# Edit Create an Image Page: Fourier Transform

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 Image Title*: Upload a Math Image A Fourier Transform changes a function's domain from time to frequency Given a function in the time domain, $f(x)$, a Fourier Transform produces a function $F(u)$ where u is a frequency and $F(u)$returns a complex number whose real component gives the amplitude of the sine wave at frequency $u$ and whose imaginary component gives the phase. The equation for the Fourier Transform where f(t) is a discrete function with domain $[0,N)$ is $F(u)=\sum_{t=0}^{N-1}f(t)e^{\frac{-2 \pi i u t}{N}}=\sum_{t=0}^{N-1}f(t)\left(\cos\left(\frac{-2 \pi u t}{N}\right)+i \sin\left(\frac{-2 \pi u t}{N}\right)\right)$ ==Demonstration== |Field=Algebra |ToDo=A more mathematical explanation and proof of the formula. |Make the applet work |Pre-K=No |Elementary=No |MiddleSchool=No |HighSchool=No |InProgress=Yes Algebra Analysis Calculus Dynamic Systems Fractals Geometry Graph Theory Number Theory Polyhedra Probability Topology Other None Algebra Analysis Calculus Dynamic Systems Fractals Geometry Graph Theory Number Theory Polyhedra Probability Topology Other None Algebra Analysis Calculus Dynamic Systems Fractals Geometry Graph Theory Number Theory Polyhedra Probability Topology Other Yes, it is.