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Unformatted text preview: Assignment #07  Solutions — p.1 ECSE2410 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.
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2(10). Express z = W, in rectangular form, i.e., z = 9ie{z}+ j3m{z} AND sketch.
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.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).
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“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) zz* 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 \“kLﬁgZ—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 ECSE2410 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
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