# EC503

```CORPORATE INSTITITUTE OF SCIENCE &amp; TECHNOLOGY, Bhopal
Important Questions
Digital Communication (EC-503)
Unit-1
1. Define random variable.
2. Write and explain different types random variables.
3. Prove the following:
a. σ2 = E[(X-&micro;)2] = E(X2) - &micro;2
where σ is variance and &micro; is mean.
Define mean, variance &amp; standard deviation.
Explain Correlation of random Variables.
Define cumulative distribution function (CDF) &amp; and its properties.
Write &amp; explain central limit theorem.
Define probability density function (PDF) and its properties.
The joint density function of two continuous random variables X and Y is given by
a. f(x,y) = 2
for 0&lt;x&lt;1, 0,y&lt;x
i. 0,
otherwise
b. Find : (i)The marginal density functions
c. (ii) The conditional density function
10. A random variable has an exponential PDF as fx(x)=ae-b|x|, where a and b are constants
Find (a) the relationship between a and b and (b) the distribution function of x.
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Unit-2
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Explain Nyquist rate.
State and prove sampling theorem. How sampled signal is recovered using LPF? What is aliasing?
Explain PAM PWM and PPM signals.
Explain the direct and indirect method of PWM &amp; PPM generation.
Why flat top sampling is preferred over natural sampling?
What is the function of companding?
With the help of block diagram explain the working of PCM system.
Describe Delta modulation. What are its limitations? How can they be overcome?
Explain quantization in detail. What is quantization error or quantization noise?
Draw and explain the working of adaptive delta modulation.
Unit -3
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ASK is the simplest of the keying system , still it is rarely used, why?
What is the merit of DPSK on BPSK.
Draw the block diagram of DPSK
What is ON-OFF keying?
Describe generation and detection of BFSK.
With the help of block diagram explain QPSK. Differentiate between offset and non offset QPSK.
Draw and explain the transmitter &amp; receiver of QAM.
Give a brief comparison between BASK, BPSK &amp; BFSK.
Explain the generation and reception of M-ary PSK scheme.
24 telephone channels each band limited to 3.4KHz, are to be time division multiplexed by using PCM.
Calculate the bandwidth of the PCM system for 128 quantization levels and an 8 KHz sampling frequency.
Unit-4
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What is Eye Pattern? Explain with diagram.
Define Interchannel Interference.
Explain regenerative repeatears.
Discuss the properties of matched filter.
Explain Intersymbol Interference.
Explain Partial response signaling.
Discuss about Duo Binary Encoding system.
Explain how pulse shaping is reduce inter-channel and inter-symbol interference.
Explain the Nyquist criteria for distortion less baseband binary transmission
Unit-5
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Define information.
Define Entropy, State its expression and units.
What is mutual information, also give its expression.
State and explain Shannon’s theorem.
What is Channel Capacity?
Derive the condition for maximum entropy for M=2 and M=3.
Apply Shannon Fano coding and find the coding efficiency of the given message for M=2.
[ 0.12 0.07 0.2 0.15 0.1 0.02 0.04 0.3]
48. Define rate of information.
49. Apply Huffman coding and find the coding efficiency of the given message for M=2.
[ 0.3 0.25 0.20 0.12 0.08 0.05]
50. Find the mutual information and channel capacity of the channel shown below. Given
P(x1) = 0.6 and P(x2) = 0.4
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