mid07_sol - Autumn 2007, ECE 161A, lvlidterm ECE 161A...

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Unformatted text preview: Autumn 2007, ECE 161A, lvlidterm ECE 161A Midterm Tuesday, October 30, 2007 Name: (Last) (First) Problem 1: _ /Z?_ Problem 2: / 7 O Problem 3: If f 0 Problem 4: /Z(7L Problem 5: . f 23%" TOTAL: [100 Rules: 1. By writing your name above, you certify that the solution is your own work. Cheating in any form (copying another student's work, using un-authorized materials, etc.) results in an immediate score of zero for the exam, and further disciplinary actions by the School of Engineering. . You are allowed one page of notes. . The exam time is exactly 75 minutes. . No calculators or any other electronic devices. . Write clearly. That is necessary to ensure that you receive partial credit. . Cross out any work you do NOT want to be graded. Wrong answers cause you to loose points. . Partial credit is given ONLY to correct solution techniques, not to correct answers from wrong procedures. 8. The exam is 11 pages and 5 Problems. ONLn-ldeN \l Autumn 2007, ECE 161A, Midterm Problem 1 |x[n/2]| if n = 2k Consider a s stem described b n = y y y[ ] {Sign(x[(n—l)/2]) ifn=2k+1 —1 if a < 0 where x[n] is real and sign(a) = . Determine whether this system has the +1 ifa a 0 foilowing properties (justify your answer mathematicaiiy in each case): a) Memory-less Answer: NO Jere-ads an ’X [i] J b) causal Answer: No CH1 'x [*1] . c) linear Answer: NO Consider min]: SB] :3? : 8T“ Jr SD14] Cit/181 JIM 11V] 2 12343:; thin—3: 2 —1— 5 [V14] lire,th DEW—5 E’s? Noi liner-1f go ' 11l“1311[n1 -2- Autumn 2007, ECE 161A, Midterm d) time-invariant NO ’. 5 1W WW. ,9; 0 1w} Answer: A3 wt“) 313‘] = 35W+fifwfl 3 Lfif 3 $11214 [u — F _ ,._. .___\ Kiln};- BEEn-iS-fSEV‘I—SB AL/ e) stabte ) .ZI: fiin‘g é NDT I Answer Yes IFM<ZL[»Q< M w for Hm A. =7 3W f "1“" f) invertible? [ ‘11., "n I SM}. “moi gab]; a‘.[-Zn].9(;[Zn-I], Answer: a I? “d” ehwdm n im 101_S~ 29% mi“ ewflg' LL” Wind E0 [ -3- Autumn 2007. ECE 161A. Midterm Problem 2 Consider y[n]=T(x[n]) to be the output of a time—varying system T such that yln] = T(x[n]) = a'"’”x[ni, where is the floor functionl. '1- n- (a) Draw the output, yl[n], when the input signal is x1[n]= E(6[lk]+ 26[Lk+ 1]). 4‘ ""°° (b) Is yl an energy signal? If it is, compute its energy. at“) mom}. curl final/(9’3, 3'15th , git’me id}[y13 gums ( . a Ca ' a In :00 unbcwdedla ch-JQ a mfor H n( ; 50 1 If you do not recall the definition of this function, see the last page of the exam. - 5 - Autumn 2007, ECE 161A, Midterm Problem 3 Consider the following discrete—time signal X2[n] = Sin(rr+ l—EMcosEn) — 1). Determine if x2[n] is periodic. If periodic, find the fundamental period (the smallest period). Answer: Ii is no} the. (tactic, l S:.n_<r(f”_1:_) z}; Sm (R+ for m-Jreaa/T i Autumn 2007. EOE 161A, Midterm Problem 4 A left—sided W signal has a z-transform of form -4z2' X(Z) =m. a) What is the ROC offiz)? Answer: “am I} ,5 [21% S’in ROC=ij%'<|§flilzl<alizfifll<£§ b) Find x[n]. A2 3 1? X0?) : ___.___..__—+ . (%-l) (2,02,) 2:] Sinfe mpg {'4 NH Ldzdfi: Mqfiugnqg— («v—)“LKH'G fig Autumn 2007, ECE 161A, Midterm Problem 5 Consider a causai LTI system with impulse response, h[n], whose difference equation is given as: y[n]—2y[n — 1] = x[n]+ x[n— 1] a) Find the output y[n]for n 2 0, when the input is of the form x[n]=1 and the initial condition is y[0]=2. (i) %C["‘]: (XXL—2019124 =0 as Qfi2:o =9 “:3” %C[nl:d2n c2» "2%?th :6? T's—4:» Pa 2? = 1+1 % L3[“3"l3c[“3+‘k9{"1=0{2:1 ——2 “03:01.21 :1 :9 out fl 3543: 4 b) Assuming the system is at rest for n <0. Calculate h[O] ancii h[1]. Deriye the hm? no}; , 14D]: h[‘qi‘ffi‘: 333493;; km?!»- nn‘xr— tan is an “>0 (“Mm 5‘“ W” @ V1. wingsotz Vnpo was mi WW 2 “2% htnfiyataiamoisin $42) + a’m- Min-Qa— ...
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This note was uploaded on 06/30/2010 for the course CSE CSE 161A taught by Professor Javaidi during the Spring '10 term at UCSD.

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mid07_sol - Autumn 2007, ECE 161A, lvlidterm ECE 161A...

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