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Unformatted text preview: ECE 301, Midterm #2
8—9pm Thursday, October 9, 2008, PHYS 114, . Enter your name, student ID number, e—mail address, and signature in the space
provided on this page, NOW! . This is a closed book exam. . This exam contains multiple choice questions and work—out questions. For multiple
choice questions, there is no need to justify your answers. You have one hour to
complete it. The students are suggested not spending too much time on a single
question, and working on those that you know how to solve. . There are 10 pages in the exam booklet. Use the back of each page for rough work.
The last page contains the formula for Fourier series. You may tear the last page
for easier reference. Do not use your own formula sheet or any kind. Using
your own formula sheet will be considered as cheating. . Neither calculators nor help sheets are allowed. Name: 50 (‘4 M7“
Student ID:
E—mail: Signature: Discrete—time Fourier series mm] = Z akejk(27r/N)n
k=(N) ak : _ Z m[n]e—jk(27r/N)n
n=(N) Continuous—time Fourier series Discrete—time Fourier transform 1 .
x[n] = g 2 X(jw)ej‘”"dw
X039“) = Z x[n]e‘jw” Continuous—time Laplace transform
1 0° ‘
33(75) = 2—6“/ X(0 + jw)ej°"tdw
7T —00 X(s) = /00 $(t)e_8tdt —OO (10) Question I: [24%] 1. [4%] What does the acronym “LTI system” stand for? 2. [6%] Let :1:[n] and y]n] denote the input and output of a discrete LTI system that
has an impulse response Mn] Consider the following two equations: $[n] = Z $[k]6[n — k] (1)
yln] = Z mlklhln—kl (2) From the perspective of coefﬁcients, test signals, the output of test signals, the
weighted sum of signals, and the LTI system, answer the following questions. What is the role of 6[n — k]? What is the role of Mn — k]? What is the role of :c[k:]? Consider a continuous—time LTI system as follows. ’I’l yln] = Z We». <3) kz—oo 3. [14%] Find out the impulse response h[n] of this system and plot h[n] for the range
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impulse response Mt): W) = 2"(W) — um — 2)). <4)
1. [4%] Is the system S memoryless? Is the system S causal?
2. [4%] Plot Mt) for the range 15 : —2 to 5.
3. [16%] Given the input being 56(t) : 2tU(—~t), ﬁnd out the output y(t). Plot y(t). 4. [4%] A system is called “a t0~delay system” if any input 55(15) generates a delayed
output y(t) = $(t * to). Find out the impulse response of the following serially concatenated system (input being x05) and output being z(t)). At) ——()———4 tO—delay s I. 157’ [£41 memdr/y 5' ;n(e if hQIA 'k/é) 716/ (6’ 2’ ﬁ/ [5/ 1‘; Cﬂwfa/ ‘7‘“! 7/ ”3?”li W9 pv’Jf'L /rgjc.,~f i/d/MJ avian/fl 1_ Alt}
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t ranges from —2 to 6. 2. [4%]
Suppose 33(75) is periodic with period 4 and 90(75): 1 t/3 ifOut<3 (5)
t—3 1f3§t<4 Suppose we also know that 2(t) = m(t) + y(t). Plot 2(t) where t ranges from —2 to
6. 3. [20%] Find out the Fourier series of z(t). ya” : z J/ez—zk) = EJH(LM/ Lei Z=kH
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1. [8%] Find out the Fourier series of $(t) = 008(8t) + sin(4t). For the remaining questions, just write down your answers. No need to write down the justiﬁcation.
Consider the following systems: System 1: y(t) = { 1
System 2: y[n] = Z 2%[71 ~ Ir] kz—l 1. [4%] For Systems 1 and 2, determine whether the systems are causal.
2. [4%] For Systems 1 and 2, determine whether the systems are linear. 3. [4%] For Systems 1 and 2, determine whether the systems are timeinvariant.  21”: 2' 1 xii): “MS/6] +:n{‘(6) T« y 2 I J ‘ ~76 4' a are a :; o<_ = «2, il{eJ“+CJ / *2; (ed ~c / 3) I J 1' d .U 1% ’ j‘f'kt a” : “1 I 2
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 Fall '06
 V."Ragu"Balakrishnan

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