ELEC 2120 Linear Signals & Systems (M. Baginski Spring 2013)

ELEC 2120 Linear Signals & Systems (M. Baginski Spring...

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Unformatted text preview: W ELEC 2120 Spring 2013 Exam 1 Name: ‘ 1. The Fourier Transform (FT) of x(t) is shown below (X(w)}. Accurately sketch only —— the FT of the following functions in the space provided ll 3) Y1(t) = x(t)exp(jmt) l 0 b) Y2(t) = x(t)cos(wt) c) If col = 10 rad/sec, what is the smallest value of me that allows the signal to be reconstructed after filtering (DD = — [O rad/Sec, Kim £31 an 2. Find the Fourier Transform of the following signals if X(w) is shown below: (place answers in spaces provided for full credit and show work) as Mt) = tzxm X09): b. y2(t)= x(t)*x(t) (convolution) 1 a+jw 821(0) c- y3(r)= az- a. .2. K9 . 3 Y1(w) = (a +42%} \O b. ' Y2(u)) : Kai?“ Jib-r)?" ,. '2- (C c “r, yam): Ok‘bw’ gm” imam Rafi/E AM) an arm (296.5: a) we we} @‘ZT 0” 7(er‘ :s/ZMVO)$(«1 5&1 : {6) (CLwagGg/‘i '\ : 2.. Linnea? M WWW xw— C.) dxél dZXLfU' pi_ { (5%} :W N < : QITIKQ Q OZGQV’M/g Viv} Ow) ( I I l i m M : Lawn} {51+ jw) : LONE”) z QALJ' (”“6016 41" 3%)“)? (CK-5w}: 1 42% I as "Ml 0v+/W“ :55in 3. Suppose x(t) = u(t) — u(t—2), what is the convolution of x(t) and 5(t—2). (make sure you state condtions)? (Place answers in spaces provided for full credit and Show work) \‘f xiwsu-2>=Mw 0,6255, 5:53:46“ or) {2254—3) I W?) Fl; {*(i—2);fi<~2=0 ti i2, 3 xl)£ Zfiéébl: l 9%”, are/:9 Mafic; O pot/58: f2(‘f-3> h. Only show a sketch of x(t) convolved with itself: x(t)*x(t)? §WOU fl _\ ., m. It/ x(t)*xlt): Ems”; ELLET CA7? l (22.4 00 Kira-i fifiQ—E Z El .4 '/ in i» m N C31 \ 3. b.) l -~-— \ f; (114%! MR 1 {£79525 az‘é : \ Pwlif. L, “gig” Hum/1&6. ”*5 2 find ma¥A03h412'2:q Siva 124"“ o 911 ‘6 MW My»! “Len 2x2=q I” 2 4. Compute the DTFT for the following signaEs: l0 “- (gum DTFT:M J l a"uCnJ<~—> T—T, 0.3—3 (EYUMJG‘KP W (3 1 § ,edfl Y, b. 11(1) u[n] DTFT = M11) 2 U336”? 3 6 mm.» (3MB: <33 é—Qé}:jn So, use: nan] 69 35}. W1} .64 ~ .. :JdTZU’ée‘JQ)‘ 5943C 3'6””(1‘3 /JJ(!~1e'Jfl)-L . I- -17. _ - 3°33) (1—3 “)1 I 2%,. 7‘0 ELEC 2120 Test 2 Spring 2013 Name: 1, A continuous time signal x(t) has the Laplace transform X(s). 5 +1 XS :— () s3+53+7 Determine the Laplace— transform for the following signals and place answers in box. I a. v(t)=x(3t—4)u(3t—4) VlSl= Sqfiqsgagsqj , 73544 l l l l l \/ 2. Determine H(s) and the time domain form of the hlt) for the circuit shown below using Laplace Transforms. Show all work and place answers in box. SKA) Determine the transfer function H(s) 9—" 5 b) Determine h(t) ifA = 4 and B = 1/2 §Q\:“‘XCS) " Agm “Q; Qlls+AB+0 : Xe) |~,1' ‘ \ L—l t‘“ " 5' m M r l = Llegé‘um a; :, M A \. 3. For the discrete—time system shown below determine the following: x[n] A ’3 3. Determine H(z) = Z’A' ZQi : AXI‘L) ‘LAQ‘ >23.) 1“ Q‘ 3. YCZ) i ’ ‘i z .3 \\ 0;: MA 3“ ‘ We (é; Mme} 2% rC‘} A 2W4 k 4 J“ ._,,...., W 2% z - A 2% C) b. For what values ofA is the system stable? __A—C> l? A: 0) MN“ 54' lies Uh (My? Lil/“CL; ' - - - N t > o if c. Determine the discrete time pulse response: h[n] : ' — A“ uCn] 8 5+4. \/4. Suppose a system has the following transfer function: H(s) 2 Compute the system response to the following signals: S/Va. x(t) : u(t) m = _(.Z_‘Z€_fl%).‘4[€}__ X6): E 8 ‘ A _ Z 2 a ram“ 3+ 3%: —- 2‘- 37; HQ—Ze “My <5 , 3"” aéng—O, A z; ig,@s=-% QieZ >«33; S?- V «I NM} 5 5'" SM 3 l 2% @5: M ) 3 *5 “3:263:69; 8“- 2 d 1’ \q‘“ :3” 3:0 7. '1. d 34441:“ {94.44}? @ > z...
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