1
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)
2
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).

Your input ____
3
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).

Your input ____
4
GATE ECE 2017 Set 1
MCQ (Single Correct Answer)
+1
-0.3
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?
A
GATE ECE 2017 Set 1 Communications - Digital Communication Systems Question 42 English Option 1
B
GATE ECE 2017 Set 1 Communications - Digital Communication Systems Question 42 English Option 2
C
GATE ECE 2017 Set 1 Communications - Digital Communication Systems Question 42 English Option 3
D
GATE ECE 2017 Set 1 Communications - Digital Communication Systems Question 42 English Option 4
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