{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ece366-06ex2sol - Name Solutions Student ID ECE 366 EXAM 2...

Info icon This preview shows pages 1–6. 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
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Name: Solutions Student ID: ECE 366 EXAM 2 November 17, 2006 N0 textbooks, notes or HW solutions. One page of hand—written notes. Calculators are allowed. Exam is 50 minutes. To maximize your score on this exam, read the questions carefully and write legibly. For those problems that allow partial credit, show your work clearly. Good luck. 1. [20] State whether the following statements are true or false. No partial credit will be given so you do not have to provide any explanation. a) b) d) e) D An audio signal with 101-112 bandwidth is transmitted over a channel using AM modulation. The minimum bandwidth of the channel should be 20Hz. .1. The Nyquist frequency of sampling for x(t) == sin C(SI) is 20 rad/sec. Xiufl 1: JIFQCT i (NS: \OY'ad/s-Fc ‘11:. 5' The signal x[n] = cos(3n) + cos(§7m) is periodic. 4' . "i: not pen and C ' For a real and even periodic signal, the Fourier series coefficients, Ck , are always real. T The power of u[n] is 1. W2) F The spectrum of a periodic signal is always periodic. ii’r’s discrete, ~— hot’ponociic 1“ g) The ideal lowpass filter is not used in practice because it is not causal. T h) If a periodic signal x(t) has Foufier series coefficients C k , the Fourier series coefficients for the signal x(—r) will also be equal to Ck . "F: i) The inverse Fourier Transform of e‘za’uMJ) is 1 . . .d 2 '4‘ Jr Duality e, um é 3+5 u.) l K’ 1;“: . 1mm Mireflwulw) j) If X(a))=tri(a)/2),then jx(¢)d:=1. 03—” ’t SxHScH: Xl0\é i§> w 2. [40] Consider the ideal sampling system given below for the continuous time signal with the spectrum given in Figure l (a). Let Q = 8x,a)2 = 1071'. a) [5] What is the Nyquist frequency of sampling for this signal? b) [6] Assume that this signal is sampled using the ideal sampler shown below with T = 0.5 . Derive an expression for the spectrum of the sampled signal, X p ((0) , in terms of X ((0) . c) [10] Sketch the spectrum of the sampled signal, X p ((0) , you found in part (b). Draw at least the first 5 terms in the summation, i.e. k = 0,:t1,i2,i3,i4. Make sure to label the frequency and the amplitude axes. cl) [6] Show that you can reconstruct the original signal from the sampled one. What are the values of A, a)“ , cab for the bandpass filter shown in the Figure? e) [7] If the sampling rate T is now increased to 1 sec, can you still reconstruct the original signal? Sketch the spectrum for the sampled signal, and discuss Whether you can recover the original signal. l) [6] Show that the sampling frequency used in part (b) is less than the Nyquist sampling frequency. Explain Why we can recover the original signal even though we sampled at a rate that is less than the Nyquist rate. XI 11.!) p(t) = goat—M) n=-w (t) plt) 1 T t H( m) A —wb —wa (9a “3b ‘0 (b) ! ------—-mvwmmmmflwngw‘ymmm"mammwlawman-pmw—---uwumummymwzrmmwmmgrmmth—m—v—mmmmwmmnwwm minwulWWm WWWmmWMH.WWH m Extra Page for Question 2: a) U.) 3 —: ZUOTT) : 201T rad/sec. I fiXkawQ {JO NVOWVC‘SJY Samph‘hS we can S‘hh rcconsWt‘r W b d QOTY ? WW g0 nag» becoLM/J e Ifi ‘5 a flarf’ow an W91 ‘ \J ‘ a} , h0+ bom d p083, gxgw" . 01$ {GIT . mmmmmmmmmmmmm -v—uWW.WWWW—_ 3. [40] Consider the system shown in the Figure below. Assume that sin(1 0721:) x(t) = sin C(ZOmf), g(t) = cos(87rt) + cos(16m‘) and Mt) = 72': a) [6] Compute and. sketch X ((0) . b) [6] Compute and sketch G(a)). c) [6] Compute and sketch H (w) . d) [6] Compute and sketch Z (w) . e) [6] Compute and sketch W ((0) . f) [10] Compute and sketch Y(a)). sin(x) Hint: sin 00:) = x 0O XKLUB: V96] V by Stub : WY 8‘0???“ +g{w+&fi\] 4*“ [Slow-SW} Skeet/61:3] (>th ’Y . U.) *iéh’ “SH 831 HWY mWWWWWWWWMWWMWWMWMWWWWW W ~2 .. . WNW WWW-VWAWquW ‘ (:\ hhfl, gm {tout} : 4OS\h(‘_UOTTJC\ *3’ refi T “W » x w fixon' 105i] 1-; i6 rec [jg->40“ MT cu - ‘ .86) +Stw+$sfi31 in g Q} : umtw K m C31 Km)H\wB —~ gr: en c " a 4 DC] *fiWkLU) mumphfcdoohmh‘m m My, my fit to 3 his mmmqu) ' Wt») 3}? :Z'Kto— 81‘) +1” %\Lo+&Tt)] sol.“ zfi Extra Page for Question 3: BL redrka Jarec‘r(wv‘<§‘w\ +~_\_ Y~€C+KW+<§T :1 3’0“ 2 BOW 20 16W T \ FZCJT (Hg; 3 [(61% \wwg-rr\ + rflfi w+§fi~\ UO 30W 20W 201‘7 Who) 3? AWWW“MWMWMWWMWMWWWWWMWUWWM ‘ w W annmww—MWWWWHW ...
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