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ps1_solns - SOIuHonf Michigan State University Department...

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Unformatted text preview: SOIuHonf Michigan State University Department of Electrical and Computer Engineering ECE 366 INTRODUCTION TO SIGNAL PROCESSING Problem Set 1 Spring 2011 Issued: Friday, January 14, 2011 Due: Friday (8:00am), January 21, 2011 R5“ 1. Problem 1.1-1 in Lathi 2. Determine the power for each of the following signals: (a) :c(t) = locos(100t + g) (b) x(t) = lOcos(100t + 335) + 163in(150t + '3') 3. Problem 1.2-2acd in Lathi 4. For each signal given below, determine mathematically if it is even, odd, or neither. Sketch the waveform to verify your results. If it is neither, then ﬁnd the even and odd parts of the signals. (a) m(t) = 5 + e“ + et (b) x(t) = sin(3t — 7r/2) (0) \$05) = 5 + 64 ECE 366 5pm} 30” P51 Sewn...” l) [gall/.300 426‘ (6))a Jt E I (3%) + 6:) 0/3,) (D E? 607%) + (03% : a/:' +V3 f (3/; +% 2 I : I © E= (0)“! + (03% +(—I)“'/z QD E:(3)39/1 +6507; : 8/; +Vy . : WWI) +00%? ”— I : L1(3/1 +V3) v :~ V (I) : LI —/\/ejm~3~lhj or" "Ema ’jLE'IE‘Hnﬂ ‘H\¢ fly/ml Aa/ no efﬂp‘)‘ on ‘Hm emch of “He, J}]na’, 0’ IbﬁCQ ' emery if Com/pain] by "MC 171+»er o f 7"}‘e f‘j’m’ thartd OinJ (fa))a : (‘ Fa))a , M“. I 1%) J1: : I (- FAWUJC a A 4),)‘6 JIWJC+¢J ﬂj’m’ f7(}/l [Ml ’Hm Jame are“. (Athr Hg, (MN/Q, frOM ‘00 +9 00 ﬂ pound/7 Hy «V‘lﬂIm’ 11.1qu In W"! ln—trj/V er} ;I V +I.Ih6j "Hue orijina' an”); (a fﬂf: [{F’ﬂ) _ If rat/Hpr’uyl 17/ K] emery Wok/J [)0 K1 ‘Hmcf 00 a A 3 0° (1 __ a -_500(H&)) J+ , {54] «you — I< Ef Dv’w‘rc Ef: £:€FC6))5LJ{ lawyer ii) P~r I “’21 4 t“ "”' ﬁfy Mac/e 00 T6 3 Tail/£2351 0 @ me): I0 w (100%: +772) , t T/ a P7,” lam IT; R OCOI 000% +TT/?)> (If I T9 ’° '7; *COIR(X) : M20 + cola—)4) Noni Tim 2; Mp He arn/’;+V\J¢/ fthanJ or A;L : mil 2 R TAMI/Hm power in o» JinuloiJ 31 all”, +0 /% and 'u ‘Hnreﬂre FhJLandcw} 07" frzzuuwc/v a—hJ ID‘IAJL, (9 16(3):“) an 0004, +177) + 10/1?" dioé +ﬂ/f) T/ F679 3 m Vrflﬂo WOW“ 77;) ugméfow '71)];11? TM #173 T : Hm VT J A600 magma #72) + 1.3—6 Jinaafoe +TZF)+I60C01(IOO€ r71/J)rin0{ot +77ny T900 7,“ \—\r—’/ KHZ from ,[email protected]’? Pf Jaimie cr gaging; o TAM! ‘Hu, [)0sz o?‘y ‘Hm, Jam 010 070 JHﬂ‘Pcrcn‘IL Fraabmmz/ if 5’5““! 0 7d +A€}f :ﬂJIVJJua/ Fowlr/r Jam w fihujo iclj +0 7% a») xéc} “rib. (Ye—VA) : *c0f(36) 1.6%) : ‘COI ('16): ‘(_01(3€) w) : 1,66) s_ ”(raw © 7‘8): f +o‘t 7&9: 5 +c/0 79%) i Let” 7&0 #‘Xéﬂ ﬁ 766% U no+ man or 04;! chF Va 6+5“ +1“): Ado we“) 7<10G); Vaéﬁe, ”f 2.3") /a(e w) (j: L 4143”“ —-> we) *9 7906c) ...
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