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# Sample_Test - Name SOLMT/O A EEE 303 Signals and Systems...

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Unformatted text preview: Name: SOLMT/O A): EEE 303: Signals and Systems Exam 1 February 27, 2006 Prof. Papandreou—Suppappola You must answer all 4 problems for full credit. The number of points for each part of a problem 18 given. For full credit, Show all steps and label all axes. u(t) is the continuous- time unit step, and 6(t) is the continuous— time impulse. >l< denotes convolution. Where appropriate: 0 Show all intermediate steps 0 label all axes o circle the ﬁnal answer This area is for ofﬁcial use only: Problem 1 Problem 2 Problem 3 Problem 4 1. Assume that 117(25) is the signal plotted below: 16(1) 3 (a) (8 pts) Evaluate the integral / \$(t) 6(t+ 1) dt ":2, X L» \3 2: Q. —3 (b) (8 pts) Compute and plot y(t) : \$(t) * 5(t + 0,5) : x “H: o‘. S) 2. Consider a discrete-time system with input signal :I:[n] and corresponding output signal y[n] = n:c[n+ 1].: T5; [n31 Clearly explaining your answer, determine Whether or not the above system is: (a) (515163) Memoryless (Vol: Angie/M60 W ’Eumﬂ “M?“ M‘M '23 I (b) (10 pts) Linear (C) (10 P“) Time-invariant (TI. > / ‘ V 1”, EV! T 1/ [”1 KW 1? Ema“, “M T; ”ﬂied-141\$ 33 c>< } z'l ~32: ‘ :QNLE ,- /3 7/101 CM~ We? Uﬂ ‘ 'Y‘ (9‘1 LL In“: ll?) ziihﬂlj' ‘9 ' XMS‘CVLQ :3 ’QJ'WEQV Y‘lﬁﬁ ‘ 9&ng Chl A— gamatafm ”3 (a) 1 Til) \6:M~ -moj73 vacmgi} {Ms «(M YEW): DLCM ”03 3. Consider a linear and time—invariant (LTI) system with impulse response h(t) = 4u(2 — t). (a) (10 pts) Is this system BIBO stable? Explain your answer. (b) (15 pts) If the input is :c(t) = u(t — 1) -— u(t — 4), ﬁnd the system output y(t).‘ my :5? %\Bo stage , W F: WEE) cit: (”Wig To pheL Q. 1 ﬁ 00 ' we - — (it ; We ~ \$-03 MIN-c; ‘9 ABC ”g’;" '4 ' Li) 2&5 B/gostatto 4. Consider the following interconnection of LTI systems: (a) (10 pts) Find the overall impulse response h[n] of the system in terms of h1[n], h2[n], h3[n],,and h4[’n]. l’\ [W1 2 Q” Enl + “ling/M3CW1)*~ ka EH“: (b) (15 pts) Determine and plot h[n] if h1[n] = h2[n] = u[n — I], ; h3[n] = 2u[n — 3], h4[n] =_ 6[n'¥ 1] Extra points: (5 pts) If \$[n] = u[n], ﬁnd and plot y[n] = 1472] * h[n] k5) ldm3z;(du£mqgﬁ.&ugwﬁl) % gtnnq r; {a scan + as war) % SEW? El sew: + Mimi ’ A Alma“ ; . l M ’V\ xi“) : QJLEM—er—r Qlch’jfx _,.—;ln:L1li;fe :civlw~el +°“’3"“‘§r1 - \$3)“: >’h : ngCVVQl “l L\ ghosj ...
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