Question

5.5 Starting with the Fourier transform pair 2 sin(S2) X(t) = u(t + 1) – ut - 1) = X(92) = S2 and using no integration, indicate the properties of the Fourier transform that will allow you to compute the Fourier transform of the following signals (do not find the Fourier transforms): (a) xz(t) = -u(t + 2) + 2u(t) – u(t – 2) (b) xz(t) = 2 sin(t)/t (C) X3 (t) = 2[u(t + 0.5) - ut - 0.5)] (d) x4(t) = cos(0.57t)[u(t+1) – ut - 1)] (e) X5 (t) = X(1) You may want to plot the different signals to help you get the answers. Answers: X|(92) = -2jX(S2) sin(S2), time-shift property; duality to get X (2)

Answer 1

act) Q F. 2 sin () a, CD = - uct+2) & Qu(tault-2) 2.00 M, CH =-*(+4) +2(t-1) 1 -2 By siusing fܒܢ Time shifting Property X, (P) = -X(14) July x (v) e 12 ا له de YIG) = x3 bass aj o Xiana - 25x (2) (+) 2 sin (t) sin et s using duality property x2(+2) = 21*(-12) 3Ct = 2 Cuctta.s)-u(1-0-s) .& (!) &g (t) = 2% (at) 2 Time scaling Property 2 -0.5 orgt X₃ (12) Eqx (o-stit) [u(t) = 4(t-D] جه) 's(t) - Cas jo-sut soosnit te e Xa(t) = do CD) 2 By using Frequency shifting property XA (می) { [x (x2-0-50) + * (ne +0.57) & CU = X(t) Apply Quality property Agt) = 2hartt Xsco = 29a (-2)