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Modulation Theorem


The important property of Fourier transforms that F_x[cos(2pik_0x)f(x)](k) can be expressed in terms of F[f(x)]=F(k) as follows,

 F_x[cos(2pik_0x)f(x)](k)=1/2[F(k-k_0)+F(k+k_0)].

See also

Fourier Transform

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References

Bracewell, R. "Modulation Theorem." The Fourier Transform and Its Applications, 3rd ed. New York: McGraw-Hill, p. 108, 1999.

Referenced on Wolfram|Alpha

Modulation Theorem

Cite this as:

Weisstein, Eric W. "Modulation Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ModulationTheorem.html

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