## Faster Fourier TransformsJanuary 23, 2012 Butterflies make multiple appearances in science and technology. There is, of course the flying insect of the order, Lepidoptera. Surprisingly, "Lepidoptera" and "Coleoptera" are part of the dialog of a Jerry Lewis movie, Three on a Couch (1966, Jerry Lewis, Director). Rutherford, an archetypal nerd and one of Lewis' four characters in this movie, lectures one of the female leads on their characteristics.[1] The engineers and experimentalists among my readership will be familiar with the butterfly valve. I worked for a time on high temperature face seals for such valves in aerospace applications with the objective of replacing the existing material, chromium. There's also the sunspot butterfly diagram that demonstrates the periodicity of sunspots. The most famous allusion to butterflies in science is the butterfly effect, the idea that nonlinear systems can be quite sensitive to initial conditions. A small change has the possibility of producing a large change at a later time. mathematical meteorologist, Edward Lorenz, who discovered this effect in weather simulations, described it in terms of a butterfly's flapping its wings causing a hurricane weeks later. Break out the bug spray!
^{2}) for the regular transform, where k is the number of non-zero Fourier coefficients and N is the number of data points.
## References:- Three on a Couch (1966, Jerry Lewis, Director) on the Internet Movie Database.
- James W. Cooley and John W. Tukey, "An algorithm for the machine calculation of complex Fourier series," Math. Comp., vol. 19 (1965), pp. 297-301. A PDF file is available, here.
- Larry Hardesty, "Explained: The Discrete Fourier Transform," MIT Press Release, November 25, 2009.
- Larry Hardesty, "The faster-than-fast Fourier transform," MIT Press Release, January 18, 2012.
- Haitham Hassanieh, Piotr Indyk, Dina Katabi and Eric Price, "Nearly Optimal Sparse Fourier Transform," arXiv Preprint Server, January 12, 2012.
Linked Keywords: Butterfly; science; technology; insect; order; Lepidoptera; Coleoptera; Jerry Lewis; Three on a Couch; nerd; engineer; experimentalist; butterfly valve; temperature; face seal; aerospace; chromium; sunspot butterfly diagram; sunspot; allusion; butterfly effect; nonlinear systems; mathematical; meteorologist; Edward Lorenz; weather simulation; hurricane; German; nomenclature; Harald Süpfle; Wikimedia Commons; electrical engineer; Cooley–Tukey algorithm; fast Fourier transform; butterfly diagram; data flow; James Cooley; John Tukey; Carl Friedrich Gauss; transform; Joseph Fourier; heat; signal; time domain; frequency domain; filter; noise; data compression; free and open source; FOSS; Audacity; histogram; computer scientist; Massachusetts Institute of Technology; MIT; algorithm; image compression; Dina Katabi; Piotr Indyk; Haitham Hassanieh; Eric Price; ACM-SIAM Symposium on Discrete Algorithms; Kyoto, Japan; Sparse Fast Fourier Transform Group; frequency; natural; music; solo instrument; Nick Michael; arXiv; derivative; Three on a Couch (1966, Jerry Lewis, Director). |
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