Test 3 - Communication Systems | Electronics and Communication (ECE)

Question 1 Multiple Choice (Single Answer)

Two independent random variables X and Y are uniformly distributed in the interval [-1, 1]. The probability that max [X, Y] is less than 1/2 is

¾
9/16
¼
2/3

Question 2 Multiple Choice (Single Answer)

c(t) and m(t) are used to generate an FM signal. If the peak frequency deviation of the generated FM signal is three times the transmission bandwidth of the AM signal, then the coefficient of the term cos[2$\pi$(1008 $\times$10³t)] in the FM signal (in terms of the Bessel coefficients) is

5j₄(3)
$\dfrac{5}{2} j_\theta (3)$
$\dfrac{5}{2} j_\theta (3)$
5j₄(6)

Question 3 Multiple Choice (Single Answer)

Consider the pulse shape s(t) as shown. The impulse response h(t) of the filter matched to this pulse is

Question 4 Multiple Choice (Single Answer)

Let m (t) = cos [ (4^{_$\pi$$\times$}10³) t] be the message signal and c(t) = 5 cos[(2^_$\pi$^$\times$10⁶)t] be the carrier. c(t) and m(t) are used to generate an AM signal. The modulation index of the generated AM signal is 0.5. Then the quantity ^{$\dfrac{Total sideband power}{Carrier power}$}is

$\dfrac{1}{2}$
$\dfrac{1}{4}$
$\dfrac{1}{3}$
$\dfrac{1}{8}$

Question 5 Multiple Choice (Single Answer)

Match the following:|||||
|---|---|---|---|
| | Column-I| | Column-II|
| P| Power efficient transmission of signals| 1| Conventional AM|
| Q| Most bandwidth efficient transmission of
voice signals| 2| FM|
| R| Simplest receiver structure| 3| VSB|
| S| Bandwidth efficient transmission of
signals with significant dc component| 4| SSB-SC|

P - 4, Q - 2, R - 1, S - 3
P - 2, Q - 4, R - 1, S - 3
P - 3, Q - 2, R - 1, S - 4
P - 2, Q - 4, R - 3, S - 1

Question 6 Multiple Choice (Single Answer)

Four messages band limited to W, W, 2W and 3 W respectively are to be multiplexed using Time Division Multiplexing (TDM). The minimum bandwidth required for transmission of this TDM signal is

2 W
3 W
6 W
W

Question 7 Multiple Choice (Single Answer)

In the following scheme, if the spectrum M(f) of m(t) is as shown, then the spectrum Y(f) of y(t) will be

Question 8 Multiple Choice (Single Answer)

Which of the following analog modulation schemes requires the minimum transmitted power and minimum channel bandwidth?

VSB
DSB-SC
SSB
AM

Question 9 Multiple Choice (Single Answer)

A binary symmetric channel (BSC) has a transition probability of 1/8. If the binary transmit symbol X is such that P(X = 0) = 9/10, then the probability of error for an optimum receiver will be

7/80
63/80
9/10
1/10

Question 10 Multiple Choice (Single Answer)

If E denotes expectation, then the variance of a random variable X is given by

E [x²] – E² [x]
E [x²] + E² [x]
E [x²]
E² [x]

Question 11 Multiple Choice (Single Answer)

At a given probability of error, the binary coherent FSK is inferior to binary coherent PSK by

6 dB
3 dB
2 dB
0 dB

Question 12 Multiple Choice (Single Answer)

An output of a communication channel is a random variable $\nu$ with the probability density function as shown in figure. The mean square value of $\nu$ is

4
6
8
9

Question 13 Multiple Choice (Single Answer)

A four-phase and an eight-phase signal constellation are shown in the figure below

Assuming high SNR and that all signals are equally probable, the additional average transmitted signal energy required by the 8-PSK signal to achieve the same error probability as the 4-PSK signal is

11.90 dB
8.73 dB
6.79 dB
5.33 dB

Question 14 Multiple Choice (Single Answer)

A DSB-SC signal is to be generated with a carrier frequency fc = 1 MHz using a nonlinear device with the input-output characteristic V₀ = a₀v_i + a₁v_i³ where a0 and a1 are constants. The output of the nonlinear device can be filtered by an appropriate band-pass filter.
Let v_i = A'_c cos (2$\pi$f'_c t) + m(t) where m(t) is the message signal. The value of f'_c (in MHz) is

1.0
0.333
0.5
3.0

Question 15 Multiple Choice (Single Answer)

A four-phase and an eight-phase signal constellation are shown in the figure below.

