Exam#01_Solutions - ECSE-2410 SIGNALS AND SYSTEMS SPRING...

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Unformatted text preview: ECSE-2410 SIGNALS AND SYSTEMS SPRING 2008 Rensselaer Polytechnic Institute EXAM #1 (110 minutes) February 11, 2009 NAME: gCDLU \ l OM $ SECTION: 8:30 am 10:00 am Do all work on these sheets. One page (both sides) of handwritten crib notes allowed. Calculators allowed. Label and Scale axes on all sketches and indicate all key values Show all work for full credit Total Grade for Exam #1: Problem Points Grade 1 5 l 2 1 5 3 10 4 9 5 L 7 6 10 7 7 ‘ L 8 _L 7 9 10 L 10-13 8 14-16 6 a 17-19 6 __ 20-22 6 23-24 4 r TOTAL 100 Exam#01 —— Spring’09 — p.1 1(5). Sketch the even part of x(t), where Label and scale your plot. Exam#01 — Spring’09 — p.2 3(10). The step response of a LTI system is Label and scale your plot. Exam#01 — Spring’09 — p3 mgk‘w 9}?"- 4(9). Evaluate and simplify t‘ , 1 *3 -Lgt ‘ ,L (20(3) x(t)= [flaw—1m fig 82 gag” —_—. e Z éC’F-M’i‘ m a a) e“0.9 [ mgx‘fivc gr— d €04) _ (b)(3) x(t)=;t—w(t) There w(t)=e u(t 2). figzanl) ~~£4 Qt: Q ‘21 get—z) + M(i*9( e i) d4: -3. “LUVQ 2 5f gawk-é- Z uUc-z) vx K 1’ i W W) x[n1= :wm == ZC‘E) == i 2 *1? a [(2—06 2: G - E, Exam#01 — Spring’09 — 13.4 s O 5(7). A discrete—time LTI system has an impulse response, = {1, 0, 2, 0, l}. (a)(5) Find the output —~ expressed in sequence form —- when the input is x[n] z {1, l, 2}. Am 1 7 0 7 r as? (b)(2) Is this system causal? Circle on . YES NO filth h Exam#01 — Spring’09 — p.5 6(10). Find the differential equation for the circuit, relating input x(t) to output y(t). 131:1 Exam#01 —- Spring’09 ~ p.6 7(7). A discrete—time LTI system has an impulse response, h[n] = Find the system output when the input is also x[n] = Express answer as a formula, not as a sequence. (>8 Hag}; mama) :- E Lttk] wan—id F—=~~06 J 2? 7:- Vl‘O‘H} “30 ~ WWW kflo 3513:.- @+t>btfll\ M Exam#01 — Spring’09 — p.7 8(6). Find the step response of a LTI system described by the difference equation y[n]— l y[n — 1] = lx[n — 1]. Express the solution in closed form. 2 4 at flax—lips: 2950 Exam#01 — Spring’09 -— p.8 9(10). Perform the convolution, C(t) = a(t) * 170‘), where 610) Qt?” W) “Hi “E ’C‘ Just set up the integrals for each range and denote the range of t Where the limits on the integrals are valid. Do NOT evaluate the integrals. 2:3 5 4.. t i i W RH. vtt-‘i: Ll ¢t>zg7 Zéfigég Exam#01 - Spring’09 ~ p.9 fJO I; 0x 10(2). The following MATLAB code produces which result? Circle your answer. [—21 —l/ OI 1/ 2! ~ heaviside(t) NW 1“ o 0 NaN 1 1 1 (b) o o 1 o o o (c) o 0 Inf 0 0 0 0K 0 o 1 1 1 1 11(2). The following MATLAB code produces which result? Circle your answer. t = [‘2, ‘1; O] 1/ 2! x = dirac(t) O NaN (b) O O l O Inf 0 Hoot—4 Hoot—J HOOP-A 12(2). Which MATLAB statement computes ej 2”” 7 (a) e" (j *2 *pi*w) @exp (j *2 *pi *w) (c) cos(2*pi*w) + imag(sin(2*pi*w)) (d) all of the above 13(2). In Matlab, which subplot command would be used when plotting the sinusoidal signal x(t) in this figure window? Signal x(t) 1 t t ‘ ‘ t 7' V ‘10 10 20 30 40 50 60 70 80 90 100 subplot(311) t x 10“ Signal y(t) (c) subplot(313) 3:{”“* ' v ‘ ‘ x :3 (d) subplot(131) 00 10 20 3‘0 40 50 6O 70 80 90 100 t (e) subplot(132) 2 “Tml ‘ [Signéllm ‘ l 00 1’0 “:6” 50 4:0 50 60 7:0 8:0 9'0 100 ’( Exam#01 — Spring’09 — p.11 14(2) {.wiagg- m {2133: {Ir} a”; {It} {V'iigfi} 32%? m1} {a} {35" Erie“ “1} was mu 5 15(2) if she impuisse msgwnseé {if & k’i‘i symm 1% firm, mm whim mam 13f 'th ffiitms‘ifig if: alwaya flue? W,AmemwwMWMMWWMMWWWXMW WW,»wawwwmwmwwwwwmwmakwww/MVWQ«wmmuVm“W“WMMMMMMMWM 16(2) Eff fit? S‘E’Xfi‘m 3mm: may-mm? i5 Hum his imyam ,Mspnmw is @mmwflwywowm“ wwwmw WMWW WM. V WNWNMWMWMWMWNMWWMWWwa~www~wm=- m!) r V Exam#01 — Spring’09 - p.12 18(2) Tim flap l’fifipfillfii’ (3f m: LT} sygwm izs ywitw SH}. its impnlxe :rmgmnse ire WWM-WW»MWWWMWWMWymmmwwmwv\wmwxww”.4wwvWmmwwW‘~,MWWWMVW~¢,WW {a} 93H? E {I w 6”" EM” Eb} i’fififizfi gyflé {6) $3335ng wgéfiii‘ef} {43} $3“; wifif} ism dict} - 33:2; mth in” i, Wham/31mm? I makm wiflfim} M3? {a} f 22 «i {1;} 1:2? {z Exam#01 — Spring’09 ~— p.13 i , 3 20(2). Iéimimsw 5313'}. a zeapzwofi 1: %2‘_ § 4»-r»,flwwmmwmwwxmwm4wWWWMWMM o W WWW/w. ¢>&v\ {gm my l 21(2) if f3§fiE¥§§€§$i :2 that: 3:3} (is: w 11* figs? w E} m- g??? M {E3} 5%; w 1% Mn w» fi 43%: m is: M we My; g} ., {fig}, fl 3} éaié ifffl - a} g 13%? —- m €533] K: 00"“ ~ a0“— C“ . 22(2) fs'“%;g:fhs~::}ge‘&’i‘: -61 - "’ Q 1’- I 0 Exam#01 -— Spring’09 —~ p.14 23(2) W313i it; the maximum mhm at“ {if}, My??? {22} 1 £335} {gflnf {it} 333%} § {:1} if hint} fifty] 31:5} 33:! 3 {iii/i1? E m»% m; g Exam#01 — Spring’09 —~ p.15 ...
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Exam#01_Solutions - ECSE-2410 SIGNALS AND SYSTEMS SPRING...

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