1
GATE ECE 2024
+1
-0.33

A digital communication system transmits through a noiseless bandlimited channel $[-W, W]$. The received signal $z(t)$ at the output of the receiving filter is given by $z(t) = \sum\limits_{n} b[n]x(t-nT)$ where $b[n]$ are the symbols and $x(t)$ is the overall system response to a single symbol. The received signal is sampled at $t = mT$. The Fourier transform of $x(t)$ is $X(f)$. The Nyquist condition that $X(f)$ must satisfy for zero intersymbol interference at the receiver is ______.

A

$$\sum\limits_{m=-\infty}^{\infty} X \left( f + \frac{m}{T}\right) = T$$

B

$$\sum\limits_{m=-\infty}^{\infty} X \left( f + \frac{m}{T}\right) = \frac{1}{T}$$

C

$$\sum\limits_{m=-\infty}^{\infty} X (f + mT) = T$$

D

$$\sum\limits_{m=-\infty}^{\infty} X (f + mT) = \frac{1}{T}$$

2
GATE ECE 2024
+1
-0.33

A white Gaussian noise $w(t)$ with zero mean and power spectral density $\frac{N_0}{2}$,

when applied to a first-order RC low pass filter produces an output $n(t)$. At a particular time $t = t_k$, the variance of the random variable $n(t_k)$ is ________.

A

$\frac{N_0}{4RC}$

B

$\frac{N_0}{2RC}$

C

$\frac{N_0}{RC}$

D

$\frac{2N_0}{RC}$

3
GATE ECE 2024
Numerical
+1
-0.33

An amplitude modulator has output (in Volts)

$$s(t) = A \cos(400 \pi t) + B \cos(360 \pi t) + B \cos(440 \pi t)$$.

The carrier power normalized to $1\Omega$ resistance is 50 Watts. The ratio of the total sideband power to the total power is 1/9. The value of $B$ (in Volts, rounded off to two decimal places) is _______.

4
GATE ECE 2024
Numerical
+1
-0.33

A source transmits symbols from an alphabet of size 16. The value of maximum achievable entropy (in bits) is _______ .

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