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Transformations of Functions and Signals

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Computational Methods in Physics

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Abstract

The Fourier transformation \(\mathcal{F}\) of the function f on the real axis is defined as \(F(\omega ) = \mathcal{F}[f](\omega ) = \int _{-\infty }^\infty f(x)\, \mathrm {e}^{-\mathrm {i}\omega x } \, \mathrm {d}x \>. \) The sufficient conditions for the existence of F are that f is absolutely integrable, i.e. \(\int _{-\infty }^\infty |f(x)| \, \mathrm {d}x < \infty \), and that f is piecewise continuous or has a finite number of discontinuities.

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia

    Simon Širca & Martin Horvat

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  1. Simon Širca
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  2. Martin Horvat
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Correspondence to Simon Širca .

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Širca, S., Horvat, M. (2018). Transformations of Functions and Signals. In: Computational Methods in Physics. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-78619-3_4

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