exam3soln - EEE 203 Exam 3 This is a closed book closed...

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Unformatted text preview: EEE 203: Exam 3 April 23, 2009 This is a closed book, closed notes exam. You are allowed one cheat—sheet. to get full credit. Good Luck I Please Show all work 1. Consider the following interconnection of discrete—time LTI systems. If h1[n] = (0.5)” is Hfiej‘“)? If MM 2 cos(0.27rn), What is Hfiejw)? What is H(ej“’)? Lgvi’b‘V 14) 7 “9m 4 Mn], what “*3 M ‘ 9:11 i410?) )3 #1,“ #WO‘ Pages” hgifl] : 03$ (ED-211%,) w 142(9)”) 2fi<sgmwo2® + $010+ can» £391,504 2n _ kiwi-MSW W] 33: LnCéMMCe“) = We“) Wow) : Ti 1»— Y 3 (on 43:21?) «iv gape-man )] \Ovfi LE" 2. (1) Compute the Discrete Time Fourier Transform( (DTFT) of the signal shown below. 5')? CA 11:11] W MWM am PM? #4471?” N 1‘ min? M 3W (00 ('2 +15) : £13 $72) 113“] .5 «E31: En .,., \1 ém-w‘v E? “.300 . Amp” ééfi) fima fl N ‘2. mE—h] ém% 1 {mm 10‘?’6 3. Compute the Nyquist rate of the signal $(t) = ( sampled at T = 0.25 millisecond. ~gaoOfi' Sin! 20007rt) 7rt )2. Plot the Spectrum if the signal is gum [2000 n ‘0 4.(i) If 33(t ) is a signal with Nyquist rate can, what 15 the Nyquist rate of the signal 32(t) cos (wot)? MLW; HWQT—WW O 030[\ y‘aWEg/wa ”WW9 [\5000/ (ii) The frequency spectrum of a signal is shown below. Plot the sfiectrum if the sampling frequency is 100w. How much of the signal can be completely recovered? X003) 1... ‘ , 211 a {non 5.0 7:50 5.(i) The Continuous Time Fourier Transform of a signal 33(t) is given by X (jw) = sinc(w/2). What is LIEU“)? 2T1 4'9“! (W?) W H7 as ‘ “fl T! If???“ _ ,4va [DJ/L) Q a wesii fxgéfie L06E+DQD““!A€L Vi) (ii) A signal has the impulse train spectrum X ( jw) shown below. Comment on whether the signal is (a) periodic, (b) even/odd. Add a brief justification in each case. XQw) ":2— -—l O 1 2- (a) {:th :m PMOW gdvmol'i‘w’ ”L“ mm W as pmm (wow 1M 41‘m oiOMW‘ m) : Awe-4; +%m2t a» ammo-3w) “9mm ,1: s? fifilfi XC%) ”@ %¥m9fiuq ...
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