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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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