Fourier series and transform
Series y transformada de Fourier
- Date
- 1807 · confidence high
- Place
- Grenoble and Paris, France
- Credited to
- Joseph Fourier (1807 memoir; Théorie analytique de la chaleur, 1822)
- People
- 👤 Jean-Baptiste Joseph Fourier1768–1830
- Field
- Knowledge & symbols
What was discovered
Every reasonable periodic function decomposes into a sum of sines and cosines, which solves the heat equation and creates harmonic analysis. The claim forced the concepts of function, convergence and integral to be made precise.
Lagrange and Laplace objected to the rigour of the 1807 memoir, which was not published until 1822.
What it led to
- harmonic analysis
- the Lebesgue integral
- Cantor's set theory
- the fast Fourier transform
- signal processing
Built on
- vibrating string (d'Alembert, Euler, Bernoulli)
- calculus
Made possible
- Rigorous analysis: limits, continuity, epsilon-delta1817-1821
- Heat equation1822
- Measure theory and Lebesgue integral1902
- Hilbert spaces and functional analysis1906-1912
- Fast Fourier transform1965
- Magnetic resonance imaging (MRI)1973-1977
- MP3 audio compression1993
- telecommunications
- audio and image compression (MP3, JPEG)
- X-ray crystallography