MathLiveFourier transform
Converts a function of time into a function of angular frequency by integrating the function against a complex exponential. It is used to analyse the frequency content of signals and to solve linear differential equations.
\mathcal{F}(\omega) = \int_{-\infty}^{\infty} f(t) \, e^{-i \omega t} \, dtWhat the symbols mean
| Fourier transform of f, a function of angular frequency \omega | |
| the original function of time t | |
| time (real variable) | |
| angular frequency (real variable), in radians per unit time | |
| imaginary unit, \sqrt{-1} |
About this formula
- FieldMathematics
- TopicIntegral transforms
- LevelUniversity
- Also calledcontinuous Fourier transform, time to frequency transform, Fourier integral, transform of f(t) to frequency domain
- SourceWikidata Q6520159
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