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Unformatted text preview: Midterm #2 of ECE301, Prof. Wang’s section
8—9pm Thursday, October 13, 2011, EE 170, . Please make sure that it is your name printed on the exam booklet. Enter your
student ID number, email 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 12 pages in the exam booklet. Use the back of each page for rough work. . Neither calculators nor help sheets are allowed. Name: " ” Student ID:
E—mail: Signature: Question 1: [27%, Work—out question, Outcome 3]
1. [2%] What is an “impulse response”? 2. [10%] Consider a system with the input / output relationship being y(t) = (1:0 x(s)e—2t+2sds> + ([0 $(s)e2t‘2sds). (1) Find the impulse response Mt) of this system. 3. [15%] Let 2(t) = etLl(—t). Find the convolution integral w(t) = z(t) >l< Mt). If you do not know the answer h(t) of the previous question, you can assume that
h(t) : L106) — U(—t) and solve w(t) accordingly. You will receive 13 points if your
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ﬁlgt<3 ' #0 3. [10%] Compute the Fourier series of Hint: Consider another signal: z(t) is periodic with period T = 4 and { We know that the Fourier series coefﬁcients of z(t) are 1
0 ﬁ~1§tgl
ﬁigt<3‘ uk=0
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period T = 4 and t+1if—1§t<0
:c(t)= 1—t1fogt<1 ,
0 ﬁ1§t<3 then the corresponding FS coefﬁcients are 3;
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I2 2k27rg2) Answer the following questions: 1. [7%] Compute the value of ZZ:_OO oi. 2. [7%] Consider a different signal y(t), which is periodic with period T = 4 and t+1if~1§t<0
1 if0§t<1
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and there is no need to justify your answers. Consider the following two systems:
System 1: When the input is $105), the output is _ [foo $1(28)d8 ifO gt
Wt) * {0 1ft < 0' (9) System 2: When the input is $2M], the output is
3/2 = min(0, x2[n + (10)
Answer the following questions 1. [4%, Outcome 1] Is System 1 memoryless? ls System 2 memoryless? [\3 . [4%, Outcome 1] Is System 1 causal? Is System 2 causal?
3. [4%, Outcome 1] Is System 1 stable? ls System 2 stable?
4. [4%, Outcome 1] Is System 1 linear? Is System 2 linear? 5. [4%, Outcome 1] Is System 1 time~invariant? Is System 2 time—invariant? NC) r i N O /
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 Spring '06
 V."Ragu"Balakrishnan

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