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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
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LE" 2. (1) Compute the Discrete Time Fourier Transform( (DTFT) of the signal shown below. 5')? CA 11:11] W MWM am PM?
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{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;
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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“)?
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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) : Awe4; +%m2t a» ammo3w) “9mm ,1: s? fiﬁlﬁ XC%) ”@ %¥m9ﬁuq ...
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