GATE 2025 Electronics & Communication PYQ

Question

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

$$ f(t)=\sum\limits_{k = - \infty }^\infty c_k e^{j \frac{2 \pi}{T_0} k T} ext { and } y(t)=\sum\limits_{k = - \infty }^\infty d_k e^{j \frac{2 \pi}{T_0} \alpha k T} . $$

Which of the following statements is/are TRUE?

Accepted Answer

$c_k=d_k$ for all $k$

Answer

$y(t)$ is periodic with a fundamental period $\alpha T_0$

Answer

$c_k=d_k / \alpha$ for all $k$

Answer

$y(t)$ is periodic with a fundamental period $T_0 / \alpha$