1
GATE ECE 2007
+2
-0.6
An input to a 6-level quantizer has the probability density function f(X) as shown in the figure. Decision boundaries of the quantizer are chosen so as to maximize the entropy of the quantizer output. It is given that 3 consecutive decision boundaries are ‘-1’, ‘0’ and ‘1’.

The values of a and b are

A
a = 1/6 and b = 1/12
B
a = 1/5 and b = 3/40
C
a = 1/4 and b = 1/16
D
a = 1/3 and b = 1/24
2
GATE ECE 2007
+2
-0.6
An input to a 6-level quantizer has the probability density function f(X) as shown in the figure. Decision boundaries of the quantizer are chosen so as to maximize the entropy of the quantizer output. It is given that 3 consecutive decision boundaries are ‘-1’, ‘0’ and ‘1’.

Assuming that the reconstruction levels of the quantizer are the mid-points of the decision boundaries, the ratio of signal power to quantization noise power is

A
$${152 \over 9}$$
B
$${64 \over 3}$$
C
$${76 \over 3}$$
D
$$28$$
3
GATE ECE 2007
+2
-0.6
Two 4-ray signal constellations are shown. It is given that $${\phi _1}$$ and $${\phi _2}$$ constitute an orthonormal basis for the two constellations. Assume that the four symbols in both the constellations are equiprobable. Let $${{{N_0}} \over 2}$$ denote the power spectral density of white Gaussian noise.

The ratio of the average energy of Constellation 1 to the average energy of Constellation 2 is

A
$$4{a^2}$$
B
$$4$$
C
$$2$$
D
$$8$$
4
GATE ECE 2007
+2
-0.6
Two 4-ray signal constellations are shown. It is given that $${\phi _1}$$ and $${\phi _2}$$ constitute an orthonormal basis for the two constellations. Assume that the four symbols in both the constellations are equiprobable. Let $${{{N_0}} \over 2}$$ denote the power spectral density of white Gaussian noise.

If these constellations are used for digital communications over an AWGN channel, then which of the following statements is true?

A
Probability of symbol error for Constellation 1 is lower
B
Probability of symbol error for Constellation 1 is higher
C
Probability of symbol error is equal for both the constellations
D
The value of N0 will determine which of the two constellations has a lower probability of symbol error.
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