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Challenge_9

# Challenge_9 - InvestiGATOR 1 EEL 3135 Dr Fred J Taylor...

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EEL 3135 Dr. Fred J. Taylor, Professor Lesson #9 Synergy Challenge 09 The reconstructed signal can also be derived from the synthesis equation: T kt j k k e c t x / 2 ) ( π -∞ = = where c -8 = -0.043+0.033j, c -6 = -0.027+0.061j, c 0 =0.217+0j, c 6 = -0.027-0.061j, and c 8 = -0.043-0.033j (machine calculated). What is x(t)? Required Challenge response: What is the 6 th harmonic of x(t)? ------------------------------------------------ Laying down some key parameters, c 8 = -0.043-j0.033 = 0.0542 -152.5 ° ; c -8 = -0.043+j0.033=c 8 *=0.0542 152.5 ° c 6 = -0.027+j0.061 = 0.0663 113.9 ° , c -6 = -0.027-j0.061=c 6 *= 0.0663 -113.9 ° , c 0 =0.217+j0 = 0.217 Remember that it was posted that the frequency resolution of the machine computed Fourier series is given by f=135 Hz/256 harmonics = 0.527 Hz/harmonic. You are also told that you process T 0 =1.8975 seconds of data with an FFT for each displayed spectrum (i.e., 256 samples at T s =1/f s sec/sample). T s = 1/135, T 0 = 1.8975 The 0 th harmonic is 0 f= 0 Hz. The 6 th harmonic is at 6 f= (6)( 0.527)=3.162 Hz The 8 th harmonic is at 8 f= (8)( 0.527)=4.216 Hz

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Unformatted text preview: InvestiGATOR 1 EEL 3135 Dr. Fred J. Taylor, Professor------------------------------------------------------Direct substitution: ( 29 { } ( 29 { } ( 29 ( 29 ( 29 ( 29 ) . ) . ( cos( . ) . ) . ( cos( . . . . . . . . . . . . ) ( . / . / . / . / / . / . / . / . / / / / / 5 152 216 4 2 1084 9 113 162 3 2 1326 217 0542 0542 0663 0663 217 0542 0542 0663 0663 217 5 152 16 5 152 16 9 113 12 9 113 12 16 5 152 16 5 152 12 9 113 12 9 113 16 8 16 8 12 6 12 6 2-+ + + = = + = + + + = = + + + + + = = + + + + = = =---+-+------∞-∞ = ∑ t t e e e e e e e e e e e e e a e a e a e a a e a t x o o o o o o o o o o o o o T t j T t j T t j T t j T t j j T t j j T t j j T t j j T t j T t j T t j T t j T kt j k k π assuming the arithmetic is correct. The 6 th harmonic component is therefore: ) . ) . ( cos( . ) ( 9 113 162 3 2 1326 6 + = t t x 2...
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Challenge_9 - InvestiGATOR 1 EEL 3135 Dr Fred J Taylor...

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