Electrical Engineering > GATE 2026 > Fourier Series
A time-limited waveform g(x) is specified as follows:
g(x) = −k for −π < x ≤ 0, +k for 0 < x ≤ π, 0 otherwise
A new waveform f(x) is constructed from g(x) as follows:
f(x) = ∑m=−∞∞ g(x + 2πm), for all x ∈ R
The sum of the coefficients of the third harmonics of the sine and cosine terms in the trigonometric Fourier series expansion of f(x) is 2/3π.
What is the value of k?
g(x) = −k for −π < x ≤ 0, +k for 0 < x ≤ π, 0 otherwise
A new waveform f(x) is constructed from g(x) as follows:
f(x) = ∑m=−∞∞ g(x + 2πm), for all x ∈ R
The sum of the coefficients of the third harmonics of the sine and cosine terms in the trigonometric Fourier series expansion of f(x) is 2/3π.
What is the value of k?
Correct : a
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