This document discusses properties of the Fourier sine and cosine transforms. It states that the Fourier sine and cosine transforms have a linearity property where the transform of a sum of two functions is equal to the sum of the individual transforms. It also describes a change of scale property where scaling the input function by a factor results in scaling the transform by the inverse of that factor.

4. Convolution Property of the Fourier
Transform
The convolution of two functions in
time is defined by:

8. Properties of Fourier sine and cosine Transforms
If Fs(s) and Fc(s) are the Fourier sine and cosine transforms of f(x)
respectively, the following properties and identities are true.
(1) Linearity property
Fs [a f(x) + b g(x) ] = a Fs { f(x) } + b Fs { g(x) }.
and Fc [a f(x) + b g(x) ] = a Fc { f(x) } + b Fc { g(x) }.
(2) Change of scale property
Fs [ f(ax) ] = (1/a) Fs [ s/a ].
and Fc [ f(ax) ] = (1/a) Fc [ s/a ].