Fourier Transform
Symbol
ℱ
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
-
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}