1
GATE ECE 2007
MCQ (Single Correct Answer)
+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. GATE ECE 2007 Communications - Noise In Digital Communication Question 20 English

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
$$8$$
2
GATE ECE 2007
MCQ (Single Correct Answer)
+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. GATE ECE 2007 Communications - Noise In Digital Communication Question 19 English

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.
3
GATE ECE 2007
MCQ (Single Correct Answer)
+1
-0.3
If the Laplace transform of a signal y(t) is $$Y\left(s\right)\;=\;\frac1{s\left(s\;-\;1\right)}$$ , then its final value is:
A
-1
B
$$0$$
C
1
D
unbounded
4
GATE ECE 2007
MCQ (Single Correct Answer)
+2
-0.6
The frequency response of a linear, time-invariant system is given by $$H\left(f\right)\;=\;\frac5{1\;+\;j10\mathrm{πf}}$$ .The step response of the system is:
A
$$5\left(1\;-\;e^{-5t}\right)u\left(t\right)$$
B
$$5\left(1\;-\;e^{-\frac15}\right)u\left(t\right)$$
C
$$\frac15\;\left(1\;-\;e^{-5t}\right)u\left(t\right)$$
D
$$\frac15\;\left(1\;-\;e^{-\frac15}\right)u\left(t\right)$$
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