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

References

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