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The Discrete Fourier Transform: Theory, Algorithms and Applications

4 August 2010**The Discrete Fourier Transform: Theory, Algorithms and Applications**

4 August 2010

World Scientific Publishing Company 2001 | 374 | ISBN: 9810245211 | PDF | 11 Mb

This book provides comprehensive coverage of practical Fourier analysis. It develops the concepts right from the basics and gradually guides the reader to the advanced topics. It presents the latest and practically efficient DFT algorithms, as well as the computation of discrete cosine and Walsh-Hadamard transforms. The large numbers of visual aids such as figures, flow graphs and flow charts makes the mathematical topic easy to understand. In addition, the numerous examples and the set of C-language programs (a supplement to the book) help greatly in understanding the theory and algorithms. Discrete Fourier analysis is covered first, followed by the continuous case, as the discrete case is easier to grasp and is very important in practice. This book should be useful as a text for regular or professional courses on Fourier analysis, and also as a supplementary text for courses on discrete signal processing, image processing, communications engineering and vibration analysis. ...A First Course in Fourier Analysis

27 March 2010

**David W. Kammler, "A First Course in Fourier Analysis"**

Cambridge University Press | 2008 | ISBN: 0521709792 | PDF | 864 pages | 13,8 MB

This unique book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ideas can be used to study sampling theory, PDEs, probability, diffraction, musical tones, and wavelets. The book contains an unusually complete presentation of the Fourier transform calculus. It uses concepts from calculus to present an elementary theory of generalized functions. FT calculus and generalized functions are then used to study the wave equation, diffusion equation, and diffraction equation. Real-world applications of Fourier analysis are described in the chapter on musical tones. A valuable reference on Fourier analysis for a variety of students and scientific professionals, including mathematicians, physicists, chemists, geologists, electrical engineers, mechanical engineers, and others.

27 March 2010

Cambridge University Press | 2008 | ISBN: 0521709792 | PDF | 864 pages | 13,8 MB

This unique book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ideas can be used to study sampling theory, PDEs, probability, diffraction, musical tones, and wavelets. The book contains an unusually complete presentation of the Fourier transform calculus. It uses concepts from calculus to present an elementary theory of generalized functions. FT calculus and generalized functions are then used to study the wave equation, diffusion equation, and diffraction equation. Real-world applications of Fourier analysis are described in the chapter on musical tones. A valuable reference on Fourier analysis for a variety of students and scientific professionals, including mathematicians, physicists, chemists, geologists, electrical engineers, mechanical engineers, and others.

A First Course in Fourier Analysis

16 February 2011

**A First Course in Fourier Analysis**

English | 2008 | 864 pages | PDF | 13.6 MB

This unique book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ideas can be used to study sampling theory, PDEs, probability, diffraction, musical tones, and wavelets. The book contains an unusually complete presentation of the Fourier transform calculus. It uses concepts from calculus to present an elementary theory of generalized functions. FT calculus and generalized functions are then used to study the wave equation, diffusion equation, and diffraction equation. Real-world applications of Fourier analysis are described in the chapter on musical tones. A valuable reference on Fourier analysis for a variety of students and scientific professionals, including mathematicians, physicists, chemists, geologists, electrical engineers, mechanical engineers, and others.

16 February 2011

English | 2008 | 864 pages | PDF | 13.6 MB

This unique book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ideas can be used to study sampling theory, PDEs, probability, diffraction, musical tones, and wavelets. The book contains an unusually complete presentation of the Fourier transform calculus. It uses concepts from calculus to present an elementary theory of generalized functions. FT calculus and generalized functions are then used to study the wave equation, diffusion equation, and diffraction equation. Real-world applications of Fourier analysis are described in the chapter on musical tones. A valuable reference on Fourier analysis for a variety of students and scientific professionals, including mathematicians, physicists, chemists, geologists, electrical engineers, mechanical engineers, and others.

