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hwk1_solns - ECE 300 Signals and Systems Homework 1 Due...

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Unformatted text preview: ECE 300 Signals and Systems Homework 1 Due Date: Tuesday September 11, 2007 at the beginning of class Reading: ZTF pages 1-28 and your course notes. Problems 1) ZTF, Problem 1.8. 2) ZTF, Problem 1-10. 3) ZTF, Problem 1-14. 4) ZTF, Problem 1-30. 5) ZTF, Problem 1-32. 6) Simplify the following as much as possible, giving numerical answers where possible a) o]e"u(t — 5)a’t b) a]? [u(t — 6) - u(t —5)]a’t c) ojtzfia — 2)dt d) Gift26(t—2)dt e) o]sin(lyrr)6(t — 2)dt f) sin(zfyzr)§(t — 2) g) 03.60 —3)§(t —4)dt h) 03W —3)5(t —4)dt i) TuU —x + 5)6(t ~4)dt Fall 2007 j) lu(t—x+5)6(z—4)dt k) t5(t —2)+t3§(t—1) I) H(w)§(w—1) + A(a)~x +1)6(a)) m) Iii-Mt + 3)u(t — 2)dt 7) For each of the following signals, determine if the signal is periodic and, if so, the fundamental period. a) x(t) = sin(2t) + cos(3t + 30") b) x(t) = cos(2t) + cos(7rt) C) x(t) = e" cos(t) d) x(t) = 2ej2’ + Bem’”) Matlab Problems 8) Using Matlab, plot each signal from Problem 7 for three fundamental pen'ods if the signal is periodic, or three times the longest period in the signal if the signal is not periodic. Be sure there are at least 50 samples per period for each waveform and your graphs are neatly labeled. Notes: (1) Matlab works in radians, so all angles must be converted to radians, (2) use exp in Matlab to get an exponential, (3)j is Matlab’s way of indicating the square root of -1, and if you want x(t) = efl’ you should type something like x = exp(i*2*t), and (4) if the waveform is complex, plot the real and imaginary parts separately. The Matlab commands real and imag are very useful for this. Turn in your plots. For the following two problems, save the files stp_fn.m and rmp_fn.m from the course website to the directory in which you will be using MATLAB. This directory is called the “working directory” in Matlab. If you do this correctly, you can use the functions stp_fn and rmp_fn just as you would any other built-in matlab function. Use these supplied MATLAB functions to generate the function x(t) = 3u(t — 2) + 4r(t — 3) from t= O to 10, you might type the following in Matlab t = linspace(0,10,1000); x = 3*stp__fn(t-2)+4*rmp_fn(t-3); 9) ZTF, Computer Exercise 1-1. 10) ZTF, Computer Exercise 1-2 (only plot parts b and c). Use subplot to plot both functions on one page. Fall 2007 @ ; 27/77/ WraZén/g /"‘Y . a) Z/g) : 77/4/5) :- 7/5) w/WK r/(Jj d/fléLp/fl/ 0) am/27495>/: ’Xch :@ Pr/B I =E:o.a$/+flofl‘7 I B 5., @+;3‘)(S +~§fim® WWW... 5)}??? AD m EEQTM) Prawn/x 1-30 rm) : oat) 2 24%) wins-27 L «re—43 “may ch 4. Eu(+-u\»u(+~%fl [1 ‘ (4:403? 1' 2WD -— attic—>5 + u(£-—\£\ +MC€'Q\[‘? {—2 -— (é—‘Q\\ —,,— {AH-wail ~ 64» (0] ~ 2mg) flange) +mce—tb -— (Rob mach 7L (e’fluw-t?) ‘ M L ”16%) ’ 2W6)- uzé 7) ,Lut’zé'V) —- rare) + r09?) WWW é.- Q’cIQ: N’c D+w£ IQ ”Mté 1QA1MI 1§+m+ 3) WM M..W_.._—~ [MW ”WMM “fl 1} + Me’b a- Cuu— IIQ naps—2mg II ,W W ,,,,,,,,, I 00 m 0o @ f 8'2/1939/5: I 6,322: “e’t/S 3 8’5 1’26? 05097) V“) 5 @ fizz; [é'6> wu/krflfl/g; ‘féz[H/é'§) ~wré/o)}/¥ Q 4; .. 2/31' :.- 3 __ __ 3’ 3 .. ’- ' £5 ‘55 @35/-130332 © Evflikg/{~2§o/a¢=fl won giag/vf/z) 9/2}; 5 ; (>0 > @ J: 5?» /2§/if>g/¢vz)0/g:‘5m @ytT)’ ® Sin ($1133 3&1) rig“; (Q wBSflt-ZB C3) 5: §{£*;3§/5~z/) 5/5 =E firm) gawk/24:: u/J—zB/ : E i=7 M @ f//£</> g/W’/> fA/W’KJL/B wa) ‘: {/H(/>(S;M)'l>+fl{/rx) g/w) /0 @éazmflz/H-b/é (2/5le :/%0/ f) _3 (/(fé’z) ‘// A/ LL72 /0 www- 2 ., @ fig) ’1 507/20 4* Dog/ELL +30") L 47694;) 1’9}; (2:323) 7Loo§fgé+37o #300) 7 VI/f> {7p 97; rig/7:31”) 37B ‘3 ff???» 2) r .ngg ’25 0?? 3’ i c 2 r2: ado/KS flaw/z 70 c «2/? ‘ 27:) ’ wS/zt)v‘ $871779 Yaw/7;) 5: @S/2é+2/o)/— cog 7ffifZB) 7 717$) up 272 7f/2/7> 7773 : r/zn> Zr] /‘ [Wémf Tiff: 2/ x90 ;// [559945 Mjrf/ra/N fi7fl7z zoo/ft, :OUYSB :70 Q )O—‘o’flfig m 442: flue mLaCc1t/k4flmtg To —. HOD.‘Utoogc £- 2 (OD 004:) ” 2601+32M3€+ 3 Aommv mEfi €me mEF cm 3 or m o . Aommv 9E... Aommv mEc. or m w v N o om mp or m o ZT M, Exercise 1-1 Time (sec) ZT M, Exercise 1-2 (b) -1 0 1 2 3 4 5 Time (sec) ZT M, Exercise 1-2 (0) 2 Time (sec) ...
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