Question

A CT window signal is given as x(t) = u(t+4) – uſt-4) The frequency response of a CT LTI system is a given as H(jw) = {2e-jw 1w 5 31/16 HV) 0 otherwise if xz(t) = x(t)* 8(t - 16k) is applied to this CT LTI system, k=-00 a) Sketch the magnitude spectrum of the output. b) Sketch the phase spectrum of the output. c) Give the mathematical expression for the output y(t)

Answer 1

s2 et Hong => 101s 37/16 Otherwise Xrt) - altty)-ult-4) - 44 * It is xlt) * ē sit-i6k) - 6 Kas 94) > 014 * x (t) (ov) (jw) - Hlju) X(jw). H(jw) - 2e jw y hits = 28 (t-1) * =) ylt) = 28(t-1) alt) * E slt- 16k) K=-0 > a{tit * & s((E-) - 16X)] K= 0 § t-KT) = 21 86-K 4 ) KE T KE-o Jourier transform from eq-o, Moyek) = XzCju) = X(ju) ~ 2 (6+*24) - 2 § x(K:21). Y (8w) = H (W) X ₂ (W) - 20 Jw 21 & XC k.2x) (W1 & 34 Kara Karo otherwise

rect() = 2t, sine (WT1/x) in xt), 27, = 48 att) = hect ( ) = 84 sinc ( 849) - x(w). >> rew) = (Qevw) ( 21 psinc(. K 24) K=- From T=16 given Question į S(-KT) - Ê $(t-16K) KE- KED rew) - 2 e JW. A { sine (k) (wis 37116 K=-D elę ewhere s slt-16K) KE- - 32 -16 01632 sinak) x = 5 Sik (F) - * Sinclosinca azsin(2) - 4K : -21 To (2x) 4x (a) H(w)) 1Y6w) T 42x Sine) w

(B) < y1w) a fza >w L HOW 1 LY(0) LH (W) + LXq (W). L&Xq (W) = 0 at & wer w=+27 so crow) z LH(W) from eq-6 (C). 94 - O É 6€*x17 - 16K -1) K=-D