Let the signal $x(t) = \sum_{k=-\infty}^{+\infty} (-1)^k \delta (t - \frac{k}{2000})$ be passed through an LTI system with frequency response H($\omega$), as given in the figure below. The Fourier series representation of the output is given as

$4000+4000\cos(2000\pi t) + 4000\cos(4000\pi t)$

$2000+2000\cos(2000\pi t) + 2000\cos(4000\pi t)$

GATE 2018 Electrical Engineering Q31 — Electrical Engineering

GATE 2018Set CombinedQ31MCQanswer keyexplanation soonmedium

Electrical Engineering · Signals and Systems - Fourier Series

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Drill mode: LTI system · 16/44

Figure from the original GATE 2018 paper. (IIT Guwahati archive)

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Recurring concept

Signals and Systems - Fourier Series has appeared in GATE Electrical Engineering 4 times across 4 years (2018, 2019, 2025, 2026).

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Fourier SeriesLTI SystemFrequency ResponseSignals