Table of Common Fourier Transforms 2.8 2001/06/14 2004/08/10 13:16:03.731 GMT-5 Melissa Selik mselik@alumni.rice.edu Richard G. Baraniuk richb@rice.edu Justin Romberg jrom@rice.edu Melissa Selik mselik@alumni.rice.edu Richard G. Baraniuk richb@rice.edu Ricardo Anthony Radaelli-Sanchez ricky@alumni.rice.edu Mariyah Poonawala mariyah@rice.edu Prashant Singh prash@ece.rice.edu signals systems fourier transform continuous time Lists time domain signal, frequency domain signal, and condition for twentytwo Fourier transforms. Time Domain Signal Frequency Domain Signal Condition a t u t 1 a ω a 0 a t u t 1 a ω a 0 a t 2 a a 2 ω 2 a 0 t a t u t 1 a ω 2 a 0 t n a t u t n a ω n 1 a 0 δ t 1 1 2 δ ω ω0 t 2 δ ω ω0 ω0 t δ ω ω0 δ ω ω0 ω0 t δ ω ω0 δ ω ω0 u t δ ω 1 ω sgn t 2 ω ω0 t u t 2 δ ω ω0 δ ω ω0 ω ω0 2 ω 2 ω0 t u t 2 δ ω ω0 δ ω ω0 ω0 ω0 2 ω 2 a t ω0 t u t ω0 a ω 2 ω0 2 a 0 a t ω0 t u t a ω a ω 2 ω0 2 a 0 u t τ u t τ 2 τ ω τ ω τ 2 τ sinc ω t ω0 ω0 t ω0 t ω0 sinc ω0 u ω ω0 u ω ω0 t τ 1 u t τ 1 u t τ t τ 1 u t τ u t τ 1 triag t 2 τ τ sinc ω τ 2 2 ω0 2 sinc ω0 t 2 2 ω ω0 1 u ω ω0 1 u ω ω0 ω ω0 1 u ω ω0 u ω ω0 1 triag ω 2 ω0 n δ t n T ω0 n δ ω n ω0 ω0 2 T t 2 2 σ 2 σ 2 σ 2 ω 2 2