{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Exam#03_Solutions - ECSE—2410 SIGNALS AND SYSTEMS SPRING...

Info icon This preview shows pages 1–16. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
Image of page 3

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

View Full Document Right Arrow Icon
Image of page 4
Image of page 5

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

View Full Document Right Arrow Icon
Image of page 6
Image of page 7

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

View Full Document Right Arrow Icon
Image of page 8
Image of page 9

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

View Full Document Right Arrow Icon
Image of page 10
Image of page 11

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

View Full Document Right Arrow Icon
Image of page 12
Image of page 13

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

View Full Document Right Arrow Icon
Image of page 14
Image of page 15

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

View Full Document Right Arrow Icon
Image of page 16
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 2007 Rensselaer Polytechnic Institute EXAM #3 (1 hour and 50 minutes) Check One: April 11, 2007 3 Sect. 1 8:30am (Wozny) _ Sect. 2 10:00am (Desrochers) NAME: 6’ , ‘ Do all work on these sheets. Tables will be handed out separately. One page of crib notes allowed. Calculators allowed. Label and Scale axes on all sketches and indicate all key values. Show all work for full credit. Total Grades for Exam: Grades for Points . Score fl Part I 40 Part II 38 ___fl Part III 22 TOTAL 100 PART I Problem Points Grade A 1 w 6 2 6 J 3 .. 8 4 12 V 5 8 TOTAL 40 1(6). Find the Laplace transform, Y (S), of 320‘) = 5(t — 2) * 3 cos (2t) u(t) where * denotes convolution. W 775 «a ){f/ a #6? K0) :: 6/2.; 3 5 KW” 2(6). Find the Laplace transform of v(t) 2' (t —1)e'(“‘)u(t). 3(8). Find x0), the inverse Laplace transform of X(s) = e (s + aXS + 2) ,wherea>0and c1962. 1?) l s ”44" + ”’6" Y‘ ”(Ha/(5+2; 9“” 5’” / ,1. = j”; ’4' {14.2 j: ~61 4(12). Find x(t), the inverse Laplace transform of X(s)= /3 , x3 : fl WIN 3;? 1/) flKx/r-C‘ )m 1 ? [2 ,. 9,52 I “3:; {4'2— .. - (5W ; ' ’ ’77? 2. ,1.» +~’:’ x(s)> J” [f7 :2- .2»- == ,4 * 3 5’2»? 13 (S + 2)(s‘2 + 9) . 587 ’11,..fi/ 52+? 5(8). A two-stage amplifier system is shown below Y where G, (S) = a and G2 (S) = 7 c . Performance Specifications require that the poles of S + a S“ + 195 + c ' Y (S) . . . 9, H (S) = he on a Circle of radius 2 as shown. Jm X(S) s—plane a.)(2) Is the system 02(3) (circle one) 5 A. overdamped, '9‘ fie B. underdamped, C. or critically damped? b.)(6) Find the constants a, b, and c so that H(s) has the required poles shown in the figure above. flo/e, keg/22w f «2—, We? ECSE-2410 SIGNALS AND SYSTEMS SPRING 2007 Rensselaer Polytechnic Institute EXAM #3 (1 hour and 50 minutes) April 11, 2007 Check One: _ Sect. 1 8:303m (Wozny) _ Sect. 2 10:00am (Desrochers) NAME: 301—4) Tl 0N3 Do all work on these sheets. Tables will be handed out separately. One page of crib notes allowed. Calculators allowed. Label and Scale axes on all sketches and indicate all key values. Show all work for full credit. PART 11 Problem Points Grade 6 12 T 7 10 8 8 9 . 8 TOTAL 38 lOOja) 6(12). A certain linear system has the transfer function H(a)) == ———-————~————~——. (5+jco)(1+jco/20) (a)(6) If the input to this system is x(t)= 5cos (lOt) find the exact, complete steady—state output, y(t). Complete means that you should include magnitude and phase in your answer. . 