For the constraint that the minimum distance between pairs of signal points be d for both constellations, the radii r₁, and r₂ of the circles are

r₁ = 0.707d, r₂ = 2.782d
r₁ = 0.707d, r₂ = 1.932d
r₁ = 0.707d, r₂ = 1.545d
r₁ = 0.707d, r₂ = 1.307d

Question 16 Multiple Choice (Single Answer)

During transmission over a certain binary communication channel, bit errors occur independently with probability p. The probability of AT MOST one bit in error in a block of n bits is given by

pⁿ
1 – pⁿ
np(1 – p)^n-1 + (1 – p)ⁿ
1 – (1 – p)ⁿ

Question 17 Multiple Choice (Single Answer)

A uniformly distributed random variable X with probability density function
f_x (x) = $\dfrac{1}{10}$(u (x + 5) - u (x - 5))
Where u (.) is the unit step function is passed through a transformation given in the figure below. The probability density function of the transformed random variable Y would be

f_y =$\dfrac{1}{5}$(u (y + 2.5) - u (y - 2.5))
f_y = 0.5$\delta$ (y) + 0.5$\delta$ (y -1)
f_y = 0.25$\delta$ (y + 2.5) + 0.25$\delta$ (y -2.5) + 0.5$\delta$(y)
f_y = 0.25$\delta$ (y + 2.5) + 0.25$\delta$ (y -2.5) + $\dfrac{1}{10}$(u (y + 2.5) - u (y - 2.5))

Question 18 Multiple Choice (Single Answer)

A zero-mean white Gaussian noise signal is passed through an ideal lowpass filter of bandwidth 10 kHz. The output is then uniformly sampled with sampling period 0.03 m. The samples so obtained would be

correlated
statistically independent
uncorrelated
orthogonal

Question 19 Multiple Choice (Single Answer)

Consider the frequency modulated signal
10 cos [2$\pi$ x 10⁵ t + 5 sin (2$\pi$ x 1500 t) + 7.5 sin (2$\pi$ x 1000 t)] with carrier frequency of 10⁵ Hz. The modulation index is

12.5
10
7.5
5

Question 20 Multiple Choice (Single Answer)

The distribution function F_x (x) of a random variable x is shown in the figure. The probability that x = 1 is

zero
0.25
0.55
0.30

Question 21 Multiple Choice (Single Answer)

In the output of a DM speech encoder, the consecutive pulses are of opposite polarities during time interval t₁^$\le$t ^$\le$t₂. This indicates that during this interval,

the input to the modulator is essentially constant
the modulator is going through slope overload
the accumulator is in saturation
the speech signal is being sampled at the Nyquist rate

Question 22 Multiple Choice (Single Answer)

A 100 MHz carrier of 1 V amplitude and a 1 MHz modulating signal of 1 V amplitude are fed to a balanced modulator. The output of the modulator is passed through an ideal high-pass filter with cut-off frequency of 100 MHz. The output of the filter is added with 100 MHz signal of 1 V amplitude and 90⁰ phase shift as shown in the figure. The envelope of the resultant signal is

constant
$\sqrt{1+sin(2\pi \times 10^6 t)}$
$\sqrt{ \dfrac{5}{4} - sin(2\pi - 10^6 t)}$
$\sqrt{ \dfrac{5}{4} + cos(2\pi - 10^6 t)}$

Question 23 Multiple Choice (Single Answer)

Directions :The amplitude of a random signal is uniformly distributed between - 5 V and 5 V.

If the signal to quantization noise ratio required in uniformly quantizing the signal is 43.5 dB, the step of the quantization is approximately

0.033 V
0.05 V
0.0667 V
0.10 V

Question 24 Multiple Choice (Single Answer)

Directions :The amplitude of a random signal is uniformly distributed between - 5 V and 5 V.

If the positive values of the signal are uniformly quantized with a step size of 0.05 V, and the negative values are uniformly quantized with a step size of 0.1 V, the resulting signal to quantization noise ration is approximately

46 dB
43.8 dB
42 dB
40 dB

Question 25 Multiple Choice (Single Answer)

A communication channel with AWGN operating at a signal to noise ration SNR >> 1 and bandwidth B has capacity C₁. If the SNR is doubled keeping constant, the resulting capacity C₂ is given by

C₂ ^_$\approx$ 2C₁
C₂ ^_$\approx$ C₁ + B
C₂^_$\approx$C₁ + 2B
C₂^_$\approx$C₁ + 0.3 B

Test 3 - Communication Systems | Electronics and Communication (ECE)

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