1
GATE ECE 2017 Set 1
+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
2
GATE ECE 2001
MCQ (More than One Correct Answer)
+2
-0.6
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
$$aS_g (\omega)\; and\; aP_g$$
3
GATE ECE 1992
MCQ (More than One Correct Answer)
+2
-0.6
Which of the following signals is/are periodic?
A
S (t) = cos2t + cos3t + cos5t
B
S (t) = exp ( j8$$\pi$$t )
C
S (t) = exp (−7t ) sin10$$\pi$$t
D
S (t) = cos2t cos 4t
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