The Fourier Transforms

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

   ${\mathcal {F}}[a*x(t)+b*y(t)]=a*X(f)+b*Y(f)$

Shifting the function changes the phase of the spectrum

   ${\mathcal {F}}[x(a*t)]={\frac {1}{a}}X({\frac {f}{a}})$

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