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fa2003_exam2soln

# fa2003_exam2soln - ECE 210f211 Analog Signal Pracessing...

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Unformatted text preview: ECE 210f211 Analog Signal Pracessing Fall 2003 University of Illineis Sarwate. Mitefsky. Kudeki Exam 2 Thursday. ICicrcrher 30, 2003 — T:Dﬂ~3:15 PM Name: (Please Print) 0mm ECE 21c ECE 211 (circle one) Secticn : {circle one} Please PRINT ycur name and circle ycur ccurse and section in the bcaes abuse. This is a clcsed back and clcssd nctea eaarn. Calculatcrs are net allcwed. Please shcw all year wcrk. Backs cf pages may be used fcr scratch wcrk if necessary. All answers should include units wherever appropriate. Gccd luck! — — — — — F'rdblern 1 (40 points): ET FZ—L—u Hr L/ W a) (lﬂpte) :. l f 43:: 2- 1. Haw mueh average pewer ie the eeuree delivering to the lead Z L? d 2. What lead Z; will draw the largest are-aunt of average pewer from the eeuree? b) {1Dpte} 1. Find the eenetant W: fj— :- f NE:- 1 “1a, 2. Find the eurrerit ﬁt]. c) {ﬁpte} Let Mt) denete the stead}.r etate reepenee ef the system to input ﬁt). flit) eff} 1.er False? The system with input and eutput eheam belew eannet be mg ,. . —~ and _I__ i *9 59% , We”; liﬂEElI. _ L4- I'm: '{ M Cw {st—«c , 2. True [email protected] that ﬁt) = 2 and ﬁt} 2 D, the eyetern can he a law-peas er. g“ law._'7h.h 51¢an f[{j:2 M! W W WWJE“ r 3. True er® If fft] = (leaﬂet) and yft) g —u.1 ein[wt) then the frequent};r r n in =—'r.u. ’ ' eepe SE S f } .i' ltd—Fl j 1(:(__,LJ)(#J):JOJH F I :- d) [11pte) Ceneider the signal ﬁt) = 3 + 2 eeeﬁﬂt] + 4 (3::th + U L! L! .ee Cw : 1 LWht'th £15? a. “Z '1 = “w- ale eaveragepewere L3} 13:61:?) +éci féﬁl:ﬁ+2+g 2. What is the fundamental frequeme},ir of ﬁt}? pm “if: : 2 3. What is the Feurier eeefﬁeie er the Feurier eeriee in expenential fern]? Problem 2 (2D paints): a) What is the value 0f the phasm‘ V}; in polar form? Preblem 3 (2D paints): Censider the fellewing system with the frequent}:r reepenee H (ti) = % > May it R run, IL\ 3 {L +- +_5_JWL- n, H0“) ; 1 = ‘2? 3) Find Hut). F {ZwLﬂ ___ H, H(W): L E * K461“); ""_'—"'__"'.-: b] What is H(|'.U} in the limit as n: —+ DD? L‘ru— H (“1) i 2— “ ﬁcTWhat it Hen) in the limit at t: —. n? H (ﬂ) I I dirt}! (a) ti) When ftt} = 2 + ttttttt} it it ttttd that the tutttt it ttt) = A + e ttttttt + 6?}. RHIH (“H”)! 1. Find A. A: :2 J‘- H (I?) I: :2. 2. Find a nnrnerieel veine fer B in the limit as Lt: —t ee. B r: ‘24 Minuet)! = 2 3+ Find rt nnrnerieel value fer f? in the limit as tn —: ere. 6:0 r’ﬁq‘nu— 4 H(f"'3‘”>= C3. 5 Prpblern 4 (2!) points): a) A periedie signal ﬁt) is the input te en LTI system with fre-tplene}r respense HEw) = ij. The entpnt is p(t) = E?=_m ﬁrs-5”“. Find the expenentiel ferm ef the Fenrier series fer the input ﬁt). r , E Y *1 :y—L—ZQ M F? a; Ym "J L :__:____"_":_._._-+ 71mins) Haws) How) Jaw F 2 "HO-4M1) b) A periedie signal pm with peried T = 1s hes the value pl[t) = e“ en the interval D s: t s: 1. . e“ 1. Find the DC level, ['33, for ﬁt). . {C Q &\ 2. Find the Fpuner series fer pEt) 1n exppnentlsl fprrn. ___l__,___ i- _(____ 1 37 1| 1 { ti— ‘ E “Fa-"L" air: aidsifﬂrrrﬁ“ 6M:...-|- ‘( Q «a DUC- f" I f’ H(I+j£np>t __ (wan-n54; L mam) "’ f 6' 0H: : a" :: if, PHI _- ' _Hh' Fﬂ______———-———""'——-|- '3 '- (HJEW‘) r([62‘m) :51 I F-irl fﬁ ML 6 ————- ___P______.__-_ _._. -l F3? ...
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