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Electric circuits miscellaneous

  1. The Fourier series expansioncos nωt + bn sin nωt
    of the periodic signal shown below will contain the following nonzero terms

    1. a0 and bn , n = 1, 3, 5, ....... ∞
    2. a0 and an , n = 1, 2, 3,.... ∞
    3. a0, an and bn, n = 1, 2, 3,... ∞
    4. a0 and an, n = 1, 3, 5,... ∞
Correct Option: D

The given periodic signal is even as f(– t) = f(t) and also holes half-wave symmetry since

ft +
T
= f(t)
2

Hence, the signal will only have cosine terms and only odd harmonics will be present.
i.e. bn = 0
an = 0
for n = 2, 4, 6,... ∞ .
Hence the correct choice is (d).



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