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= \frac{1}{\sqrt{2\pi}} \int_{-\infty}^\infty F(\omega) e^{i\omega t}\,d\omega.</math>
This is actually the ''inverse'' continuous Fourier transform, whereas the Fourier transform expresses ''F''(ω) in terms of ''f''(''t''); the original function and its transform are sometimes called a ''transform pair''. See [[continuous Fourier transform]] for more information, including a table of transforms, discussion of the transform properties, and the various conventions. A generalization of this transform is the [[fractional Fourier transform]], by which the transform can be raised to any real "power".
The continuous transform is itself 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 (mathematics)|series]] of sinusoids:
:<math>f(x) = \sum_{n=-\infty}^{\infty} F_n \,e^{inx} ,</math>
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