1
GATE ECE 2025
MCQ (More than One Correct Answer)
+2
-0

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

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

Which of the following statements is/are TRUE?

A
$c_k=d_k$ for all $k$
B
$y(t)$ is periodic with a fundamental period $\alpha T_0$
C
$c_k=d_k / \alpha$ for all $k$
D
$y(t)$ is periodic with a fundamental period $T_0 / \alpha$
2
GATE ECE 2023
Numerical
+2
-0

Let $$\mathrm{x_1(t)=u(t+1.5)-u(t-1.5)}$$ and $$\mathrm{x_2(t)}$$ is shown in the figure below. For $$\mathrm{y(t)=x_1(t)~*~x_2(t)}$$, the $$\int_{ - \infty }^\infty {y(t)dt} $$ is ____________ (rounded off to the nearest integer).

GATE ECE 2023 Signals and Systems - Representation of Continuous Time Signal Fourier Series Question 3 English

Your input ____
3
GATE ECE 2017 Set 1
MCQ (Single Correct Answer)
+2
-0.6
Let x(t) be a continuous time periodic signal with fundamental period T = 1 seconds. Let {ak} be the complex Fourier series coefficients of x(t), where k is integer valued. Consider the following statements about x(3t):

I. The complex Fourier series coefficients of x(3t) are {ak} where k is integer valued

II. The complex Fourier series coefficients of x(3t) are {3ak} where k is integer valued

III. The fundamental angular frequency of x(3t) is 6$$\mathrm\pi$$ rad/s

For the three statements above, which one of the following is correct?
A
only II and III are true
B
only I and III are true
C
only III is true
D
only I is true
4
GATE ECE 2001
MCQ (More than One Correct Answer)
+2
-0
The PSD and the power of a signal g(t) are, respectively, Sg($$\omega$$) and Pg. The PSD and the power of the signal ag(t) are, respectively
A
$$a^2S_g (\omega)\; and\; a^2P_g$$
B
$$a^2S_g (\omega)\; and\; aP_g$$
C
$$aS_g (\omega)\; and\; a^2P_g$$
D
$$aS_g (\omega)\; and\; aP_g$$
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