Category:Definitions/Fourier Transforms
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This category contains definitions related to Fourier Transforms.
Related results can be found in Category:Fourier Transforms.
The Fourier transform of a Lebesgue integrable function $f: \R^N \to \C$ is the function $\map \FF f: \R^N \to \C$ given by:
- $\ds \map {\map \FF f} {\mathbf s} := \int_{\R^N} \map f {\mathbf x} e^{-2 \pi i \mathbf x \cdot \mathbf s} \rd \mathbf x$
for $\mathbf s \in \R^N$.
Here, the product $\mathbf x \cdot \mathbf s$ in the exponential is the dot product of the vectors $\mathbf x$ and $\mathbf s$.
In this context $\map \FF f$ is to be considered the operator.
Subcategories
This category has the following 2 subcategories, out of 2 total.
D
F
Pages in category "Definitions/Fourier Transforms"
The following 15 pages are in this category, out of 15 total.
F
- Definition:Fast Fourier Transform
- Definition:Fourier Transform
- Definition:Fourier Transform of Real Function
- Definition:Fourier Transform of Tempered Distribution
- Definition:Fourier Transform/Also defined as
- Definition:Fourier Transform/Also denoted as
- Definition:Fourier Transform/Real Function
- Definition:Fourier Transform/Real Function/Also known as
- Definition:Fourier Transform/Real Function/Formulation 1
- Definition:Fourier Transform/Real Function/Formulation 2
- Definition:Fourier Transform/Real Function/Formulation 3