Interval and Discrete Transforms with Application and Error Analysis (Pure and Applied Mathematics)

10 October 2010

**Interval and Discrete Transforms with Application and Error Analysis (Pure and Applied Mathematics)**

This reference/text desribes the basic elements of the integral, finite, and discrete transforms - emphasizing their use for solving boundary and initial value problems as well as facilitating the representations of signals and systems.;Proceeding to the final solution in the same setting of Fourier analysis without interruption, Integral and Discrete Transforms with Applications and Error Analysis: presents the background of the FFT and explains how to choose the appropriate transform for solving a boundary value problem; discusses modelling of the basic partial differential equations, as well as the solutions in terms of the main special functions; considers the Laplace, Fourier, and Hankel transforms and their variations, offering a more logical continuation of the operational method; covers integral, discrete, and finite transforms and trigonometric Fourier and general orthogonal series expansion, providing an application to signal analysis and boundary-value problems; and examines the practical approximation of computing the resulting Fourier series or integral representation of the final solution and treats the errors incurred.;Containing many detailed examples and numerous end-of-chapter exercises of varying difficulty for each section with answers, Integral and Discrete Transforms with Applications and Error Analysis is a thorough reference for analysts; industrial and applied mathematicians; electrical, electronics, and other engineers; and physicists and an informative text for upper-level undergraduate and graduate students in these disciplines. ...

10 October 2010

CRC Press 1992 | 825 | ISBN: 0824782526 | PDF | 17 Mb

This reference/text desribes the basic elements of the integral, finite, and discrete transforms - emphasizing their use for solving boundary and initial value problems as well as facilitating the representations of signals and systems.;Proceeding to the final solution in the same setting of Fourier analysis without interruption, Integral and Discrete Transforms with Applications and Error Analysis: presents the background of the FFT and explains how to choose the appropriate transform for solving a boundary value problem; discusses modelling of the basic partial differential equations, as well as the solutions in terms of the main special functions; considers the Laplace, Fourier, and Hankel transforms and their variations, offering a more logical continuation of the operational method; covers integral, discrete, and finite transforms and trigonometric Fourier and general orthogonal series expansion, providing an application to signal analysis and boundary-value problems; and examines the practical approximation of computing the resulting Fourier series or integral representation of the final solution and treats the errors incurred.;Containing many detailed examples and numerous end-of-chapter exercises of varying difficulty for each section with answers, Integral and Discrete Transforms with Applications and Error Analysis is a thorough reference for analysts; industrial and applied mathematicians; electrical, electronics, and other engineers; and physicists and an informative text for upper-level undergraduate and graduate students in these disciplines. ...

Fourier Analysis in Probability Theory

30 September 2011

**Fourier Analysis in Probability Theory**

The methods and results of Fourier analysis have been effectively utilized in the analytic theory of probability. Moreover, simple analogs of some results in Fourier analysis have actually given rise to many significant results in probability theory. However, one often hears the complaint that in seeking pertinent results from Fourier analysis which are needed in the study of probability, the standard texts give a presentation that is, in most cases, too detailed to be useful. The author's primary purpose, therefore, was to present useful results from the theories of Fourier series, Fourier transforms, Laplace transforms, and other related topics, in a fashion that will enable the student easily to find the results and proofs he desires before he proceeds to more detailed investigations. To further this purpose, particular attention has been given to clarification of the interactions and analogies among these theories. ...

30 September 2011

1972 | 668 | ISBN: 0124036503 | DJVU | 4 Mb

The methods and results of Fourier analysis have been effectively utilized in the analytic theory of probability. Moreover, simple analogs of some results in Fourier analysis have actually given rise to many significant results in probability theory. However, one often hears the complaint that in seeking pertinent results from Fourier analysis which are needed in the study of probability, the standard texts give a presentation that is, in most cases, too detailed to be useful. The author's primary purpose, therefore, was to present useful results from the theories of Fourier series, Fourier transforms, Laplace transforms, and other related topics, in a fashion that will enable the student easily to find the results and proofs he desires before he proceeds to more detailed investigations. To further this purpose, particular attention has been given to clarification of the interactions and analogies among these theories. ...

Discrete Time Signal Processing

12 June 2010

**Discrete-Time Signal Processing**

Publisher: Prentice Hall 1999 | 870 Pages | ISBN: 0137549202 | PDF | 8 MB

This is the standard text for introductory advanced undergraduate and first-year graduate level courses in signal processing. The text gives a coherent and exhaustive treatment of discrete-time linear systems, sampling, filtering and filter design, reconstruction, the discrete-time Fourier and z-transforms, Fourier analysis of signals, the fast Fourier transform, and spectral estimation. The author develops the basic theory independently for each of the transform domains and provides illustrative examples throughout to aid the reader.

