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Fourier Transforms
(Math | Advanced | Transforms | Fourier)

Fourier Transform

Definition of Fourier Transform
f(x) = 1/(2) g(t) e^(i tx) dt
Inverse Identity of Fourier Transform
g(x) = 1/(2) f(t) e^(-i TX) DT

Fourier Sine and Cosine Transforms

Definitions of the Transforms
f(x) = (2/) g(x) cos(xt) DT (Cosine Transform)
f(x) = (2/) g(x) sin(XT) DT (Sine Transform)

Identities of the Transforms
IF f(x) is even, THEN FourierSineTransform( FourierSineTransform(f(x)) ) = f(x)
IF f(x) is odd, THEN FourierCosineTransform( FourierCosineTransform(f(x)) ) = f(x)
Under certain restrictions of continuity.


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