GATE 2022 MN – Question 13
A 2π-periodic function is f(x)=−k for −π<x<0 and f(x)=k for 0<x<π, with constant k. Find its Fourier-series constant term.
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Correct answer: (D) 0
Explanation
The function is odd, so its integral over a symmetric period is zero. The average, and therefore the Fourier constant term a₀/2, is zero. Thus D. Whether the convention calls a₀ or a₀/2 the constant coefficient makes no difference here because both vanish.