• Preface--
• 1. Introduction. A Bit of History-- An Application-- Problems--
• 2. The Discrete Fourier Transform (DFT). Introduction-- DFT Approximation to the Fourier Transform-- The DFT-IDFT pair-- DFT Approximations to Fourier Series Coefficients-- The DFT from Trigonometric Approximation-- Transforming a Spike Train-- Limiting Forms of the DFT-IDFT Pair-- Problems--
• 3. Properties of the DFT. Alternate Forms for the DFT-- Basic Properties of the DFT-- Other Properties of the DFT-- A Few Practical Considerations-- Analytical DFTs-- Problems--
• 4. Symmetric DFTs. Introduction-- Real sequences and the Real DFT (RDFT)-- Even Sequences and the Discrete Cosine Transform (DST)-- Odd Sequences and the Discrete Sine Transform (DST)-- Computing Symmetric DFTs-- Notes-- Problems--
• 5. Multi-dimensional DFTs. Introduction-- Two-dimensional DFTs-- Geometry of Two-Dimensional Modes-- Computing Multi-Dimensional DFTs-- Symmetric DFTs in Two Dimensions-- Problems--
• 6. Errors in the DFT. Introduction-- Periodic, Band-limited Input-- Periodic, Non-band-limited Input-- Replication and the Poisson Summation Formula-- Input with Compact Support-- General Band-Limited Functions-- General Input-- Errors in the Inverse DFT-- DFT Interpolation - Mean Square Error-- Notes and References-- Problems--
• 7. A Few Applications of the DFT. Difference Equations - Boundary Value Problems-- Digital Filtering of Signals-- FK Migration of Seismic Data-- Image Reconstruction from Projections-- Problems--
• 8. Related Transforms. Introduction-- The Laplace Transform-- The z- Transform-- The Chebyshev Transform-- Orthogonal Polynomial Transforms-- The Discrete Hartley Transform (DHT)-- Problems--
• 9. Quadrature and the DFT. Introduction-- The DFT and the Trapezoid Rule-- Higher Order Quadrature Rules-- Problems--
• 10. The Fast Fourier Transform (FFT). Introduction-- Splitting Methods-- Index Expansions (One ---> Multi-dimensional)-- Matrix Factorizations-- Prime Factor and Convolution Methods-- FFT Performance-- Notes-- Problems-- Glossary of (Frequently and Consistently Used) Notations-- References.
• (source: Nielsen Book Data)

Just as a prism separates white light into its component bands of colored light, so the discrete Fourier transform (DFT) is used to separate a signal into its constituent frequencies. Just as a pair of sunglasses reduces the glare of white light, permitting only the softer green light to pass, so the DFT may be used to modify a signal to achieve a desired effect. In fact, by analyzing the component frequencies of a signal or any system, the DFT can be used in an astonishing variety of problems. Among the applications of the DFT are digital signal processing, oil and gas exploration, medical imaging, aircraft and spacecraft guidance, and the solution of differential equations of physics and engineering. The DFT: An Owner's Manual for the Discrete Fourier Transform explores both the practical and theoretical aspects of the DFT, one of the most widely used tools in science and engineering.
(source: Nielsen Book Data)

• 1. Signals and Systems.
• 2. The Fourier Transform.
• 3. Fourier Inversion.
• 4. Basic Properties.
• 5. Generalized Transforms and Functions.
• 6. Convolution and Correlation.
• 7. Two Dimensional Fourier Analysis.
• 8. Memoryless Nonlinearities. A: Fourier Transform Tables.
• (source: Nielsen Book Data)

The Fourier transform is one of the most important mathematical tools in a wide variety of science and engineering fields. Its application - as Fourier analysis or harmonic analysis - provides useful decompositions of signals into fundamental ('primitive') components, giving shortcuts in the computation of complicated sums and integrals, and often revealing hidden structure in the data. "Fourier Transforms: An Introduction for Engineers" develops the basic definitions, properties and applications of Fourier analysis, the emphasis being on techniques for its application to linear systems, although other applications are also considered. The book will serve as both a reference text and a teaching text for a one-quarter or one-semester course covering the application of Fourier analysis to a wide variety of signals, including discrete time (or parameter), continuous time (or parameter), finite duration, and infinite duration.It highlights the common aspects in all cases considered, thereby building an intuition from simple examples that will be useful in the more complicated examples where careful proofs are not included. "Fourier Analysis: An Introduction for Engineers" is written by two scholars who are recognized throughout the world as leaders in this area, and provides a fresh look at one of the most important mathematical and directly applicable concepts in nearly all fields of science and engineering. This book is suitable for engineers, especially electrical engineers. The careful treatment of the fundamental mathematical ideas makes the book suitable in all areas where Fourier analysis finds applications.
(source: Nielsen Book Data)

• 1 Introduction 2 Groundwork 3 Convolution 4 Notation for Some Useful Functions 5 The Impulse Symbol 6 The Basic Theorems 7 Obtaining Transforms 8 The Two Domains 9 Waveforms, Spectra, Filters and Linearity 10 Sampling and Series 11 The Discrete Fourier Transform and the FFT 12 The Discrete Hartley Transform 13 Relatives of the Fourier Transform 14 The Laplace Transform 15 Antennas and Optics 16 Applications in Statistics 17 Random Waveforms and Noise 18 Heat Conduction and Diffusion 19 Dynamic Power Spectra 20 Tables of sinc x, sinc2x, and exp(-71x2) 21 Solutions to Selected Problems 22 Pictorial Dictionary of Fourier Transforms 23 The Life of Joseph Fourier.
• (source: Nielsen Book Data)

This text is designed for use in a senior undergraduate or graduate level course in Fourier Transforms. This text differs from many other Fourier transform books in its emphasis on applications. Bracewell applies mathematical concepts to the physical world throughout this text, equipping students to think about the world and physics in terms of transforms. The pedagogy in this classic text is excellent. The author has included such tools as the pictorial dictionary of transforms and bibliographic references. In addition, there are many excellent problems throughout this book, which are more than mathematical exercises, often requiring students to think in terms of specific situations or asking for educated opinions. To aid students further, discussions of many of the problems can be found at the end of the book.
(source: Nielsen Book Data)

• Fourier series Fourier transform Convolution Distributions and their Fourier transforms $\delta$ hard at work Sampling and interpolation Discrete Fourier transform Linear time-invariant systems $n$-Dimensional Fourier transform A list of mathematical topics that are fair game Complex numbers and complex exponentials Geometric sums Index.
• (source: Nielsen Book Data)

This book is derived from lecture notes for a course on Fourier analysis for engineering and science students at the advanced undergraduate or beginning graduate level. Beyond teaching specific topics and techniques--all of which are important in many areas of engineering and science--the author's goal is to help engineering and science students cultivate more advanced mathematical know-how and increase confidence in learning and using mathematics, as well as appreciate the coherence of the subject. He promises the readers a little magic on every page. The section headings are all recognizable to mathematicians, but the arrangement and emphasis are directed toward students from other disciplines. The material also serves as a foundation for advanced courses in signal processing and imaging. There are over 200 problems, many of which are oriented to applications, and a number use standard software. An unusual feature for courses meant for engineers is a more detailed and accessible treatment of distributions and the generalized Fourier transform. There is also more coverage of higher-dimensional phenomena than is found in most books at this level.
(source: Nielsen Book Data)