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ipedia.com: Fourier transform Article (Site not responding. Last check: 2007-11-06) |
 | | The transforms are linear operators and, with proper normalization, are unitary as well (a property known as Parseval's theorem or, more generally, as the Plancherel theorem, and most generally via Pontryagin duality). |
| | The continuous transform is actually a generalization of an earlier concept, a Fourier series, which was specific to periodic (or finite-domain) functions f(x) (with period 2π), and represents these functions as a series of sinusoids: |
| | These Fourier variants can also be generalized to Fourier transforms on arbitrary locally compact abelian topological groups, which are studied in harmonic analysis; there, one transforms from a group to its dual group. |
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