TABLE A6.2 Fourier-Transform Pairs Time Function Fourier Transform rect(4) T sinc (/T) sinc (2Wt) 2 w rect 2 W Tale Wet exp(-at )u(t), 420 24 Take a=1 exp(-at ), 420 a2 + (2x/ )2 exp(-wt] ) exp( - w/ 2 ) lo. T sinc (fT) S(t) 1 6(1 - to) exp(-12ofto) exp(i2afet ) 8(f - fc) cos(2w/d) 18( - () + 8(/ + 10)] sin (2 a/ !) [a(f - () - 8 (f + f2)] 1 sgn (t) 1 -/ sgn (f) 1 8(t - iTo) Tale TF1 To Notes: w() = unit step function 6(t) = Dirac delta function rect(r) = rectangular function son (t) = signum function sinc(f) = sinc function