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CRC Press Inc
22 August 1996
Functional analysis & transforms
This text provides a clear treatment of Fourier series, Fourier tranforms, and FFTs. The sofware included with the book and updated for this edition enables you to generate images of Fourier analysis described in the text. Topics include applications to vibrating strings (including computer animation), heat conduction, removal of noise and frequency detection, filtering of Fourier series and improvement of convergence, electron diffraction, imaging with coherent and incoherent monochromatic light, spectral analysis with diffraction gartings, Fourier transform properties of lenses, Poisson summation, sampling theory and aliasing.
By:   James S. Walker (University of Wisconsin Eau Claire USA)
Imprint:   CRC Press Inc
Country of Publication:   United States
Edition:   2nd New edition
Volume:   24
Dimensions:   Height: 235mm,  Width: 156mm,  Spine: 33mm
Weight:   771g
ISBN:   9780849371639
ISBN 10:   0849371635
Series:   Studies in Advanced Mathematics
Pages:   464
Publication Date:   22 August 1996
Audience:   College/higher education ,  Professional and scholarly ,  Professional & Vocational ,  A / AS level ,  Further / Higher Education
Format:   Hardback
Publisher's Status:   Active
Chapter 1. Basic Aspects of Fourier Series Definition of Fourier Series Examples of Fourier Series Fourier Series of Real Functions Pointwise Convergence of Fourier Series Further Aspects of Convergence of Fourier Series Fourier Sine Series and Cosine Series Convergence of Fourier Sine and Cosine Series References Exercises Chapter 2. The Discrete Fourier Transform (DFT) Derivation of the DFT Basic Properties of the DFT Relation of the DFT to Fourier Coefficients Relation of the DFT to Sampled Fourier Series Discrete Sine and Cosine Transforms References Exercises Chapter 3. The Fast Fourier Transform (FFT) Decimation in Time, Radix 2, FFT Bit Reversal Rotations in FFTs Computation of Sines and Tangents Computing Two Real FFTs Simultaneously Computing a Real FFT Fast Sine and Cosine Transforms Inversion of Discrete Sine and Cosine Transforms Inversion of the FFT of a Real Sequence References Exercises Chapter 4. Some Applications of Fourier Series Heat Equation The Wave Equation Schroedinger's Equation for a Free Particle Filters Used in Signal Processing Designing Filters Convolution and Point Spread Functions Discrete Convolutions Using FFTs Kernels for Some Common Filters Convergence of Filtered Fourier Series Further Analysis of Fourier Series Partial Sums References Exercises Chapter 5. Fourier Transforms Introduction Properties of Fourier Transforms Inversion of Fourier Transforms The Relation between Fourier Transforms and DFTs Convolution-An Introduction The Convolution Theorem An Application of Convolution in Quantum Mechanics Filtering, Frequency Detection, and Removal of Noise Poisson Summation Summation Kernels Arising from Poisson Summation The Sampling Theorem Aliasing Comparison of Three Kernels Sine and Cosine Transforms References Exercises Chapter 6. Fourier Optics Introduction - Diffraction and Coherency of Light Fresnel Diffraction Fraunhofer Diffraction Circular Apertures Interference Diffraction Gratings Spectral Analysis with Diffraction Gratings The Phase Transformation Induced by a Thin Lens Imaging with a Single Lens Imaging with Coherent Light Fourier Transforming Property of a Lens Imaging with Incoherent Light References Exercises A. User's Manual for Fourier Analysis Software B. Some Computer Programs C. The Schwarz Inequality D. Solutions to Odd-Numbered Exercises Bibliography Index

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