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20111ee102_1_homework6

# 20111ee102_1_homework6 - tf t and sin w tf t in terms of...

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WINTER 2011: Put Discussion section number in the corner →→→ (* Otherwise Your HW will be LOST) Name(Print) (LAST, Middle, First): ————————————— Student ID : ——————————————————– HW: # 6 NO LATE HOMEWORK POLICY! Posted: February 10 Hand In: February 17 IN CLASS Attach This Sheet To Your HW 1. Given f ( t ) = f ( t + T ) and f ( t ) = s n = -∞ F n e inw 0 t , show that (i) If f ( t ) = f [ t + T 2 ], then F n = 0 for n odd. (ii) If f ( t ) = - f [ t + T 2 ], then F n = 0 for n even. 2. Find and sketch the amplitude and phase spectra of the signals shown in Fig. 1 (only one cycle is shown). Figure 1: Q2 1

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3. Let f ( t ) be a periodic function with period T and let w 0 = 2 π T . Find the Fourier coe±cients of cos w
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Unformatted text preview: tf ( t ) and sin w tf ( t ) in terms of the Fourier coe±cients of f ( t ). 4. Show that the periodic function f ( t ) shown in Fig. 2 has the Fourier series representation: f ( t ) = 1 2 + 2 π ∞ s k =1 1 2 k-1 sin(2 k-1) t. Figure 2: Q4 This function is now applied to a linear, time-invariant system whose system function is H ( s ) = s s 2 + 1 . Find the Fourier series representation of the corresponding output. 5. Find the Fourier coe±cients F n of the periodic signal f ( t ) shown in Fig. 3. 2 Figure 3: Q5 Find the mean square error when f ( t ) is approximated by F + F 1 e iπt + F-1 e-iπt . 3...
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20111ee102_1_homework6 - tf t and sin w tf t in terms of...

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