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A#07_Solutions - Assignment#07 Solutions — p.1 ECSE-2410...

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Unformatted text preview: Assignment #07 - Solutions — p.1 ECSE-2410 Signals & Systems — Spring 2009 Due Fri 02/06/09 (1+ jfi) 1(10).Express z = ejarg“), — 7: < arg(z) S it. Write arg(z) as [771' in polarform, i.e., z = {Z jx/EejZ radians, Where p is a fraction. AND sketch z in complex plane. ~ T" t J VZ Z J. .1 (ft) g t: 26 3 17; 1 ,fl' “J . . 4 2(10). Express z = W, in rectangular form, i.e., z = 9ie{z}+ j3m{z} AND sketch. j... 1+ 6 2 J ‘17 “’7? . .32- 3? 5%- «228 e M_ Assignment #07 — Solutions —— p.2 ECSE—2410 Signals & Systems - Spring 2009 Due Fri 02/06/09 3(32). Given z = 2010 3g) , calculate the following and show that (a)=(b), and (c)=(d). + J . 2.2.- :a , ‘="- ‘2’ gruff) iii-e93“ “0 “f 2 1' + z 2 2014143 :- 2 H15 {:5 Rel (b) 29Te{z} .5; lfiév/ié-‘SWCFB‘I: 2J2 C052. vs. 2. .32 yr (0) z-z* 2 (J36 «Xi/EC; 4):; (d) Izlz a. k 55%;: (2.):- 4(18). (20(9) Express the periodic signal x(t) = 1+ 2cos(t) + 400s2 (2t) as an exponential Fourier series. (b)(9) Sketch the exponential Fourier series spectrum, ak , for part (a). ya at 5% 4‘”: “l; ~“l: ‘25 $sz XS}: L_§.Z’(CJ+CJ)+-4‘<6J :63 )3 [+6 +5 +6 “52"‘5 Z (a) :3 ‘liwadl? “dart ~34: 3t fit 1 \“kLfi-gZ—flké) =.- a +6 +96 +8 V~saq~3~z~ialz§fi5 Assignment #07 - Solutions — p.3 ECSE~2410 Signals & Systems - Spring 2009 Due Fri 02/06/09 5(30).Use properties (Text Table 3.1) to find the exponential Fourier series coefficients, ak, (including a0) of the following periodic waveforms. Note that we derived a very general formula for square pulse trains. Feel free to use this formula and results from one part of the problems below in any other part. :7 2 ‘0 3—E2 75‘ T , o ,2/ (3X15) XG) ”as Assignment #07 —- Solutions -— p.4 ECSE-2410 Signals & Systems - Spring 2009 Due Fri 02/06/09 5(30). Continued. (b)(15) -8 —7 .6 —5 4 -3 Q -1 l0 1 2 3 4 5 6 7 8 ’t fikWé—‘S’EK $919ch 44.3. Diiiljj + ~~\* r; 4 3 ’1‘ 7+ <3 Z— W M 44 WK) : PEHHPK; 2"? wheat-gm) ”1* [E m _. . a? ”H k i Era” ”‘1 \ f ‘ «t t s t “'2. 2. Mar“ AAG‘): ’X‘L‘H+X;(39 H kaz. bKat-CK ...
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