1
GATE ECE 2024
MCQ (Single Correct Answer)
+2
-1.33

A source transmits a symbol $s$, taken from $\\{-4, 0, 4\\}$ with equal probability, over an additive white Gaussian noise channel. The received noisy symbol $r$ is given by $r = s + w$, where the noise $w$ is zero mean with variance 4 and is independent of $s$.

Using $Q(x) = \frac{1}{\sqrt{2\pi}} \int\limits_{x}^{\infty} e^{-\frac{t^{2}}{2}} dt$, the optimum symbol error probability is _______.

A

$\frac{2}{3} Q(2)$

B

$\frac{4}{3} Q(1)$

C

$\frac{2}{3} Q(1)$

D

$\frac{4}{3} Q(2)$

2
GATE ECE 2024
Numerical
+2
-1.33

Let $X(t) = A\cos(2\pi f_0 t+\theta)$ be a random process, where amplitude $A$ and phase $\theta$ are independent of each other, and are uniformly distributed in the intervals $[-2,2]$ and $[0, 2\pi]$, respectively. $X(t)$ is fed to an 8-bit uniform mid-rise type quantizer.

Given that the autocorrelation of $X(t)$ is $R_X(\tau) = \frac{2}{3} \cos(2\pi f_0 \tau)$, the signal to quantization noise ratio (in dB, rounded off to two decimal places) at the output of the quantizer is _________.

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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
Numerical
+2
-0.67

Let X(t) be a white Gaussian noise with power spectral density $$\frac{1}{2}$$W/Hz. If X(t) is input to an LTI system with impulse response $$e^{-t}u(t)$$. The average power of the system output is ____________ W (rounded off to two decimal places).

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