Fourier analysis
E173
Fourier analysis is a mathematical method for decomposing functions or signals into sums of sinusoidal components, widely used in fields such as signal processing, physics, and engineering.
Aliases (7)
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
area of harmonic analysis
→
branch of mathematics → mathematical method → |
| application |
MRI reconstruction
→
audio signal processing → crystallography → data compression → heat equation → image reconstruction → medical imaging → optics → radar signal processing → signal filtering → solution of differential equations → spectral analysis → vibration analysis → wave equation → |
| basedOn |
representation of functions as sums of sinusoids
→
superposition principle → |
| field |
acoustics
→
communications engineering → control theory → electrical engineering → image processing → mathematics → partial differential equations → physics → quantum mechanics → signal processing → |
| goal |
analyze frequency content of signals
→
decompose functions into sinusoidal components → |
| historicalDevelopment |
19th century
→
|
| historicalFigure |
Jean-Baptiste Joseph Fourier
→
|
| namedAfter |
Joseph Fourier
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|
| relatedTo |
Laplace transform
→
distribution theory → harmonic analysis → time–frequency analysis → wavelet analysis → |
| usesConcept |
Fourier series
→
Fourier transform → Hilbert spaces → L2 spaces → convolution → discrete Fourier transform → fast Fourier transform → frequency domain → inner product spaces → orthogonality of functions → time domain → |