{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

A#04_Solutions - Assignment#4 ~— Solutions ECSE—2410...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 10
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Assignment #4 ~— Solutions ECSE—2410 Signals & Systems ~ Fall 2006 Due Tue 09/12/06 1(20). Carry out the convofution, y(t) = v(t) =£= w(r) , of the signals shown, and sketch your result. (a) v1(t) yv1(t) h * II I , Z I e 2 e 2 121(1') For t<0, 3110) = v10) * w1(t) m 0 1 h 1' For O<z<2, . G 2 w,(z~z') i T Qfl : (5) mm) / at at —[email protected] w m C :: (fyéé -zx-t 't i 3 .51” 2‘4 ai‘t LE 7? if $4 335‘; «a: fiffigaE-Mfi} as} km; 2.. mag-~24) 1569 == are) 'ifiw— 326-? = Ugéfi WW .._.. “#544 wait-2; = g: m; Assignment #4 ..,_ Solutions —- p.2 BOSE-2410 Signals & Systems - Fali 2006 Due Tue 09/12f06 Assignment #4 w Solutions — 9.3 ECSE—241 0 Signals & Systems — Fall 2006 Due Tue 09/ 121’06 1(a) continued. we, mealsgjfla P a» W dflwgwfiw fweafiar, Nae MWfiifi‘tfivi-fijé—é~zfig e @9va “fies. Q‘rfil 1: Wgfiflmfififigm ogg+)%<vjija}-tlfi&-ZD == 078-1sz +mfifvifit"2§ Essa? ems-um aegis} 1E3}; % Cewefifmgi} a L fiLifim giifi "y gsifi‘a “E 3% 2(25). This example illustrates the distributive property of convolution, namely, that convolution distributes over addition: x(r) =I= (1110) + kg (0) m x(r) * 2210) + x(1)* [12 (t). For the system shown, let h, (t) = l12 (t) 2 11(5) w u(t 4*» I) . x(r)=u(t) Determine and sketch Z Qi-iw'g‘z” “” WM”) New ; 1%) QELH+~¢Q2L9 a; ‘D + E g ? ‘9 i t c) E t <23 3 ~17 (b) x(f)*(hl(t)+h2(r)) like fla‘i‘iz’ LE: 35 g E if 13%;?) Assignment #4 — Solutions —- p.4 ECSE—2410 Signals & Systems .. Fail 2006 Due Tue 09/12/06 2 Continued (C) X(I)*hl(f) = 'ézfi'} (d) x(:) we) .2:ng 321*) 3%; M. (6)1 i f C) E (e) m * h} (r) + x0) * hz (r) —.-.~. 3*“ flag.) féiL-H Mew...» "t Assignment #4 — Solutions ~— 13.5 ECSE—24EO Signais & Systems - Fail 2006 Due Tue 09/ 12/06 3(20). This example iliustrates the associative property of convolution, namely, that the order in which cascaded terms are convolved is irrelevant: x(r) * (h, (I) * kg (0) m (x(t) * h1(t))* #12 (I). For the system shown, let h, (I) = h, (t) = MU) — u(r — 1) . (a) hmmhzm slew Age} , % Assignment #4 —- Solutions — 9.6 ECSE-2410 Signais & Systems — Fall 2006 Due Tue 09/ 12/06 3(20).C0nt1nued (C) 960)“? (I) -~ 3%) ii My?) % as is fig )m ) (d) (mm (x) *h (r) Assignment #4 — Solutions — [1.7 ECSE-2410 Signais & Systems — F311 2006 Due Tue 09/ 12/06 4120) w) (20(8) Sketch y(r) = x(t) =5< Mr) {A XLfiL Hiya —£ 4:4; (b)(8) Sketch 34(1) = x(~r+2)*h(t)‘ Assignment #4 w Solutions «w p.8 ECSE-2410 Signals & Systems — Fall 2006 Due Tue 09/12/06 4.0.0) Continued. £21135 mike; +2.12» Pwéw Mmé We dfikfiz'ékfi‘aa Fwy? “ i KG} (Maia gag; Macias) 1.011% a. i 9&9 i' i: 1 {— a 3 “j «:32 i a... 6%; mmafim/figm 29 W 3%}: {aflwvfliflyfi‘ 44545 ”‘1‘ Z£Q¥%w*/£&4}Mw m) 1‘11 M £62? kamlww ‘gg: w 0 t 3- Assignment #4 — Solutions — {1.9 ECSE-2410 Signals & Systems - Fall 2006 Due Tue 09/12/06 5(15). The input 9(0) 2 e‘m is appiied to a LTI system whose impulse response is Mt) : um —u(t — E) . (a)( 10) COmputo analyticaiiy (1.6. give a formuia for) ya) : 2cm * Mt) . Use graphicai approach. 1'. g {4) s .4: e is: e ads-i-oué—é-fi «4 N19 "‘1'" a «8:- M?) Assignment #4 — Soiutions — p.10 ECSE~2410 Signals & Systems - Fail 2006 Due Tue 09/ 12/06 (3) Continued. Matlab plot of 320*). 03 10.5%,} = 6.78% - s ‘ ' i a 1 : a 5/ \ tm[u4:.01:4}; g1 mt<m0; g2:t>0&t<1 ; g3fit>xl ; WW-6Xp(-1))-*eXP(t))-*g1+(2~€Xp(’£*1)~eXp(*i))-*g2+((eXp(1)4)-*eXp(~i))-*g3; p10t(t,y) grid (b)(5) At what value of t does y(r) reach its maximum value? Justify your answer. (Picture will ...
View Full Document

{[ snackBarMessage ]}