“Know how to solve every problem that has been solved.” “What I cannot create, I do not understand.” — Richard Feynman

Any orthogonal-basis expansion (Fourier, Legendre, Chebyshev, Hermite, spherical harmonics, …) is computable by numerical integration of the weighted inner product cₙ = ⟨f, φₙ⟩_w / ⟨φₙ, φₙ⟩_w. The Fourier/FFT case is one instance among many.

Claims

Any orthogonal-basis expansion (Fourier, Legendre, Chebyshev, Hermite, spherical harmonics, …) is computable by numerical integration of the weighted inner product cₙ = ⟨f, φₙ⟩_w / ⟨φₙ, φₙ⟩_w. The Fourier/FFT case is one instance among many.

✓ supported computational 90% stub numerical-methodsspectral-methodsorthogonal-basesprojectionfourier
id: orthogonal-projection-by-numerical-integration created: 2026-05-21 ← all claims