# Properties of Fourier Transforms

*Linearity**a*,*b*, âˆˆ*C*, then*f*(*t*) and*g*(*t*) exist.*Scaling**F*{*f**t*)} =*F*(*Ï‰*) and*c*âˆˆ*R*, then*Time shifting**Frequency shifting**Symmetry**Modulation**Differentiation in time**n*âˆˆ*N*and suppose that*f*^{(n)}is piecewise continuous. Assume that , then*Frequency differentiation**n*âˆˆ*N*and suppose that*f*is piecewise continuous. Then