The Fourier Transforms

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

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Properties of a Fourier Transform:

Convolution

$f(t)*g(t)$	$\stackrel{{ℱ}}{⟺}\sqrt{2\pi }\cdot F(\omega )\cdot G(\omega )$	(unitary convention)
	$\stackrel{{ℱ}}{⟺}F(\omega )\cdot G(\omega )$	(non-unitary convention)
	$\stackrel{{ℱ}}{⟺}F(f)\cdot G(f)$	(ordinary frequency)