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quiz03_sol

quiz03_sol - ECE 108 Signals and Systems Spring 2007...

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Unformatted text preview: ECE 108 Signals and Systems Spring 2007, Instructor: Tiffany Li QUIZ 3 (50 minutes) 30 (MM as Name: l. (20) True or False: M (a) ( i; (c) ( F ) In the exponential Fourier series, the pair of coefﬁcients Dn and D_Tl always appear in complex conjugates. (f and“ 0118 If ‘b/u ﬁfij, {is Irma ) Fourier series exist only for real signals“ ) Fourier series exist only for periodic signals. (b) ( amt are-Noah's gag/M1 we a ‘f WT:ng ('n r‘ be ride-V Wu”. I,” (d) ( ) If the signal is an odd function, the DC term and all the cos(.) terms will not be present in the Fourier series. 2. (25 points) For the signals f(t) and 330:) shown below, ﬁnd the compoenent of the form a:(t) contained in ﬁt)" In other words, ﬁnd the optimum value of c in the approximation ﬁt) = [IL-(t) so that the error signal is minimum, x(t) 1 '5" C: ijtewjem _ j; 750% ; i 333:” Ween: ” 3; we 2 3. (30 points) Find the trigonometric Fourier series for the feilowing waveform (15 points), and sketch the respective amplitude spectrum and phase spectrum (15 points). ’1'“ 7“” ﬁt) "a" 2 I I t -5 —.3 ——i 3 5 “‘*—— «ﬂ «"ZE; 3F” (ﬂow hTa. mi 7’ WM? §ymmavaj 3'; MC SIM farms 5’0 {>0 fee) 2: a”; nnwsaﬂgr) x, 2, Q9 zen/em a, Vac/1w oak/W 7; % area 22x2 2:4 gym-“- 2:.) 4. (25 points) Find the exponential Fourier series of the signal in the last problem (10 points), and sketch the respective amplituée spectmm and phase spectrum (15 points)“ To {70+ w spew/M” : [/1561 VHS f’élﬁ'ﬁéﬂ [pm] 3-, a 3: .. a. Y QM Cat" ﬂab dafKETF'f—QI?” 1 :ﬂL ‘ "I. at Dr) fame in“ ate 15:» Gilda/ail Db ...
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