1
GATE ECE 2023
Numerical
+2
-0.67

A sample and hold circuit is implemented using a resistive switch and a capacitor with a time constant of 1 $$\mu$$s. The time for the sampling switch to stay closed to charge a capacitor adequately to a full scale voltage of 1 V with 12-bit accuracy is ___________ $$\mu$$s (rounded off to two decimal places).

Your input ____
2
GATE ECE 2023
MCQ (More than One Correct Answer)
+1
-0.33

For a real signal, which of the following is/are valid power spectral density/densities?

A
$${S_x}(\omega ) = {2 \over {9 + {\omega ^2}}}$$
B
$${S_x}(\omega ) = {e^{ - {\omega ^2}}}{\cos ^2}\omega $$
C
GATE ECE 2023 Communications - Random Signals and Noise Question 5 English Option 3
D
GATE ECE 2023 Communications - Random Signals and Noise Question 5 English Option 4
3
GATE ECE 2023
MCQ (Single Correct Answer)
+2
-0.67

A random variable X, distributed normally as N(0, 1), undergoes the transformation Y = h(X), given in the figure. The form of the probability density function of Y is

(In the options given below, a, b, c are non-zero constants and g(y) is piece-wise continuous function)

GATE ECE 2023 Communications - Random Signals and Noise Question 6 English

A
$$a\delta (y - 1) + b\delta (y + 1) + g(y)$$
B
$$a\delta (y + 1) + b\delta (y) + c\delta (y - 1) + g(y)$$
C
$$a\delta (y + 2) + b\delta (y) + c\delta (y - 2) + g(y)$$
D
$$a\delta (y + 2) + b\delta (y - 2) + g(y)$$
4
GATE ECE 2023
MCQ (Single Correct Answer)
+2
-0.67

Let a frequency modulated (FM) signal $$x(t) = A\cos ({\omega _c}t + {k_f}\int_{ - \infty }^t {m(\lambda )d\lambda )} $$, where $$m(t)$$ is a message signal of bandwidth W. It is passed through a non-linear system with output $$y(t) = 2x(t) + 5{(x(t))^2}$$. Let $${B^T}$$ denote the FM bandwidth. The minimum value of $${\omega _c}$$ required to recover $$x(t)$$ from $$y(t)$$ is

A
$${B_T} + W$$
B
$${3 \over 2}{B_T}$$
C
$$2{B_T} + W$$
D
$${5 \over 2}{B_T}$$
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