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Modulation Theorem

The important property of Fourier Transforms that ${\mathcal F}[cos(2\pi k_0x)f(x)]$ can be expressed in terms of ${\mathcal F}[f(x)] = F(k)$ as follows,

{\mathcal F}[cos(2\pi k_0x)f(x)] = {\textstyle{1\over 2}}[F(k-k_0)+F(k+k_0)].

See also Fourier Transform


Bracewell, R. ``Modulation Theorem.'' The Fourier Transform and Its Applications. New York: McGraw-Hill, p. 108, 1965.

© 1996-9 Eric W. Weisstein