Lesson_42 - = = =- For n=1 a 1 =sin π/2 π ~ 0.318...

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EEL 3135 Dr. Fred J. Taylor, Professor Lesson #4 Spectral Representation Challenge A periodic pulse process is shown in Figure below. The fundamental period of the signal is T 0 =2 sec. The pulse process “duty cycle” of 50% ( on half the time). What is the value of the 1 st harmonic of Fourier series expansion of x(t)? Pulse Process Challenge Response The nth Fourier coefficient, a n , is given by: ( 29 ( 29 value DC dt dt t x T a T T 2 1 1 2 1 1 2 / 1 0 0 2 / 1 2 / 2 / 0 0 = = = - - ( 29 ( 29 π n n jn e dt e dt e t x dt e t x T a t jn t jn t jn t jn T T n ) 2 / sin 2 1 1 2 1 ) ( 2 1 1 2 / 1 2 / 1 2 / 1 1 2 / 2 / 0 2 / 1 1 0 0 = - =
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Unformatted text preview: = = =--------∫ ∫ ∫ For n=1, a 1 =sin( π /2)/ π ~ 0.318 Notice for n even (except n=0), that sin(n π /2)=0, therefore the corresponding Fourier coefficients are likewise zero. The signal spectrum therefore contains only odd harmonics with a DC bias of a =1/2. InvestiGATOR …-2.0 |-1.0 | 0.0 | 1.0 | 2.0 … 1.0 0.0 1...
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