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 2022
MCQ (More than One Correct Answer)
+1
-0.33

Let H(X) denote the entropy of a discrete random variable X taking K possible distinct real values. Which of the following statements is/are necessarily true?

A
H(X) $$\le$$ log2 K bits
B
H(X) $$\le$$ H(2X)
C
H(X) $$\le$$ H(X2)
D
H(X) $$\le$$ H(2X)
3
GATE ECE 2022
Numerical
+1
-0.33

A symbol stream contains alternate QPSK and 16-QAM symbols. If symbols from this stream are transmitted at the rate of 1 mega-symbols per second, the raw (uncoded) data rate is _________ mega-bits per second (rounded off to one decimal place).

4
GATE ECE 2022
Numerical
+1
-0.33

Consider a channel over which either symbol xA or symbol xB is transmitted. Let the output of the channel Y be the input to a maximum likelihood (ML) detector at the receiver. The conditional probability density functions for y given xA and xB are :

$${f_{\left. Y \right|{x_A}}}(y) = {e^{ - (y + 1)}}u(y + 1)$$,

$${f_{\left. Y \right|{x_B}}}(y) = {e^{(y - 1)}}(1 - u(y - 1))$$,

where, u( . ) is the standard unit step function. The probability of symbol error for this system is _________ (rounded off to two decimal places).