1772.. L140”! ”122ml...— _, W (W6)- Given H(a)) = 'K0w+U 20 200 number, not in dB!) so that the magnitude of H(a)) is zero dB when a) = 400 radians/sec. Note. You must use the Bode approximation. No other answer is acceptable (“+900 0 (W74: K‘U ‘ We Made .Using the Bode magnitude approximation, find the value of K (a View" 3;” 1+ J;°°l (75°30) "we: K S) l-A 10(jco+10) (WHEN) a described by 1H (60)] > - 20 dB for a) > 500 rad/sec. 7(10). Given H(a)) = find the largest value of a which avoids the forbidden region, T }H(w)| in dB ‘ E ; ; §,\,,F,thidden _ r, , I, :Region 8(8). A signal x(t) With spectrum X (co) (shown below) is ideally sampled (i.€., with delta functions) at l, a) < 5 sampling frequency cos = 10 rad/sec and then filtered with an ideal filter H (60) = i 1 . Sketch the signal 0, else spectrum Y (0)) at the output of the filter. Scale vertical axis! X(co) sampling 2” 2” 27f operation —12 —5 5 12 9(8) (a)(4). Find Y“) X( ) , expressed in terms of G1(S), G2 (3), H1 (3), and H 2 (s) for the following feedback system. s X(S) Y(s) 11 9(8) Continued. (b)(4). For the block diagram shown, if E(s) = X (s) — Y (s) , find 1ime(t) when x(t) :2 tu(t) . X“) +_.G(S)=s(::1> W) 1: a“ 25) g 613) 1 > «t9 5%! m) EQ— , WA 79% My _ \ _. 313) 1+ to SLSH) +7960 3+0 Sac 1.9T]; : é » l ==.1031. ] Saw $4219... W 12 ECSE-2410 SIGNALS AND SYSTEMS SPRING 2007 ég Rensselaer Polytechnic Institute n‘y EXAM #3 (1 hour and 50 minutes) NAME: Do all work on these sheets. Tables will be handed out separately. One page of crib notes allowed. Calculators allowed. Check One: April 11, 2007 D Sect. 1 8:30am (Wozny) D Sect. 2 10:00am (Desrochers) Label and Scale axes on all sketches and indicate all key values. Show all work for full credit. PART III Problem Points Grade 10 6 fi 11 L 8 , 12 8 TOTAL 22 13 10(6). Suppose the frequency response for a certain system is H1(a)) = 1H1(a))jej‘”' (w) . x(t>———~>- m) (a)(3). If the magnitude of H ‘ (60“) at some frequency (on is ~6 dB, then its absolute value (not in dB) is A. :9. 20 B. -6 c. l E. 2. (b)(3). The Bode plot (magnitude and/or phase) of H 2 (co) : (1 / j (0)111 1 (wje’w ‘0”) , compared to the original Bode plot of H1(a)) , changes as follows: A. The phase plot, AH} (co) , is shifted up 90 degrees. he phase plot is shifted down 90 degrees. C. The magnitude plot, 1H 1 (co) , shifts up by 10 dB. D. The magnitude plot shifts up by 20 dB. E. There is no change in the magnitude or phase plot. 11(8 ). On the next page, match the step response to the correct Bode magnitude plot. Place the appropriate number (1 ,2,3,4) in the boxes below. The scales on all step response plots are the same. The scales on all Bode magnitude plots are NOT the same. 14 1‘: Hwy (radius) Tm (soc) Sup Rama ; 1 z i 5 150: 00 2‘5 05 Rwy (radius) Tm (use) m an 20 33 €3.23: {.33. . :. iii: _i|(.|, .10 - ~20 35%.5 150 menu“- 5°T“" IO 10' 10' Tm (lac) nufiuiuJifirl “Muununnu “HUME «:owulx¢r~»nuu....»n»xv xur+»u-oruux.7:|wyno as 835.: Frequency (Ind/w) TM (sec) 14 (12)(8)MATLAB Questions. a.)(4) What does the following Simulink model simulate? Circle your answer. [ll—+3 u(t) d2)» dy A.——-—~ —-—— z: t dtz dt y() u() dy l B.——+— + z=0 dt 2y “0 C (z)~u(z)[i——1——1) b.)(4). Given the transfer functions H1(S) = 53 ~35 +1 and H2 (S) = 35 + 453 —— 252 +5 + 5, 6(5) = Hl (3)112 (s) can be calculated by which MATLAB statement? Circle your answer. A.G = H1 * H2; B. H conv([ll '31 1]! [ll 4! -21 1: 5]); , conv([ll OI 4! -2! ll 5]: [ll 0! '31 1]); D.G = poly(Hl) * poly(H2); l6 ...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern