sol_test1

# sol_test1 - 1(30 A digital communication link carries...

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Unformatted text preview: 1. (30%) A digital communication link carries binary-coded words representing samples of an input signal ma(t) = 5cos(5007rt) + 23in(15007rt) The link is operated at 20 kbits/s and each input sample is quantized into 1024 different voltage levels. ' (a) What is the sampling frequency and the folding frequency ? (b) What are the frequencies in the resulting discrete-time signal ? (c) What is the resolution A ? (3}' 1:}: 0“ His /\$am?le_ s: [062102.4- =10 E 20 000 lads/s = . g = 2000 samFLs/sec lo bu‘l‘S/sawk .‘Félclihg F04- 1:3; loco Hz (b) cos SOOTT‘l: -——> ‘VQC‘UQBU1 2.2.50 Hz a F. sin \Soo'n't A. frequenu) = 750 it: = F1 iheve is ho aliasing actnla Scos 500111; + Isin (sooTrgL F5 F5 .. S‘cos Soo1T-n + 23]“ "scams 7.000 7.000 » '-‘ SCOS 11"“ +~ Zsin 31TH a—n—u. 4' ‘t L—‘r—J L__..¢\I 4': VB 2" 5/8 “l A:- xm-xm = 1—H), _\_‘L 1024 --1 102.3 102.3 2. (30%) Determine the convolutien y[n] of the signals \$[n]__ %n, ogngs _ 0, elsewhere 1, —1 S n S 1 Mn] - { 0, elsewhere analytically. at“) = 45n l HEB] "' uEn~cjf Min] = uEnH] ~«En-1] 1 :=> SEA]: kana: 1C5]: Z ktkjoxtn-K] -.-. thh‘l‘] [(2-00 K...‘ = a‘llh’ril+aL|‘_n3+:chn--1] ﬁr n\$~2 9Cn]=o .o 0 3&1] = 3E°1+xw1+xtﬂl a J3...o O 5E0]:- ‘ Ji'i + _L.O : 3Cl]= xCZl +xC13+x[o).-. luv; 3E2] = 1Csj+xfzjx+xﬂn= 1.3+ 15,24,1“1 : Z 3 3 3(3): xE‘tl HCD'J +xE13= 13-.Lr+g—~3+J3--2 = 3 BB]: xESJ-t-xi‘ﬂa-xDJ: -%-5+.gt+ +153, :4 3C5] g 1713+;E'53 +xl‘ffl = %-.5 +15% = 3 rate]: 471111;?) +xtsg , is g ,5}, 3 n7,‘1 jmz-o 3. (20%) Express the z—transform of “711:; wik] in terms of X(z). n-S. ‘ 5Lh-11' Z. “LE-K] ua—w ‘ » 5-1 ' ‘ , a 3m: 2; MIR] 4- a.th =3Ln-11+xtn] KJ-ﬂb A Pp h) inf) 2-+ransfom\“ «(aux-271% 54(2) 4. (20%) Show that the following systems are equivalent (a) y[n] = 0.11471 — 11+ m] — 0.5422 — 1] + 0.04947; — 2], (b) y[n] = — 0.4a:[n - 1]. ' Apply‘mg Z—hanslovm +0 Cal ‘ﬂzltl- 0.1 i‘] = Iii-0527' +0.04i21' 34(2) Now, ‘ applying 'Zw'hramlom 4-0 (In) «(an D ~0~4i']><(2] Tlxuutue , (g ...
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## This note was uploaded on 02/26/2012 for the course EE 4150 taught by Professor Wu during the Fall '10 term at LSU.

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sol_test1 - 1(30 A digital communication link carries...

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