- Filters and Distributions.- Sampling and Discrete Filters.- Current Trends: Time-Frequency Analysis.- References.
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