Fourier Transform

Mathematics · 1822

Equation: f̂(ω) = ∫ f(t)·e^(−iωt) dt
Field: Mathematics
Named After: Joseph Fourier
Year: 1822

Symbols

f(t) a signal in time (or space) · f̂(ω) the same signal as a recipe of pure frequencies · e^(−iωt) the probe oscillation · the transform runs both ways

Significance

Any signal — a chord, a heartbeat, an image — is a sum of pure waves, and this integral finds the recipe. Fourier invented it to solve heat flow; today it is spectroscopy, MRI, JPEG and MP3, and the reason position and momentum can't both be sharp: Heisenberg's uncertainty is a Fourier fact wearing physics clothes.

Heisenberg Uncertainty Principle Diffraction Grating Equation Wave Equation Shannon–Hartley Channel Capacity Euler's Identity Heat Equation Airy Diffraction Pattern