12 June 2010

Publisher: Prentice Hall 1999 | 870 Pages | ISBN: 0137549202 | PDF | 8 MB

This is the standard text for introductory advanced undergraduate and first-year graduate level courses in signal processing. The text gives a coherent and exhaustive treatment of discrete-time linear systems, sampling, filtering and filter design, reconstruction, the discrete-time Fourier and z-transforms, Fourier analysis of signals, the fast Fourier transform, and spectral estimation. The author develops the basic theory independently for each of the transform domains and provides illustrative examples throughout to aid the reader.

Discrete Choice Modelling and Air Travel Demand

5 January 2011

**Discrete Choice Modelling and Air Travel Demand**

In recent years, airline practitioners and academics have started to explore new ways to model airline passenger demand using discrete choice methods. This book provides an introduction to discrete choice models and uses extensive examples to illustrate how these models have been used in the airline industry. These examples span network planning, revenue management, and pricing applications. Numerous examples of fundamental logit modeling concepts are covered in the text, including probability calculations, value of time calculations, elasticity calculations, nested and non-nested likelihood ratio tests, etc. The core chapters of the book are written at a level appropriate for airline practitioners and graduate students with operations research or travel demand modeling backgrounds. Given the majority of discrete choice modeling advancements in transportation evolved from urban travel demand studies, the introduction first orients readers from different backgrounds by highlighting major distinctions between aviation and urban travel demand studies. This is followed by an in-depth treatment of two of the most common discrete choice models, namely the multinomial and nested logit models. More advanced discrete choice models are covered, including mixed logit models and generalized extreme value models that belong to the generalized nested logit class and/or the network generalized extreme value class. An emphasis is placed on highlighting open research questions associated with these models that will be of particular interest to operations research students. Practical modeling issues related to data and estimation software are also addressed, and an extensive modeling exercise focused on the interpretation and application of statistical tests used to guide the selection of a preferred model specification is included; the modeling exercise uses itinerary choice data from a major airline. The text concludes with a discussion of on-going customer modeling research in aviation. "Discrete Choice Modelling and Air Travel Demand" is enriched by a comprehensive set of technical appendices that will be of particular interest to advanced students of discrete choice modeling theory. The appendices also include detailed proofs of the multinomial and nested logit models and derivations of measures used to represent competition among alternatives, namely correlation, direct-elasticities, and cross-elasticities. ...

5 January 2011

2010 | 272 | ISBN: 0754670511 | PDF | 12 Mb

In recent years, airline practitioners and academics have started to explore new ways to model airline passenger demand using discrete choice methods. This book provides an introduction to discrete choice models and uses extensive examples to illustrate how these models have been used in the airline industry. These examples span network planning, revenue management, and pricing applications. Numerous examples of fundamental logit modeling concepts are covered in the text, including probability calculations, value of time calculations, elasticity calculations, nested and non-nested likelihood ratio tests, etc. The core chapters of the book are written at a level appropriate for airline practitioners and graduate students with operations research or travel demand modeling backgrounds. Given the majority of discrete choice modeling advancements in transportation evolved from urban travel demand studies, the introduction first orients readers from different backgrounds by highlighting major distinctions between aviation and urban travel demand studies. This is followed by an in-depth treatment of two of the most common discrete choice models, namely the multinomial and nested logit models. More advanced discrete choice models are covered, including mixed logit models and generalized extreme value models that belong to the generalized nested logit class and/or the network generalized extreme value class. An emphasis is placed on highlighting open research questions associated with these models that will be of particular interest to operations research students. Practical modeling issues related to data and estimation software are also addressed, and an extensive modeling exercise focused on the interpretation and application of statistical tests used to guide the selection of a preferred model specification is included; the modeling exercise uses itinerary choice data from a major airline. The text concludes with a discussion of on-going customer modeling research in aviation. "Discrete Choice Modelling and Air Travel Demand" is enriched by a comprehensive set of technical appendices that will be of particular interest to advanced students of discrete choice modeling theory. The appendices also include detailed proofs of the multinomial and nested logit models and derivations of measures used to represent competition among alternatives, namely correlation, direct-elasticities, and cross-elasticities. ...

