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Created page with "The Fourier transform decomposes a signal (i.e. a time series) into multiple sine and cosine waves. ==Background== Suppose we have signal<math>f(x)</math>.<br> Then the Fourier transform <math>\hat{f}(\xi)</math>is defined as: <math display="block">\hat{f}(\xi) = \int_{-\infty}^{\infty} f(x) e^{-i2 \pi \xi x} dx</math> Recall that Euler's formula states: <math>e^{ix} = cos(x) + i \sin(x)</math>. Hence, <math>e^{-i2 \pi \xi x} = cos(2 \pi \xi x) + i \sin(2 \pi \xi x)<..."
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