Abstract
We introduce the discrete Fourier transform and give algorithms for its fast computation. Implementations and optimization considerations for complex and real-valued transforms are given. The fast Fourier transforms are the basis of the algorithms for fast convolution described in chapter 22.These are in turn the core of the fast high precision multiplication routines treated in chapter 28.The number theoretic transforms are treated in chapter26. Algorithms for Fourier transforms based on fast convolution like Bluestein's algorithm and Rader's algorithm are given in chapter 22.
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© 2011 Springer Berlin Heidelberg
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Arndt, J. (2011). The Fourier transform. In: Matters Computational. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14764-7_21
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DOI: https://doi.org/10.1007/978-3-642-14764-7_21
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Publisher Name: Springer, Berlin, Heidelberg
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Online ISBN: 978-3-642-14764-7
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