Fourier Series and Integrals

12 December 2010

**Fourier Series and Integrals**

DJVUThe ideas of Fourier have made their way into every branch of mathematics and mathematical physics, from the theory of numbers to quantum mechanics. Fourier Series and Integrals focuses on the extraordinary power and flexibility of Fourier's basic series and integrals and on the astonishing variety of applications in which it is the chief tool. It presents a mathematical account of Fourier ideas on the circle and the line, on finite commutative groups, and on a few important noncommutative groups. A wide variety of exercises are placed in nearly every section as an integral part of the text. ...

12 December 2010

1972 | 295 | ISBN: 0122264509 | PDF | 4 Mb

DJVUThe ideas of Fourier have made their way into every branch of mathematics and mathematical physics, from the theory of numbers to quantum mechanics. Fourier Series and Integrals focuses on the extraordinary power and flexibility of Fourier's basic series and integrals and on the astonishing variety of applications in which it is the chief tool. It presents a mathematical account of Fourier ideas on the circle and the line, on finite commutative groups, and on a few important noncommutative groups. A wide variety of exercises are placed in nearly every section as an integral part of the text. ...

Discrete Calculus: Applied Analysis on Graphs for Computational Science

27 July 2010

**Discrete Calculus: Applied Analysis on Graphs for Computational Science**

Publisher: Springer | 2010 | PDF | 377 pages | ISBN: 1849962898 | 8.2Mb

The field of discrete calculus, also known as “discrete exterior calculus”, focuses on finding a proper set of definitions and differential operators that make it possible to operate the machinery of multivariate calculus on a finite, discrete space. In contrast to traditional goals of finding an accurate discretization of conventional multivariate calculus, discrete calculus establishes a separate, equivalent calculus that operates purely in the discrete space without any reference to an underlying continuous process. This unique text brings together into a single framework current research in the three areas of discrete calculus, complex networks, and algorithmic content extraction. Although there have been a few intersections in the literature between these disciplines, they have developed largely independently of one another, yet researchers working in any one of these three areas can strongly benefit from the tools and techniques being used in the others. Many example applications from several fields of computational science are provided to demonstrate the usefulness of this framework to a broad range of problems. Readers are assumed to be familiar with the basics of vector calculus, graph theory, and linear algebra.

27 July 2010

Publisher: Springer | 2010 | PDF | 377 pages | ISBN: 1849962898 | 8.2Mb

The field of discrete calculus, also known as “discrete exterior calculus”, focuses on finding a proper set of definitions and differential operators that make it possible to operate the machinery of multivariate calculus on a finite, discrete space. In contrast to traditional goals of finding an accurate discretization of conventional multivariate calculus, discrete calculus establishes a separate, equivalent calculus that operates purely in the discrete space without any reference to an underlying continuous process. This unique text brings together into a single framework current research in the three areas of discrete calculus, complex networks, and algorithmic content extraction. Although there have been a few intersections in the literature between these disciplines, they have developed largely independently of one another, yet researchers working in any one of these three areas can strongly benefit from the tools and techniques being used in the others. Many example applications from several fields of computational science are provided to demonstrate the usefulness of this framework to a broad range of problems. Readers are assumed to be familiar with the basics of vector calculus, graph theory, and linear algebra.

Fourier Transform Methods in Finance

21 March 2013

**Fourier Transform Methods in Finance by Umberto Cherubini, Giovanni Della Lunga, Sabrina Mulinacci and Pietro Rossi**

2010-02-15 | ISBN: 0470994002 | 256 pages | PDF | 2,1 MB

In recent years, Fourier transform methods have emerged as one of the major methodologies for the evaluation of derivative contracts, largely due to the need to strike a balance between the extension of existing pricing models beyond the traditional Black-Scholes setting and a need to evaluate prices consistently with the market quotes.

21 March 2013

2010-02-15 | ISBN: 0470994002 | 256 pages | PDF | 2,1 MB

In recent years, Fourier transform methods have emerged as one of the major methodologies for the evaluation of derivative contracts, largely due to the need to strike a balance between the extension of existing pricing models beyond the traditional Black-Scholes setting and a need to evaluate prices consistently with the market quotes.