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1 1 X V n sin n=2 1 X nV cos n=2 V V V cos !t cos n!t sin !t sin n!t 2 1 2 2 4  n  1 n2 n 2 n 2
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Fig. 17-48
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Fig. 17-49
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CHAP. 17]
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FOURIER METHOD OF WAVEFORM ANALYSIS
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Find the exponential Fourier series for the waveform shown in Fig. 17-49 and plot the line spectrum. Convert the coe cients obtained here into the trigonometric series coe cients, write the trigonometric series, and compare it with the result of Problem 17.4. Ans:      1 1 j3!t 1 j2!t 1 1 j!t 1 f t V e e e j j 2 j 6 4 2 4 92       1 1 1 j2!t 1 1 2 j j e j!t j e e j3!t 2 4 6  92
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Find the exponential Fourier series for the waveform shown in Fig. 17-50 and plot the line spectrum. Ans:      1 1 j3!t 1 j2!t 1 1 j!t 1 e e e j j 2 j f t V 6 4 2 4 92       1 1 1 j2!t 1 1 e e j!t j e j3!t j 2 j 2 4 6  92
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Fig. 17-50
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Fig. 17-51
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Find the exponential Fourier series for the square wave shown in Fig. 17-51 and plot the line spectrum. Add the exponential series of Problems 17.29 and 17.30 and compare the sum to the series obtained here. Ans:   1 j3!t 1 1 1 1 j3!t e e f t V j j e j!t j e j!t j 3  2  3
Find the exponential Fourier series for the sawtooth waveform shown in Fig. 17-52 and plot the spectrum. Convert the coe cients obtained here into the trigonometric series coe cients, write the trigonometric series, and compare the results with the series obtained in Problem 17.19. Ans:   1 j2!t 1 j!t 1 1 j!t 1 j2!t e e e j e j j f t V j 4 2 2 2 4
Fig. 17-52
Fig. 17-53
Find the exponential Fourier series for the waveform shown in Fig. 17-53 and plot the spectrum. Convert the trigonometric series coe cients found in Problem 17.20 into exponential series coe cients and compare them with the coe cients of the series obtained here. Ans:   1 j2!t 1 1 1 j2!t e e f t V j j e j!t j e j!t j 2   2
FOURIER METHOD OF WAVEFORM ANALYSIS
[CHAP. 17
Find the exponential Fourier series for the waveform shown in Fig. 17-54 and plot the spectrum. Convert the coe cients to trigonometric series coe cients, write the trigonometric series, and compare it with that obtained in Problem 17.21.        1 j3!t 2 1 j!t 2 1 j!t 2 j 2 j e e e 3       1 e j3!t 3
Ans:
2 f t V j 92  2 j 92
Fig. 17-54
Fig. 17-55
Find the exponential Fourier series for the square wave shown in Fig. 17-55 and plot the line spectrum. Convert the trigonometric series coe cients of Problem 17.22 into exponential series coe cients and compare with the coe cients in the result obtained here. Ans: f t 2V 1 e j5!t 1 e j3!t e j!t e j!t 1 e j3!t 1 e j5!t 5 3 3 5 
Find the exponential Fourier series for the waveform shown in Fig. 17-56 and plot the line spectrum.       V 2 j2!t V V V sin e j!t sin e j!t sin e Ans: f t 2 6  6 6  6   V 2 j2!t sin e 2 6
Fig. 17-56
Fig. 17-57
Find the exponential Fourier series for the half-wave-recti ed sine wave shown in Fig. 17-57. Convert these coe cients into the trigonometric series coe cients, write the trigonometric series, and compare it with the result of Problem 17.24. Ans: f t V j4!t V j2!t V j!t V V j!t V j2!t V j4!t e e e e e e 15 3 4  4 3 15
Find the exponential Fourier series for the full-wave recti ed sine wave shown in Fig. 17-58 and plot the line spectrum. Ans: f t 2V j4!t 2V j2!t 2V 2V j2!t 2V j4!t e e e e 15 3  3 15
CHAP. 17]
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