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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 unauthorized 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. ONLnldeN \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) Memoryless Answer: NO Jereads 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 liner1f
go ' 11l“1311[n1 2 Autumn 2007, ECE 161A, Midterm d) timeinvariant NO ’. 5 1W
WW. ,9; 0 1w} Answer: A3 wt“)
313‘] = 35W+ﬁfwﬂ
3 Lﬁf 3 $11214 [u —
F _ ,._. .___\ Kiln}; BEEniSfSEV‘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(;[ZnI], 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 chJQ 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 mJreaa/T
i Autumn 2007. EOE 161A, Midterm
Problem 4 A left—sided W signal has a ztransform 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 MinQa— ...
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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.
 Spring '10
 Javaidi

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