ece340_exam_2_fall2007_solution

ece340_exam_2_fall2007_solution - FALL 2007...

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Unformatted text preview: FALL 2007 (10/30/07) ECE340 (Engineering Systems Analysis) Name: If larlfor Che/Z Exam II 2» 1. (10 pts) Show that the set of signals {¢5,,,(t) = e" T , m e Z} is orthogonal on the interval Are these functions orthonormal? Ifnot. show how to create an orthonormal basis. To? 144.7) E Z W4 VVf—jéfl, (duet), ¢n(+)>: dw(+)¢;“(+)cfic -21 .. 7/a 'Hmt - Int 'l 6” ‘ e” 0H" '72 —11’ ., .: V2; 6).],(711 '7 . I); -171 .' 7" " ;j%fi(mrfl)t}; {PI/Ami”) 21,6 4m, l : /-m : ’ fl .'Tl _, - / 071'” flme 71) 2) ,r( > FALL 2007 (10/30/07) _. (10 pts) Show that the coefi'lcients ofthe exponential Fourier series for a real and even signal are real. W” W 3. (20 pts) State and proof the Parseval’s theorem. 7/6 OW/Mg/é aww 0% a Parka/Tc 9%va 1w) _ 7%0 gum 07f +k¢ FOWaKS 7n 7%: [okasw /§ \ — CWfWQ’W'Lé 07L ({9 Rwy/‘82” Cali/S. P ()(Hfl’Lfl/‘tr: M c To ’41—'09 FALL 2007 (10/30/07) 4. (25 pts) Plot the phase spectrum of the periodic signal f(t). f (I) FALL 2007 (10/30/07) 5. (20 pts) The periodic signal x(t) is passed through an ideal high pass filter with cutoff frequency of y . Ideal x0) High-pass filter y(t) with cutoff freq. y For the input signal x(t) shown: 5 a) (15 pts) Find the range of [u so that the power of the output signal, Py , is — of the power of the 8 input signal, PX. we have A~ I‘C >(n : fl 9 r! FALL 2007 (10/30/07) b) (5 pts) Plot the output signal y(t) based on the cutoff frequency y you found in a). Zle’mfll’TYl? {Vii/p0 Iowan m1, nyncj it] 6. (15 pts) Find the Fourier transform of the following signals. a) (3 pts) xa(l‘) =1 $05) é~> i 4: b) (3 pts) xh(t)=u(1) t g MU) : l ,u . }. Xm) : (jam ~X(~+)'+ Emmet) <4 c) (3 pts) x6 (I) = Sinc(l‘) ma <—*> “new b3 dmoxlilj >{( W) : Tflt) d) (3 pts) xd(t)=Coswof '—' COS (“HBO—t) 67191,th 2527,50) é/‘urft d’é M (a w -—- CI __ 1 0° )Zflfic'flf g7z"(f+7£°)t elf , :L e -.: /1(<§(.§—+)+§(f+§o)> } A 1 e) (3 pts) xe(t)=A-A[%]cos(w0t) V§A.A(—:~)§ : ATsmc (UL) ALA (F \yga‘onH; r. ng—f )+ $9090) ’4. FALL 2007 (10/30/07) ...
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This note was uploaded on 10/06/2008 for the course ECE 340 taught by Professor Djordjevic during the Fall '08 term at Arizona.

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ece340_exam_2_fall2007_solution - FALL 2007...

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