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The trigonometric Fourier series of an even function of time does not have ___________

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The trigonometric Fourier series of an even function of time does not have ___________

(a) The dc term

(b) The cosine terms

(c) The sine terms

(d) The odd harmonic terms

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Question is from Common Fourier Transforms topic in portion Fourier Transform of Signals and Systems

1 Answer

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The correct choice is (c) The sine terms

To explain: For periodic even function, the trigonometric Fourier series does not contain the sine terms since sine terms are in odd functions. The function only has dc term and cosine terms of all harmonics. So, the sine terms are absent in the trigonometric Fourier series of an even function.

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