A Discrete Fourier Transform Based on Simpson's Rule
Title | A Discrete Fourier Transform Based on Simpson's Rule PDF eBook |
Author | Dan Behlule Sibandze |
Publisher | |
Pages | 118 |
Release | 2013 |
Genre | Eigenvalues |
ISBN |
Simpson's Discrete Fourier Transform
Title | Simpson's Discrete Fourier Transform PDF eBook |
Author | Dan Sibandze |
Publisher | LAP Lambert Academic Publishing |
Pages | 76 |
Release | 2015-02-27 |
Genre | |
ISBN | 9783659342516 |
In this text we derive the Simpson Discrete Fourier Transform (SDFT) by applying numerical quadrature to approximate Fourier coefficents of periodic functions. This a an alternative transformation to the Classical Discrete Fourier Transform (DFT). A purely mathematical approach is taken to derive several properties including time reversal, even time shift, frequency shift, convolution, duality and Plancherel's theorem. Using the duality property recursively a detailed analysis of the discrete spectrum is provided. A two dimensional transform is subsequently derived and applied to encryption and watermarking in the frequency domain. The amplitude spectrum is distinctively different from that of the DFT due to the appearance of extra bright regions. Here the emphasis is on the mathematics and structure of the transform with the applications being coincidental. We envisage that this transform will find many applications in several engineering fields.
The DFT
Title | The DFT PDF eBook |
Author | William L. Briggs |
Publisher | SIAM |
Pages | 446 |
Release | 1995-01-01 |
Genre | Mathematics |
ISBN | 0898713420 |
This book explores both the practical and theoretical aspects of the Discrete Fourier Transform, one of the most widely used tools in science, engineering, and computational mathematics. Designed to be accessible to an audience with diverse interests and mathematical backgrounds, the book is written in an informal style and is supported by many examples, figures, and problems. Conceived as an "owner's" manual, this comprehensive book covers such topics as the history of the DFT, derivations and properties of the DFT, comprehensive error analysis, issues concerning the implementation of the DFT in one and several dimensions, symmetric DFTs, a sample of DFT applications, and an overview of the FFT.
Algorithmic Number Theory
Title | Algorithmic Number Theory PDF eBook |
Author | Florian Hess |
Publisher | Springer |
Pages | 609 |
Release | 2006-10-05 |
Genre | Mathematics |
ISBN | 354036076X |
This book constitutes the refereed proceedings of the 7th International Algorithmic Number Theory Symposium, ANTS 2006, held in Berlin, July 2006. The book presents 37 revised full papers together with 4 invited papers selected for inclusion. The papers are organized in topical sections on algebraic number theory, analytic and elementary number theory, lattices, curves and varieties over fields of characteristic zero, curves over finite fields and applications, and discrete logarithms.
Numerical Methods
Title | Numerical Methods PDF eBook |
Author | Germund Dahlquist |
Publisher | Courier Corporation |
Pages | 596 |
Release | 2012-04-26 |
Genre | Mathematics |
ISBN | 0486139468 |
"Substantial, detailed and rigorous . . . readers for whom the book is intended are admirably served." — MathSciNet (Mathematical Reviews on the Web), American Mathematical Society. Practical text strikes fine balance between students' requirements for theoretical treatment and needs of practitioners, with best methods for large- and small-scale computing. Prerequisites are minimal (calculus, linear algebra, and preferably some acquaintance with computer programming). Text includes many worked examples, problems, and an extensive bibliography.
Applications of Discrete and Continuous Fourier Analysis
Title | Applications of Discrete and Continuous Fourier Analysis PDF eBook |
Author | H. Joseph Weaver |
Publisher | Wiley-Interscience |
Pages | 398 |
Release | 1983-09 |
Genre | Mathematics |
ISBN |
An applications oriented, introductory text covering the concepts and properties of Fourier Analysis. Emphasizes applications to real scientific and engineering problems. Defines the Fourier series, Fourier transform, and discrete Fourier transform. Includes over 200 illustrations.
The Heston Model and Its Extensions in VBA
Title | The Heston Model and Its Extensions in VBA PDF eBook |
Author | Fabrice D. Rouah |
Publisher | John Wiley & Sons |
Pages | 359 |
Release | 2015-04-27 |
Genre | Business & Economics |
ISBN | 111900330X |
Practical options pricing for better-informed investment decisions. The Heston Model and Its Extensions in VBA is the definitive guide to options pricing using two of the derivatives industry's most powerful modeling tools—the Heston model, and VBA. Light on theory, this extremely useful reference focuses on implementation, and can help investors more efficiently—and accurately—exploit market information to better inform investment decisions. Coverage includes a description of the Heston model, with specific emphasis on equity options pricing and variance modeling, The book focuses not only on the original Heston model, but also on the many enhancements and refinements that have been applied to the model, including methods that use the Fourier transform, numerical integration schemes, simulation, methods for pricing American options, and much more. The companion website offers pricing code in VBA that resides in an extensive set of Excel spreadsheets. The Heston model is the derivatives industry's most popular stochastic volatility model for pricing equity derivatives. This book provides complete guidance toward the successful implementation of this valuable model using the industry's ubiquitous financial modeling software, giving users the understanding—and VBA code—they need to produce option prices that are more accurate, and volatility surfaces that more closely reflect market conditions. Derivatives pricing is often the hinge on which profit is made or lost in financial institutions, making accuracy of utmost importance. This book will help risk managers, traders, portfolio managers, quants, academics and other professionals better understand the Heston model and its extensions, in a writing style that is clear, concise, transparent and easy to understand. For better pricing accuracy, The Heston Model and Its Extensions in VBA is a crucial resource for producing more accurate model outputs such as prices, hedge ratios, volatilities, and graphs.