Fourier Transform
A mathematical transform that decomposes a function into its constituent frequencies.
Also: FFT · spectral transform
Definition
The Fourier Transform is a mathematical operation that transforms a function of time (or space) into a function of frequency, decomposing it into its constituent sinusoidal components. It reveals the frequency spectrum of a signal and is invertible, allowing reconstruction of the original signal. The Fast Fourier Transform (FFT) algorithm makes it computationally efficient, and it is indispensable in signal processing, image analysis, and solving differential equations.
Example
“Audio engineers use the Fourier Transform to analyze a music recording, visualizing it as a frequency spectrum that shows which pitches are present and at what volumes, enabling precise equalization and mastering.”
Synonyms
- frequency transform
- spectral analysis
- harmonic analysis
Antonyms / Opposites
- inverse Fourier transform
Images
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Related Terms
- Signal Processing
- Differential Equation
- Wavelength
- Spectrum Analysis