Table of Fourier Transform Properties

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Fourier Transform Properties
Property (contributor) Expanation
Convolution (Ben Henry) If h(x)=\left(f*g\right)(x), becomes    \hat{h}(\xi)=\hat{f}(\xi)\cdot \hat{g}(\xi).
Scaling (Chris Lau) Given a, which is non-zero and real, and \ h(x)=f(ax) , then \hat{h}(\xi)=\frac{1}{|a|}\hat{f}\left(\frac{\xi}{a}\right). If a=−1, then the time-reversal property states: if \ h(x)=f(-x), then \hat{h}(\xi)=\hat{f}(-\xi).
Linearity (Victor Shepherd) \mathcal{F}\{ax(t) + by(t)\} = a{F}\{x(t)\} + b{F}\{y(t)\}