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Solved Problems-4

Find the trigonometric Fourier series for the waveform shown in figure and sketch the spectra.
Description: Description: 4525.png
Here, Description: Description: 4536.png; for 0 < ωt < π and
= 0; for π < ω t < 2π
 Description: Description: 4542.png
⇒ Description: Description: 4549.png
Description: Description: 4555.png; for n odd.
= 0 ; for n even.
⇒ Description: Description: 4562.png
Description: Description: 4571.png; for n even.
Description: Description: 4577.png; for n odd.
∴ Description: Description: 4583.png

Line Spectra
The even harmonic amplitudes are given directly by bn coefficients, since there are no even cosine terms.
Description: Description: 777.png
But, the odd harmonic amplitudes are given by computation
Description: Description: 4591.png
∴ Description: Description: 4609.png = Description: Description: 4615.png = 0.1885 V
Description: Description: 4621.png
and C2 = Description: Description: 4633.pngC4 = Description: Description: 4639.png = –0.0397 V
= – 0.08 V

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