Introduction to Frequency Analysis: The Fourier Transformation

Sueur, Jérôme

doi:10.1007/978-3-319-77647-7_9

Jérôme Sueur²

Part of the book series: Use R! ((USE R))

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Abstract

The Fourier transformation is a key mathematical tool that connects the time and frequency domains such that sound can be parametrized in terms of frequency. The theory of the different Fourier transforms, including the inverse transform, is presented to facilitate the reading of the following chapters. Each mathematical equation is translated into R so that the basic principles can be understood and unmystified. This discovery of the Fourier transformation is accompanied with the presentation of the frequency spectrum, the phase spectrum, the different frequency scales, the Fourier window shapes, and the cepstrum.

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Notes

1.
For a complete description of the Fourier analysis, see Hartmann (1998, Chapters 5 and 8) and Das (2012, Chapters 2 and 3).
2.
The wavelet transforms are treated in other books, such as Nason (2008) that is accompanied by the package wavethresh, Percival and Walden (2000) by the package wmtsa, and Gençay et al. (2001) by the package waveslim.
3.
http://htk.eng.cam.ac.uk/
4.
See Oppenheim and Schafer (2004) for a brilliant story of the cepstrum.

References

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Muséum National d’Histoire naturelle, Paris, France
Jérôme Sueur

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Sueur, J. (2018). Introduction to Frequency Analysis: The Fourier Transformation. In: Sound Analysis and Synthesis with R. Use R!. Springer, Cham. https://doi.org/10.1007/978-3-319-77647-7_9

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DOI: https://doi.org/10.1007/978-3-319-77647-7_9
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-77645-3
Online ISBN: 978-3-319-77647-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)

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