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What is the fourier series coefficient for n=0?

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+1 vote
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in Signals and Systems by (1.2m points)
What is the fourier series coefficient for n=0?

(a) Zero

(b) Unity

(c) Depends on the situation

(d) Non zero positive

I have been asked this question in an interview for job.

My doubt is from Fourier Series Properties in portion Fourier Series of Signals and Systems

1 Answer

0 votes
by (42.1k points)
Correct option is (a) Zero

Easy explanation: The differentiation property of the continuous time fourier series is,

Y(t) = dx(t)/dt ↔ Yn = jnwXn.

Hence, the differentiation property of time averaged value of the differentiated signal to be zero, hence, fourier series coefficient for n=0 is zero.

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