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Unformatted text preview: ECE 301 Exam 3 Daniel Aguiar July 19, 2011 This exam will be 60 minutes.
It is closed notes, closed book and there are NO CALCULATORS to be used on the exam.
There are SIX problems. Name: [d/o»%;grv) Problem 1 (20 points total) Find and plot the Fourier Transform of each signal below. Part a (5 points): x (t) = i (4% (7: — 3k)
[$12—00
Part b (5 points):
31 (t) = 6"” Part c (5 points): Part d (5 points): e e ‘00
~00
 I we) a .1. t(/00’/ —L +—L = i.
_ J / + C I [24/ Ho 1
(754/6 .1” (U4! d U [7"‘4/
7’0“) Problem 2 (10 points total) Without computing X (67“), evaluate the expressions below using the plot of x[n]. Part a (5 points): Part b (5 points): 2.5 1.5 0.5 43.5 .3 a: x53 : 571: X{eJ7@JMc/U If mm M w ww w 11 g: x5304"? = Z w {J I1: 30 V
in d 2‘1 , o a
3 Z 9m) {3) =
h:— (42 (W t zed231(3)”
+ 1/0), + "(07‘ I(J)3 Problem 3 (10 points) Suppose a continuous—time system takes input x (t) : 6’71 (75) and produces output
y (t) 2 LI (t) — 21(75 — 2). Find the frequency response of the system, H (jw).  00 _ ﬁ. .6 ‘ 00 r 2'], ,t/IO‘Q) ad: ’4
)(Oo/zgeiedw Ji 4 C d 0/5 ‘ Wye /, It.”
L ~‘ :5 y ,. f l ._ ;2 v. m») =4, t = 3;; £4 = you w = mew _ '  ,  v.” , __ [f— . ~‘</
W ' ZWW ~4151/sm/v/ed Problem 4 (20 points total) Derive the following properties of the CTFT, assuming 56(75) 9 X (jw), and DTFT,
assuming 4—) X(ej“’). Part a (10 points):
a: (t) is real and even (—> X (jw) is real and even
Part b (5 points):
m [n ~ no] <—> e”j“’"°X (ejw)
Part c (5 points): $* <—> X* (69“) ’ w _~U :9 ‘d 7" :‘ J :J
'g I." X{’U) 8150‘! U : X{U/e JUUJU fin“! 3 Ai/”{/ w H van” 64 a  — 2a wzma waz wed r J w
I» 2 XO'oJe‘) v If,“ 16 e #5120 6 ) h"~l L44 i="”’0 {:0 h“ JV" A, I} 7151/
6 Z >37") Um Kme : X {e 11:36 Problem 5 (20 points) Let :1: (t) be band—limited to :2W. Let y (t) be the output of the operations below.
Create a demodulator to reconstruct x (75) from y KG) W’CX WW” mmmwwwjlmm w M" W) ~5W ~3W 3W SW C /\
N
‘ NW.
C 'W~Sk/’3V )UJL/ 7d Problem 6 (20 points total) Suppose a signal, :c(t) that is band—limited to in has been sampled at a sampling
frequency higher than the Nyquist Rate with a first—order hold sampler, as shown below. x ) mt
rm
; _n "—’
ms): Tail Ts) lt<T3 75‘
0 otherwise < i
1; 7} pot): i (Sc—M) k=«oo Part a (5 points): Sketch an example of $(t) and the resulting output from h1(t). Part b (15 points): Find the expression for the reconstruction ﬁlter, HAjw) to perfectly reconstruct 26/15 ) ...
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This note was uploaded on 02/14/2012 for the course ECE 301 taught by Professor V."ragu"balakrishnan during the Fall '06 term at Purdue UniversityWest Lafayette.
 Fall '06
 V."Ragu"Balakrishnan

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