Exam#01_Solutions

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

This preview shows pages 1–14. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 14

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

This preview shows document pages 1 - 14. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online