Abstract
Chapter 2 shows how to compute the Discrete Fourier Transform using a Fast Fourier Transform (FFT) algorithm. When the data to be transformed are real, the transforms are sped up by about a factor of two by exploiting symmetries in the data and the coefficients. The chapter ends with how to approximate the derivatives of periodic functions, thus presenting the fundamental algorithms that are needed to solve partial differential equations with periodic boundary conditions.
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Keywords
- Fast Fourier Transform
- Discrete Fourier Transform
- Complex Sequence
- Real Sequence
- Fast Fourier Transform Algorithm
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© 2009 Springer Science + Business Media B.V.
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Kopriva, D.A. (2009). Algorithms for Periodic Functions. In: Implementing Spectral Methods for Partial Differential Equations. Scientific Computation. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2261-5_2
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DOI: https://doi.org/10.1007/978-90-481-2261-5_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-2260-8
Online ISBN: 978-90-481-2261-5
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