ece340_exam_3_fall2007_solution

# ece340_exam_3_fall2007_solution - FALL 2007 (11/27/07)...

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Unformatted text preview: FALL 2007 (11/27/07) ECE340 (Engineering Systems Analysis) Name: CE/Z/m @ﬁlnﬂ, Exam III l. (20 pts) Consider the following continuous-time signal. x(t) = 5 cos(6m‘) + 3 cos(87rt) , The sampling function is given by p(1‘) = 260—117") . a) (5 pts) Determine a minimum sampling frequency/f that enables the perfect reconstruction of x(!) from uniformly spaced samples x(nT), n=0,l,2,---,where =1/T. Nam/mm w m : 4 QciWﬂ/Wy fréﬁ- '7 2 7Z‘ma/Y : 49 b) (5 pts) Plot the magnitude spectrum ofthe sampled signal x‘.(t) , :10) o, )(s )(l‘f’nis) /lll‘i:1'l0"'l’l9 dl-S ° 6+ 60vﬁ'5’7‘ "MN c) (5 pts) Plot a block—diagram of sampling of x(t) including a reconstruction ﬁlter. '1 it) 44%) i '2 Ft) L PMW, > l H (n 2 T W) C1 'l'yl d) (5 pts) Plot the output of the reconstruction ﬁlter in the frequency domain. “5/1, . l/L same, Cu ’7 4.- FALL 2007 (1 1/27/07) (20 pts) Determine if the discrete-time system y[n] = x[n] + nx[rl +1] is: a) (5 pts) Time invariant No )(W'Heﬂnxfﬂekﬂj 1‘ gmsz = 7((nvk7+(nvk> Xindh—l] I 5 Tine var/7W} b) (5 pts) Linear Yes, QITHMMﬂ—i—m‘rﬂtwﬂ VA Mun) : 0M1.th +CNL7h—(V‘) (V9 ; 0\,1;(‘n)+d;7\LK\/Q + n(0\1,(v\) Arm XL g; : 0\\(1\(V{3+7‘1\(V\+|)) a; \V‘) '+D1LKY\+|)) : 0| ifM) 4' OJ.‘ LCM] C) (5 ptS) Causal g g % fer; +0 T/u- 74/47/114. v(’\/b/1‘¢ zlyH-IJ NO) 7m) {6 mm] a d) (5 pts) Stable No (JO/mm Xi“)=u(m) #04): H(M)—+)’>~U(M+;) (707] /\_{ unéowmplzo/ (U new. i n q 3. FALL 2007 (11/27/07) (10 pts) Consider the following signal: x[n] = u[n] Suppose that this signal is the input to a LTI system with the following impulse response h[n] = u[n] a) (5 pts) Determine the output ofthe system by using convolution. k:c k=0 3- , n [i I'— '— 2) (3,)' 21’?) M .Z O b) (5 pts) Determine the output ofthe system by using Z—transform. _._.L Iii 7 “L XH); /’ {:24 3 i i ‘J: ﬂlc+imfv “(2’): a/l’ i3’i 7‘1. ‘30.!” pi? / l L a 3 7 -; -l» x W? / WW) ‘5 “’T‘Tf/fw 0:4" )’ (I,§.Z’)(l’z, ‘5 )1 i ' /' n, ( - W): «2/1) WM Mg) w w) t » ‘ Z _ 4. (20 pts) Consider the following causal signal: x[n] = 4n cos u[—n — 1] a) (10 pts) Compute the Z transform of x[n]. - , ﬂZO AW7- {0 } n .71” > ’4 f. " AF (09 ( 3 00 .-n J -n —' ,1 If) — AL ‘ X9): 2, 4 «>4: )1? E}, Y1:—0° ‘ - r 00 (1%”) Uh") n , —— - ’ +6 . t A- 2' ()2 >’:& ‘ Hi 321% 1:1? E ( ’_ ﬁila I}, |.- Ell-ff ’ —’9 4&1” L 4 : 1(6"~r€"’)?'2 _ 'e— Me—‘i‘réﬁﬂ Jr *1 . , _ 4 l - awe-9H , Jr‘a9{gﬁ)¥2'l+u,~2—L FALL 2007 (11/27/07) 1 ~ - h ~8f .>_)1:| V -11 7- ﬁjﬂ >~ 1(46'2Z “H46 ’2 a? Z '6’45’)’73"4€’~3 +2”) 4699{% -— Z-Z — '0 1' (5 gr yum} [ _ 2+" ﬂ (. 45+ H721 FALL 2007 (l 1/27/07) 5. (10 pts) Consider the following signal: xln] = (n — HG] u[n] Compute the discrete-time Fourier transform. 6. (20 pts) The LTI system has the transfer function, H (60) = A(a))eje(‘”) where b) (5 pts) Sketch the output signal y(t) FALL 2007 (11/27/07) I 271 1+AAcosLZwJ+ABcos[3—Zw] hols—T” 14(60): 2 2 27: O imp—T" @(w)=—a)a Given the input signal x(t):cos[:21—%i£t] and a210, a) (15 pts) Find the outputsignaly(t)_ )A ' km» ‘13 £7” ,);ow AA ;/%',,o)w+é’A’Q/—JQ’¥IO)W+ége/J; ’ 6 H0”): 6 + 3 e 2 Yw)‘ HMXW} V 1”", o +_E’Tﬂal AAqit+g/’°)+éfditrg”o)+ i‘ﬂ‘b‘i’ﬂ I +L ( t ) «HLjHj-édik’wﬁii w/ WT V/FZH’IHO‘J el‘cl' OW (IanCJZﬂ,Ao-:Wr _, o ; 0‘ ...
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## This note was uploaded on 10/06/2008 for the course ECE 340 taught by Professor Djordjevic during the Fall '08 term at University of Arizona- Tucson.

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ece340_exam_3_fall2007_solution - FALL 2007 (11/27/07)...

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