This is the first book dedicated to covering the basic elements of the Gibbs phenomenon as it appears in various applications where functions with jump discontinuities are represented. It is presented with detailed analysis and illustrations combined with historical information. The author covers the appearance of the Gibbs phenomenon in Fourier analysis, orthogonal expansions, integral transforms, splines and wavelet approximations. Methods of reducing, or filtering out, such phenomena that cover all the above function representations are also addressed. The book includes a thorough bibliography of some 350 references. Audience: The work is intended as an introduction for engineering and scientific practitioners in the fields where this phenomenon may appear in their use of various function representations. It may also be used by qualified students.
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In this chapter we present, primarily, the analysis of the Gibbs phenomenon in the Fourier series approximation of (periodic) functions with jump discontinuities. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Additional References, Springer-Verlag Inc, Clarendon Press, Courtesy of Oxford University Press, Fast Fourier Transform New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In this chapter we present, primarily, the analysis of the Gibbs phenomenon in the Fourier series approximation of (periodic) functions with jump discontinuities. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Additional References, Springer-Verlag Inc, Clarendon Press, Courtesy of Oxford University Press, Fast Fourier Transform New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 69
books:
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3
books
cite this book:
- Wavelets, Fractals, and Fourier Transforms (Institute of Mathematics and Its Applications Conference Ser) by M. Farge in Back Matter (1), and Back Matter (2)
- Advanced Topics in Shannon Sampling and Interpolation Theory (Springer Texts in Electrical Engineering) by Robert J.II Marks in Back Matter (1), and Back Matter (2)
- Numerical Analysis (College work out series) by Turner, Peter R. by Peter R Turner in Back Matter
- Global Behavior of Nonlinear Difference Equations of Higher Order with Applications (Mathematics and Its Applications (closed)) by V.L. Kocic in Back Matter
- Oscillation Theory of Two-Term Differential Equations (Mathematics and Its Applications (closed)) by Uri Elias in Back Matter
See all 69 books this book cites
- Introduction to Integral Equations with Applications by A. Jerri in Back Matter
- Boolean Valued Analysis (Mathematics and Its Applications) by A.G. Kusraev in Back Matter
- Hilbert Spaces, Wavelets, Generalised Functions and Modern Quantum Mechanics (Mathematics and Its Applications (closed)) by W.-H. Steeb in Back Matter
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