The Fourier Transforms

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The Fourier transform was named after Joseph Fourier, a French mathematician. A Fourier Transform takes a function to its frequency components.


Properties of a Fourier Transform:

Properties of a Fourier Transform:

Linearity

mathcal{F}[X(t)]x_{\mathrm{t}}(t) = \frac{4}{\pi} \sum_{k=1}^\infty {\sin{\left ((2k-1)2\pi ft \right )}\over(2k-1)} </math>