Researched
Fourier Analysis
Fourier shows (1822) that any signal can be built from sine waves, the working language of heat, sound, light and data.
Open in the interactive tree →Joseph Fourier presented his study of heat flow in 1807 and published it in 1822; it showed that even jagged curves can be written as sums of smooth sine waves. Frequency analysis became a standard tool in acoustics, optics, quantum physics and signal processing, and the fast algorithm of Cooley and Tukey (1965) made it cheap on computers. Radio engineering, CT and MRI scanners and X-ray crystallography all depend on it.
Prerequisites
- Calculus (Analysis)1684
- Partial Differential Equations1747Fourier created his series to solve the heat equation
Unlocks
- Set Theory & Formal Logic1874Cantor was led to sets by questions on the convergence of Fourier series
- Fast Fourier Transform1965
- CT and MRI scanning1971Scanners reconstruct images from raw signals with Fourier transforms