ℱ{f}(ξ) = ∫ f(x) e^{-2πiξx} dx. Continuous analog of Fourier series; moves between position/time and frequency domains. Invertible on L¹ ∩ L², Plancherel isometry on L². Bridge to quantum mechanics (momentum representation) and signal…
Fourier transform
Related concepts
- Riemann integral
- Complex numbers (ℂ)
- Fast Fourier transform (FFT)
- Lp space
- Schwartz space 𝒮(ℝ^n)
- Laplace transform
- Laplace transform
- Hausdorff-Young inequality
- Young's convolution inequality
- Strichartz estimates
- Fast Fourier transform
- Spectral method
- Fredholm alternative: compact K implies finite-dim eigenspace or unique solve
- Heisenberg uncertainty principle
- Dispersion relation
- Fraunhofer diffraction
- Viscoelasticity
- Distribution theory (Schwartz)
- Integral transforms in physics
- NMR spectroscopy