Fourier Transform
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Definition
The Fourier transform decomposes a function of time into its constituent frequencies.
Usage
Used in signal processing, image analysis, and solving partial differential equations.
Examples
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Continuous Fourier Transform
\hat{f}(\xi) = \int_{-\infty}^{\infty} f(x)e^{-2\pi i x \xi} dx -
Discrete Fourier Transform
X_k = \sum_{n=0}^{N-1} x_n e^{-\frac{2\pi i}{N}kn}