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Fourier Transform--Cosine


F_x[cos(2pik_0x)](k)=int_(-infty)^inftye^(-2piikx)((e^(2piik_0x)+e^(-2piik_0x))/2)dx
(1)
=1/2int_(-infty)^infty[e^(-2pii(k-k_0)x)+e^(-2pii(k+k_0)x)]dx
(2)
=1/2[delta(k-k_0)+delta(k+k_0)],
(3)

where delta(x) is the delta function.


See also

Cosine, Fourier Transform, Fourier Transform--Sine

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References

Bracewell, R. The Fourier Transform and Its Applications, 3rd ed. New York: McGraw-Hill, pp. 79-90 and 100-101, 1999.

Cite this as:

Weisstein, Eric W. "Fourier Transform--Cosine." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FourierTransformCosine.html

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