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

${ℱ}[X(t)]x_{\mathrm{t}}(t)=\frac{4}{\pi }\sum _{k=1}^{\mathrm{\infty }}\frac{\sin ((2k-1)2\pi ft)}{(2k-1)},df$