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Exam1_solutions EEE303

# Exam1_solutions EEE303 - Name SOLMTID EEE 3113 Signals and...

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Unformatted text preview: Name: SOLMTID EEE 3113: Signals and Systems Exam 1 F'elzoruar1..Ir 2?, EDDIE Prof. Papandreou—Suppappola You must answer all 4 problems for full credit. The number of points for each part of a problem is given. For full credit, show all steps and label all axes. o[t} is the eontinnons~tirne unit step, and {ﬁt} is the continuous-time impulse. an denotes convolution. 1Where appropriate: i show all intermediate steps I label all axes o circle the ﬁnal answer This area is for ofﬁcial use only: Emblem mes 1. Assume that :1'[I} is the signal platted below: mm {a} [3 pts] Evaluate thsintsgral [3 m{t]§{£+1]tﬁ : 1%?) i :1 —a {h} [3 pts} Compute and plat yﬂ) = 55H] 1: rift + (1.5} ;: I {GE-f 0- 5) [c] [9 pts} Write the equation and plot ﬁt} = ﬁt) (aﬂ + 2] — aﬂ — 2]) rat?) Us) gussxt‘cwg} 2. Consider a discrete-time system with input signal ﬁn] and corresponding output signal y[n] =nrr[n+ 1]. .—. Tf; EHJ] Clearly explaining your answer, determine whether or not the above system is: - . [1 n 3 [a] [opts] Meruoryless Not. J égfamlu an {atone MPwk 4:151:41: 2-? ~ “‘ul 1-3.15 :1 {h} {16' p13} Linear (c) (16' pm} Time—invariant (Tl) Eel . mom or :sTEIJﬂ-l M3?"qu J U”) I'll LR“; W" T; all“ EM at 3 J rig? m - «(mm mm i more Th3 ‘- oimalCnl 4+ lama-ill”: 3. Consider a ﬁnesr and time—invariant [LTI] system with impulse respense Mt} = 4 u[2 — t}. {a} (It? pts) Is this system HIRE]I stable? Explain your answer. (11} {15 gets} If the input is ﬁt} = u[t — 1} — u[t — 4), ﬁnd the system eutput ylﬁt}. ﬂ .5135: status I, w 5: W953] cu: is; 1:, as). Q. 1: = ‘3’": u—e _ _ r: U! a? u m a thug u I: & Mamet ..--"'_ Lﬂ 93 Ha Li's} cm W “3%) ; 1H3) a; Lac): L; 106 ) Theta} I ,‘p gen?— #5316 >er n‘ (a H: ff, 0 \$1 I L flail—{J OWL?!" 4. Cnnsider the fellewing interconnection of LTI systems: {a} (In? pts} Find the overall impulse response Mn] of the system in terms (if h] [71.], ﬁght], h3[n],sn:i hdn]. kin-’3: @1343, + hltnurhacnzﬁ-Mcnn {h} [15 pts} Determine and plot Mn] if Erin] = light} = u[n — 1], h3[n.] = 2n[n -— 3], Elﬁn] : rl[n — 1] Extra points: {5 pts} If :r[n] = Mn], ﬁnd and plot yin] = ache] a: Mn] ':. (Stubs-1'1 -- \$1M [Y's-"‘31) '3; {Elm—ll :(asi‘mm lath—11) * gin—:7 a Scwrll -+ J. Eﬁhez'] a, 1 3 mm swim jittelwwj mﬁ‘fmq :: gnf‘n—lX-t 9~1EWEK Alli“ semis-elﬁlﬂwﬂ Lyn >31 1 Q‘Stwr’l'l "l Li “EMA? ...
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