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ps2_solns - SO/M‘Honf Michigan State University...

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Unformatted text preview: SO/M‘Honf Michigan State University Department of Electrical and Computer Engineering ECE 366 INTRODUCTION TO SIGNAL PROCESSING Problem Set 2 Spring 2011 Issued: Friday, January 21, 2011 Due: Friday (8:00am), January 28, 2011 1. Problem 1.4-2 (only for Fig. P1.4-2a) and 1.4—5b i i 2. Problem 1.4-3d and 1.4;_4abcd in Lathi i“ 'J 3. Determine if the following systems are linear, time-invariant, dynamic, causal, and stable: (a) y(t) = 2:1:(t + 1) + 2 (13) W) = 3&0?) (0) 1105) = fix, x(T)dT EC: 3((/ j/rlnj 510/, F5; I0/M71140I7/ I'V‘Ra, (1 “I R t") I; flr(wé):£u€°) 0“ —> [email protected]+m):<‘t+m)[email protected]+w) / H —> 9414+!) ”I 13 Vr6€+l)- a r&) + «Me-a) : $66) 011/ fi(€)1‘1£+‘i , ’Iéééo {63): awwaxw/ oéJcfi-R 10] a) 3 0 j dick/Acre, 10%) : Y(€+)) [qééwLO ‘ WQU] “ag‘gd Eta) “fig—'92)] a w, +:) mew - Wm) warm—mes) mé-JMQc-a) ’ ? VGEH) (4,6614) ‘(Wc +V+9Vc40m€d +1Q-2)M,(f'ol) Fee) : VEfiH) M1624) - {£M/G7) + 1&3’J)/4a€671) mo) : Lirfm)» éréé) + 146—3) ‘I (:90 Fa): JP Vr(€+l)~6r(U+2 @ Te ~ W08“) ‘ fl— ) 6M“ +&L (t-R) J37“ “WU—WWW ah : L/ ”wwmymw 45 m” - 5 5(6) + 1 Me 2) I . ‘f _ V A“ H“, fluowh} thralj Can £6 QVfl/ua'lacl (AIM; "HVC f‘I‘F'Hnj ffefif’by 9: ma Mm)“: (2(7) @ gimme—«gm : 1(6—0) : @ 03 food?) (Mt-TH? : -00 © 5 (Mt) JWu 2 e: ““4” ~ Q) i0005(a€‘3)5}n6‘r{) (It : sin (3;) : 3' @ 73}: 9x766640+9x .m )z'({) ’5— }%,(f+/) #72 /}(€} 1 27‘; ((4’) +91 it" 768) 1 axfi) +L7<A(f) HM )zwlR[m%/&+’)+an(f+l)]+ozj\# Lu‘b “7.01) 749/310 : migxléTU-hl] +£[[email protected]+/} +2] IMF-f inpu‘i': 9a) : ng'éo) 7w: agwm = axwwo +2 W 5m mm: yea—g): gig—.160“) h; 2 — Jynmm? YE’I SMCQ. 7G) rI; szanzn+ on 7C(f+/)/}+ JZ/{ntl/ on Pu+ure Vn’MC/ 010 H16 Mpm", szwell on 'Aff‘w" VQI‘W—f 0F ;/I/M'7LI ‘ 5 +aLle/Y YE I am f9“) )8) U LOW‘JQJ 0) ya) = 3% x64) “ Linear ,?“S:E5 We) : 3% 14a) yaw : Z ‘é 7187) 310 we): Mel“ + “10“} Hmen 7(6): 3‘6[W19/G') +bx3'é] 0L;,(£) + 194%} : 3 15 (a, %,C‘€} + 5799,69] D? A0: iJ 51.7104 énpm‘; 9(4): xéc—fi) yG}; 3.5 7663—5) fl% noyl efua/ fA‘;$-€ ou+fo~+ .' y<€fieo) : 3(6’éo) 76(f’fl) only dqengd on 001”sz inptnl' (— comm/.7 YEII on'y (lapel/ulna! 0" currtn+ I‘fl/M7L , fl/o {L‘fure ;"pl~{f, * mug? NO} fln'n‘e, m/ (fw/ém V‘E/fygflé 3Jcm ‘VL‘E/ m taco ,(é/ u A/OT boundcd. é @ fie): X 74mm 00 4W, 5: 'MCUJT ; 2’94") S: ”MINT if 70G) :- Ov 70/4) + £7919” Hm ya) 3 j: @x, (T) +57% CU}! “C 3 «‘5: 70/604 “t + L£:769\®)J :5) 5 efad [email protected])+b,v2(é) 3 mi vowel“: + 12;:xaCcM? SIN?” ,npa+ jg) : 766544)) T dtl:dt FE ~6o VG): ,: 3 WW J:x(“c-éo)4“c:_£ xtc'uz' 5;"Ce. l+ }/ an ;n+¢jr‘l Fro/V1 ‘00 +0 ’6/ [17’- JLPCVIo/J 0h fafi Valau o74 “W ill/MI? 1“ Laufal 7 YE}! o—flHle J] on I’m/+011”! curr£n+ Value! 0» 'y chcn 'mfuJ‘; no {’wfure, va'wu [. name 7. A/O ) (PW/m {/(w 45:"4 (”z a} taco/l/(U) ,; unbounJeJ, ...
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