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Fast Fourier Transforms, 2nd Ed.

Walker; James S.

1996

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 Schrödinger'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

CRC - TAYLOR & FRANCIS

ISBN: 0849371635

PGS: 464

List: 146.95 YOUR PRICE: 139.60

Inside the FFT Black Box: Serial and Parallel Fast Fourier Transform Algorithms

Chu; Eleanor

1999

PRELIMINARIES An Elementary Introduction to the Discrete Fourier Transform Some Mathematical and Computational Preliminaries SEQUENTIAL FFT ALGORITHMS The Divide-and-Conquer Paradigm and Two Basic FFT Algorithms Deciphering the Scrambled Output from In-Place FFT Computation Bit-Reversed Input to the Radix-2 DIF FFT Performing Bit-Reversal by Repeated Permutation of Intermediate Results An In-Place Radix-2 DIT FFT for Input in Natural Order An In-Place Radix-2 DIT FFT for Input in Bit-Reversed Order An Ordered Radix-2 DIT FFT Ordering Algorithms and Computer Implementation of Radix-2 FFTs The Radix-4 and the Class of Radix-2s FFTs The Mixed-Radix and Split-Radix FFTs FFTs for Arbitrary N FFTs for Real Input FFTs for Composite N Selected FFT Applications PARALLEL FFT ALGORITHMS Parallelizing the FFTs: Preliminaries on Data Mapping Computing and Communications on Distributed-Memory Multiprocessors Parallel FFTs without Inter-Processor Permutations Parallel FFTs with Inter-Processor Permutations A Potpourri of Variations on Parallel FFTs Further Improvement and a Generalization of Parallel FFTs Parallelizing Two-Dimensional FFTs Computing and Distributing Twiddle Factors in the Parallel FFTs APPENDICES Fundamental Concepts of Efficient Scientific Computation Solving Recurrence Equations by Substitution Bibliography

CRC - TAYLOR & FRANCIS

ISBN: 0849302706

PGS: 336

List: 157.95 YOUR PRICE: 150.05

PRINCIPLES OF FOURIER ANALYSIS

KENNETH HOWELL

2001

PRELIMINARIES The Starting Point Basic Terminology, Notation, and Conventions Basic Analysis I: Continuity and Smoothness Basic Analysis II: Integration and Infinite Series Symmetry and Periodicity Elementary Complex Analysis Functions of Several Variables FOURIER SERIES Heuristic Derivation of the Fourier Series Formulas The Trigonometric Fourier Series Fourier Series over Finite Intervals (Sine and Cosine Series) Inner Products, Norms, and Orthogonality The Complex Exponential Fourier Series Convergence and Fourier's Conjecture Convergence and Fourier's Conjecture: The Proofs Derivatives and Integrals of Fourier Series Applications CLASSICAL FOURIER TRANSFORMS Heuristic Derivation of the Classical Fourier Transform Integrals on Infinite Intervals The Fourier Integral Transforms Classical Fourier Transforms and Classically Transformable Functions Some Elementary Identities: Translation, Scaling, and Conjugation Differentiation and Fourier Transforms Gaussians and Other Very Rapidly Decreasing Functions Convolution and Transforms of Products Correlation, Square-Integrable Functions, and the Fundamental Identity of Fourier Analysis Identity Sequences Generalizing the Classical Theory: A Naive Approach Fourier Analysis in the Analysis of Systems Gaussians as Test Functions, and Proofs of Some Important Theorems GENERALIZED FUNCTIONS AND FOURIER TRANSFORMS A Starting Point for the Generalized Theory Gaussian Test Functions Generalized Functions Sequences and Series of Generalized Functions Basic Transforms of Generalized Fourier Analysis Generalized Products, Convolutions, and Definite Integrals Periodic Functions and Regular Arrays General Solutions to Simple Equations and the Pole Functions THE DISCRETE THEORY Periodic, Regular Arrays Sampling and the Discrete Fourier Transform APPENDICES

CHAPMAN & HALL - CRC - TAYLOR & FRANCIS

ISBN: 0849382750

PGS: 776

List: 139.95 YOUR PRICE: 132.95

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