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# Fourier transform

| 🗖 nosplit | ↑ parent "Fourier series" | words: 186 | descendant words: 321 | descendants: 3
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Continuous version of the Fourier series.
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Can be used to represent functions that are not periodic: https://math.stackexchange.com/questions/221137/what-is-the-difference-between-fourier-series-and-fourier-transformation while the Fourier series is only for periodic functions.
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Of course, every function defined on a finite line segment (i.e. a compact space).
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Therefore, the Fourier transform can be seen as a generalization of the Fourier series that can also decompose functions defined on the entire real line.
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As a more concrete example, just like the Fourier series is how you solve a the heat equation on a line segment with Dirichlet boundary conditions as shown at: Section "Solving partial differential equations with the Fourier series", the Fourier transform is what you need to solve the problem when the domain is the entire real line.
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