Official PYQ · 2025Set 1 · Q45Continuous-time SignalsMSQ2 marks

GATE EC 2025 Set 1 Q45 — Continuous-time Signals

Let $f(t)$ be a periodic signal with fundamental period $T_{0}>0$ . Consider the signal $y(t)=f(\alpha t)$ , where $\alpha>1$ .

The Fourier series expansions of $f(t)$ and $y(t)$ are given by

$f(t)=\sum_{k=-\infty}^{\infty} c_{k} e^{j \frac{2 \pi}{T_{0}} k t} \text{ and } y(t)=\sum_{k=-\infty}^{\infty} d_{k} e^{j \frac{2 \pi}{T_{0}} \alpha k t}$

Which of the following statements is/are TRUE?

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Answer: A;D

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Published 10 Oct 2026

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