GATE ECE 2024 | Digital Communication Systems Question 1 | Communications

GATE ECE 2024

MCQ (Single Correct Answer)

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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 ______.

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

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

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

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

GATE ECE 2022

MCQ (More than One Correct Answer)

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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?

H(X) $$\le$$ log₂ K bits

H(X) $$\le$$ H(2X)

H(X) $$\le$$ H(X²)

H(X) $$\le$$ H(2^X)

GATE ECE 2022

Numerical

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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).

Your input ____

GATE ECE 2017 Set 1

MCQ (Single Correct Answer)

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In a digital communication system, the overall pulse shape p(t) at the receiver before the sampler has the Fourier transform P(f). If the symbols are transmitted at the rate of 2000 symbols per second, for which of the following cases is inter symbol interference zero?