Abstract
This chapter is both an introduction to the book as a whole, and to the concepts underlying the finite Fourier transform. Our topics begin with the classical Fourier transform, which underlies most of our application concepts and is the conceptual basis for most applications of the FFT. We proceed by showing the relationship between Fourier series and the Fourier transform and briefly exploring that technology. We conclude by showing the relationship between the discrete Fourier transform (DFT) and the Fourier series, and exploring the nature of this transform. Thus we show the relationship between the Fourier transform and Fourier series with the DFT, the algorithm implemented by the FFT, and show some of the similarities, differences, and properties of each.
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© 2004 Springer Science+Business Media New York
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Beard, J.K. (2004). The Fourier Transform. In: Beard, J.K. (eds) The FFT in the 21st Century. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6734-6_1
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DOI: https://doi.org/10.1007/978-1-4757-6734-6_1
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-5410-7
Online ISBN: 978-1-4757-6734-6
eBook Packages: Springer Book Archive