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quiz3_solution

# quiz3_solution - EE 228 Quiz 3 Winter 2007 Name Problem#1...

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Unformatted text preview: EE 228 Quiz 3 Winter 2007 Name: Problem #1 2 (a) Find the Fourier series coefﬁcients cm and b]; for signal x09 in the trigonometric form. 2 (b) Find the Fourier series coefﬁcients CK for- signal x(t) in the polar form. 2 (c) Find the Fourier series coefﬁcients Xﬂc] for signal x(r) in the exponential form. x(t) = 2 + igcosﬂkt) k=1 (a) a0: 1/ ak:% k =0 I k>0‘ (1')) 69:2, Ck=% 100 (C) Xro]=2 xtk]=:’2-cak-5bk)=% k>o I Problem #2 Consider a periodic signal x(t). , with fundamental period 25, shown below. The Fourier series coefﬁcients of this signal are , g, k = o, Xm = sin(0.5knr)’ k i 0, k7? so that x(t) = Emma”. ”I“, k=_m . a 2 (a) What is the average power in xﬂ)? 1 1+jm' Let yw denote the corresponding output, and its Fourier series representation be ya) = inner“. k= 'm Find Y[—1], Y [O], and Y[1] , and enter them in the following table. Your answer must be of the form Real-part + j Imaginary-part. The real and imaginary parts can either be left as expressions involving constants such as 712, or should be correct to four signiﬁcant digits. (b) If xﬂ) is the input to a LTI system with transfer function H ( jco) : value (bi/1m] = XEkj- WWW) zYto] : K[0]- Hmso) : x39] :0.5‘ ZYEIJ : KE']' Hit/0:000) : ﬁhbmfﬁ). l _ l‘jﬁ {-jE : l ‘ «+3.2 . (+31: T" I" 1“ 27% = L JL [L (I’JTL)(l+J-T() [L('+¢;\Cz) l I — ————~—- + 117m?) 3 ”ft; ...
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