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Fall 2004

# Fall 2004 - ESE 337 Exam III Fall 2004 Name ID no 1...

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Unformatted text preview: ESE 337 Exam III Fall, 2004 Name ID no. 1. Consider the CT signal x(t) = 2sint + cos 10013. The signal is to he processed digitally using the sampling period T = 0.02. Design a DT ﬁrst- order digital ﬁlter with bandwidth 0.05 to eliminate the high-frequency component. (10 points) What is its steady—state response? (10 points) Roughly how many seconds will it take to reach steady state? (5 points) p z m; ,7) a, ; pf? : M! -H l l V» ‘ I . "(2:‘212 :13 W ”M, 2+! E yji{ﬂ/flty H ) 1. 24¢ 2’23 2 3.1257; l 9(L'VI'I:Z§='.4 nf+ dad/WW7 (Trail) igs.’nuaﬁln+£~b2h J9”): _,_‘, 571‘]; v H (6’9”) : ‘7 ‘2“ .,-——-——-e ? A, ; 6.?3176J‘} :6995/7é ’31’3 €10,9L‘051‘: ' -’ , e £1.21, , Mm .‘J‘m3 ~0;0‘/é5’¥.-95v% We ) .7 u I?“ 5;; 5* 515ng ”Stella Mfg/AL yes {if} 5 2 M2. 2 #31; 5% wzn , 0.37) + My mum/Jr) ‘73 silently? £457) 4 «Hi 6W (1“ V“) ‘23 Ms‘ésm. M14431) .__.__——_————— o<: ’lhy/{n/o 5 I’LY/kh (2-7; : 3X {Sm-7.1m} H mm m : /-7é ”maﬁa 2%» vw’l SW) W“ 2. Consider the Signal in Problem 1. Design a digital resénator to pass cos 100i and eliminate sin t. Design also a notch ﬁlter to achieve the same. (10 points) 7 "’5 7‘: 6&2 (T £7912 , 7:23 ,wu-ufijdxj 11235171 binge {WWW/“3' VJ ﬂies Xtaoz .— 2 72¢, vwv'triiti‘iwfa {fifwn‘al 2f.) Suki r3 /;< 7 : .2: 02 Ma (5M safe of w ierﬁéﬁ‘ Ky) 0. 93’ 2(t’é) = aoJ’ :5 6% : ag7f New)"; {ﬁfe/L: (aim? char/32. \$73 ) > £2 ' ejavl )Ca ’ 62-11-4101) Mia) ; 2 (g ’ Delve/v.02.) ( Z “9957! 67334;) 3. Design a 2nd—order type I FIR ﬁlter to match In the least—square sense the desired ﬁlter Hd(ej”): D(w)e 5‘” with _ 1 for w in [0, 0.8] D04) ‘ { 0 for w in [1.6, 7r] at w_ - 0 2 0 6,1 7, and 3. (15 points) Compute its total error. Also select an arbitrary d[0] and d[l] and compute its total error Which 1s smaller? (5 points) 2140? [IQ/IL“, ’i’ﬂ'e ,7/‘7’3 {MW Mm: mm 1250?” +1511 '21 , 115015452) 3 -w J4me”): “mm a J 7 11(6’V}»~D(MJ6’ t> 1.1mm 649+ M07124”: ptwe’i” :7’ MIN 24507“ ""ng W) ; pm 9 AD] + 212529] Czech.) : Dies) 4% ”2507” ALJ/_a€,:27:24 z°l , i / W ,e ' v é Jﬂ“ / Dual-7 ’ / 60:9; ' , ~ 1- “ {2”[0] . / h; /. W'jujr’lé If? ,1 4’ 5/59.: I); .j l a ,, y: (m an / ,1 é‘L'f ‘ x M 3 b, ¢1.[/-u1£(¢ / I PP; ' 4: 055,5! v-l’ocJ/ / _ x J. : 2 and awe; I WI '”“‘””5” » ”W7 .; gammy; : (Pa-W) #0415 75“ / £0,1va " 6"?771 + w-31r7z+ “757; ; C49 37 Him a ,5 2,17 ' 2"; ' W ~_ '7 "144\$ (,9 “NIL-‘2 ' - 0.] 3‘1 f— 0" I (I 7 J L 7 “SI-rmtiwt ZN”? ) 59W 0150710907: 77.3" 72% {ﬁfoyf’wm ‘5 "”1371”; > ‘7- ”’7 ' -4. Take home: To be handed in by Nov. 30. (a) Use MATLAB to simulate the design in Problem 2. Which ﬁlter, resonator or notch, yield a better result? (5 points) (b) Design a discrete least-square optilnal type I 4th—order FIR ﬁlter to approximate the desired ﬁlter Hd(eJ‘") : D(w)e‘j2“’ with _ 1 for w in [0, 0.8] D(w) — { 0 for w in [1.6, 71'] by matching at frequencies w : 0.3, 0.7, and 2.2. What is its transfer function? Plot its magnitude and phase responses. Do they match exactly Hd(eJ“’) at the three frequencies? (8 points) (c) Repeat the design by matching at frequencies to = O : 0.1 : 0.8 and at w = 1.6 : 0.1 : 3.1. Does your result close to the one ob tained in MATLAB by typing f= [0 0.8/pi 1.6/pi 1]; d= [1 1 0 0] ;h=fir1s(4,f,d). (12 points) I 1 ...
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Fall 2004 - ESE 337 Exam III Fall 2004 Name ID no 1...

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