Fast Fourier transforms. ([2017?])

• Record Type: Book
• Further Information: Note: James S. Walker.
• Authors: Walker, James S
• Contents: Cover; Half Title; Title Page; Copyright Page; Dedication; Table of Contents; 1: Basic Aspects of Fourier Series; 1.1 Definition of Fourier Series; 1.2 Examples of Fourier Series; 1.3 Fourier Series of Real Functions; 1.4 Pointwise Convergence of Fourier Series; 1.5 Further Aspects of Convergence of Fourier Series; 1.6 Fourier Sine Series and Cosine Series; 1.7 Convergence of Fourier Sine and Cosine Series; References; Exercises; 2: The Discrete Fourier Transform (DFT); 2.1 Derivation of the DFT; 2.2 Basic Properties of the DFT; 2.3 Relation of the DFT to Fourier Coefficients 2.4 Relation of the DFT to Sampled Fourier Series2.5 Discrete Sine and Cosine Transform; References; Exercises; 3: The Fast Fourier Transform (FFT); 3.1 Decimation in Time, Radix 2, FFT; 3.2 Bit Reversal; 3.3 Rotations in FFTs; 3.4 Computation of Sines and Tangents; 3.5 Computing Two Real FFTs Simultaneously; 3.6 Computing a Real FFT; 3.7 Fast Sine and Cosine Transforms; 3.8 Inversion of Discrete Sine and Cosine Transforms; 3.9 Inversion of the FFT of a Real Sequence; References; Exercises; 4: Some Applications of Fourier Series; 4.1 Heat Equation; 4.2 The Wave Equation 4.3 Schrodingerâ#x80;#x99;s Equation for a Free Particle4.4 Filters Used in Signal Processing; 4.5 Designing Filters; 4.6 Convolution and Point Spread Functions; 4.7 Discrete Convolutions Using FFTs; 4.8 Kernels for Some Common Filters; 4.9 Convergence of Filtered Fourier Series; 4.10 Further Analysis of Fourier Series Partial Sums; References; Exercises; 5: Fourier Transforms; 5.1 Introduction; 5.2 Properties of Fourier Transforms; 5.3 Inversion of Fourier Transforms; 5.4 The Relation between Fourier Transforms and DFTs; 5.5 Convolution â#x80;#x94; an Introduction; 5.6 The Convolution Theorem 5.7 An Application of Convolution in Quantum Mechanics5.8 Filtering, Frequency Detection, and Removal of Noise; 5.9 Poisson Summation; 5.10 Summation Kernels Arising from Poisson Summation; 5.11 The Sampling Theorem; 5.12 Aliasing; 5.13 Comparison of Three Kernels; 5.14 Sine and Cosine Transforms; References; Exercises; 6: Fourier Optics; 6.1 Introductionâ#x80;#x94;Diffraction and Coherency of Light; 6.2 Fresnel Diffraction; 6.3 Fraunhofer Diffraction; 6.4 Circular Apertures; 6.5 Interference; 6.6 Diffraction Gratings; 6.7 Spectral Analysis with Diffraction Gratings 6.8 The Phase Transformation Induced by a Thin Lens6.9 Imaging with a Single Lens; 6.10 Imaging with Coherent Light; 6.11 Fourier Transforming Property of a Lens; 6.12 Imaging with Incoherent Light; References; Exercises; A: Userâ#x80;#x99;s Manual for Fourier Analysis Software; B: Some Computer Programs; C: The Schwarz Inequality; D: Solutions to Odd-Numbered Exercises; Bibliography; Index
• Edition: Second edition
• Publisher Details: Boca, Raton, FL : CRC Press
• Publication Date: 2017
• Copyright Date: 1996
• Extent: 1 online resource
• Subjects: 515.723; Fourier transformations; MATHEMATICS / Calculus; MATHEMATICS / Mathematical Analysis; Fourier transformations; Analise matematica; Fourier analysis; Electronic books; Electronic books
• Languages: English
• ISBNs: 9781351448871; 1351448870
• Related ISBNs: 9780849371639; 0849371635
• Notes: Note: Includes bibliographical references and index.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.