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Unformatted text preview: NAME: S clm’llokg Michigan State University
Department of Electrical and Computer Engineering ECE 366 INTRODUCTION TO SIGNAL PROCESSING Midterm Exam 1
Spring 2011
February 25, 2011 R 0 One side of 8.5” x 11” paper consisting of handwritten notes is permitted. (Please
turn these notes in with your exam. And, don’t forget to write your name on your
“cheat” sheet!) 0 Calculators are NOT allowed.
0 You will have 60 minutes to complete this exam. 0 For those problems that allow for partial credit, please show your work clearly to
maximize your score. 0 Good luck! 1. (25 points) True/ False. No partial credit will be given, so it is not necessary to show your work. You will receive 2.5 points for each correct answer, 1 point for each
incorrect answer, and 0 points for no answer. (a) All power signals are periodic. False. wet) LS mew/oar“ CLgLKl backts no‘l (PQI‘tOOhC, (b) The signal f (t) = sin(t)/t is even symmetric.
T i‘ UL e . (c) Every signal can be represented as the sum of shifted and scaled impulse functions.
Tr UL a . (d) Convolution is of no use in solving linear constant coefﬁcient differential equations.
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:33 2, 0+ LCQO 6’; +0 OJ ‘0 thug, impacts. (e) The output response of a linear and time—invariant (LTI) system cannot have
frequencies that are not present in the input. Trwe_ (f) The Fourier Series (FS) can exactly represent an aperiodic signal over a ﬁnite
interval of time. Truce, (g) Let W) =2OCOS(0.17rt+7r/4). The power of f(t) is 400. 1
ELLS‘L . no. {)0th \S 9.00 (ft (9.), (h) Let f (t) = sin(mt) + sin(nt). The Fourier Transform (FT) tells us that if m/n is
irrational, then f (t) is not periodic. Paige . "TKL E; “(1.th UkS‘ ﬂeet n“ w/w. L3 (Froc'ﬁokaf J
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TFKkC’FoFKKL‘Q (j) Conjugate symmetry of a signal means that its real part is even and its imaginary
part is odd. Trwe, 2. (25 points) Show all your work to receive partial credit. Correct answers without
accompanying work will not receive full credit. Let system 1 be y(t) = 2 f (t + 1) + 2, and let system 2 be LTI with impulse response
h(t) = e“(t“°)u(t — to). (a) (15 points) Determine if system 1 is linear, timeinvariant, dynamic, causal, and
BIBO stable. Justify your answers. (b) (10 points) For what values of a and to is system 2 causal, BIBO stable, and
marginally stable? Justify your answers. Q15 c685. L$L++Q+l 1”«° PL+)=©,—ch. “63):; So) “Hm: S'xém‘avx Ls _. ‘ La‘l' %L+l: ‘FQ‘H'llJ. ﬂak,
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3. (25' points) Show all your work to receive partial credit. Correct answers without
accompanying work will not receive full credit. Let h(t) = e‘tu(t) be the impulse response of an LTI system. g.
(a) (12 points) Compute the output yl (t) of the system in response to the input
f1(t) = e‘2‘u(t). (b) (10 points) Use your result from part (a) to compute the output y2(t) of the
system in response to the input f2(t) = 2e‘2(‘+2)u(t + 2) + 3e‘2(“2)u(t — 2) g.
(c) (3 points) Can you likewise use your result from part (a) to compute the output
y3(t) in response to the input f3(t) = e2‘u(—t)? Justify your answer. (9) ULSQ Cowuulud'wm'.
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MLM— QoM_Lmq,+t0I\ 045 s M4410! 410%}, 4. (20 points) Show all your work to receive partial credit. Correct answers without
accompanying work will not receive full credit. Let f (t) be a periodic signal as shown below. Determine the trigonometric FS (TFS) of f (t) ULSQ T?S tcrwioc‘, Mo'E'k ‘Hkoqt *(lC‘t) (s {UM/k Sidee‘trrc 4.
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