2 Some useful Fourier Transforms

\(x\left ( t\right ) \) \(X\left ( f\right ) \)
\(\sin \left ( 2\pi f_{c}t\right ) \) \(\frac {1}{2j}\left [ \delta \left ( f-f_{c}\right ) -\delta \left ( f+f_{c}\right ) \right ] \)
\(\cos \left ( 2\pi f_{c}t\right ) \) \(\frac {1}{2}\left [ \delta \left ( f-f_{c}\right ) +\delta \left ( f+f_{c}\right ) \right ] \)
\(\cos \left ( 2\pi f_{c}t+\theta \right ) \) \(\frac {1}{2}\left [ e^{j\theta }\delta \left ( f-f_{c}\right ) +e^{-j\theta }\delta \left ( f+f_{c}\right ) \right ] \)
\(\sin \left ( 2\pi f_{c}t+\theta \right ) \) \(\frac {1}{2}\left [ e^{j\theta }\delta \left ( f-f_{c}\right ) -e^{-j\theta }\delta \left ( f+f_{c}\right ) \right ] \)