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Code No: R05310404
Set No. 1
III B.Tech I Semester Regular Examinations, November 2007
DIGITAL COMMUNICATIONS
( Common to Electronics & Communication Engineering and Electronics &
Telematics)
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks

1. The threshold value of the input signal power to noise ratio ( )i in PCM system
is de ned as the value of ( )i for which the value of (S/N)o is 1dB below its
maximum.

(a) Show that the threshold occurs when e ˜ 1 [16(22N )]
(b) Plot e Versus N, for N = 2, 4, 6 and 8.

(c) Sketch the threshold values of ( )i Versus N for which N = 2, 4, 6 and 8
(Assume that a PSK signaling scheme is used) [6+5+5]

2. (a) What is Delta modulation and compare with PCM?
(b) Discuss di erent types of noise e ects in delta modulation. [8+8]

3. (a) Write down the modulation waveform for transmitting binary information over
base band channels, for the following modulation schemes: ASK, PSK, FSK
and DPSK.
(b) What are the advantages and disadvantages of digital modulation schemes?
(c) Discuss base band transmission of M-ary data. [4+6+6]

4. (a) Explain how the residual e ects of the channel are responsible for ISI?
(b) What is the practical solution to obtain zero ISI? Explain. [8+8]

5. (a) De ne Information rate.
(b) One of four possible messages Q1, Q2, Q3, Q4 having probabilities 1/8, 3/8,
3/8 and 1/8 respectively is transmitted. Calculate average Information per
message. [16]

6. An Ideal channel lowpass channel of bandwidth B Hz with additive Gaussian white
noise is used for transmitting of digital information.

(a) Plot C/B versus S/N in dB for an Ideal System using this channel.
(b) A practical signaling scheme on this channel uses one of two waveforms of
duration Tb sec to transmit binary information.
The signaling scheme transmits data at the rate of 2B bits/sec, the probability
of error is given by P(error|1sent) =Pe.
Plot graphs of


Code No: R05310404
Set No. 1
ii. Dt / B. where Dt is rate of information transmission over channel. [16]

7. Explain about blo ck codes in which each block of k message bits enco ded into block
of n k bits with an example. [16]

8. Explain various methods for describing Conventional Codes. [16]


Code No: R05310404
Set No. 2
Telematics)

1. (a) Derive the relation for signaling rate and transmission bandwidth in a PCM
system.
(b) Explain the terms:
i. Quantization noise in a PCM
ii. Nyquist rate & Nyquist interval [8+4+4]

2. (a) Write short notes on
i. Granular Noise
ii. Slope overload distortion.
(b) Derive an expression for quantization noise in Delta modulation. [8+8]

3. (a) A binary base band is passed through a raised cosine roll - o lter with a
50% roll - o factor and is then modulated on to a carrier. The data rate is
64kbits/sec. Evaluate
i. The absolute bandwidth of a resulting ASK signal.
ii. The approximate bandwidth of a resulting FSK signal when the mark
frequency is 150kHz and the space frequency is 155kHz.
(b) Write the comparisons among binary mo dulated band pass signaling scheme
(ASK, PSK and FSK). [10+6]

4. (a) What is meant by ISI? Explain how it di ers from cross talk in the PAM.
(b) What is the ideal solution to obtain zero ISI and what is the disadvantage of
this solution. [6+10]

5. De ne and explain the following in terms of joint pdf p(x, y) and marginal pdf’s
p(x) and p(y).

(a) Mutual Information.
(b) Average Mutual Information.

(c) Entropy. [16]

6. (a) Calculate the bandwidth limits of Shannon-Hartley theorem.
(b) What is an Ideal system? What kind of method is proposed by Shannon for
an Ideal system? [16]


Code No: R05310404
Set No. 2
7. Let H be the parity check matrix of (n-k) linear block code C with an o dd minimum
weight d. Construct a new code C1 whose parity check matrix is [16]
|0
|0
|0
|
1= |
|
|0
- - - - - |- - -
11 1 |1
Show that

(a) every code vector in C1 has not o dd weight.
(b) the minimum weight of C1 is d+1.
[16]



Code No: R05310404
Set No. 3
Telematics)

1. The speci cations of a PCM signal of a digital telephone system is as follows:
Audio voice frequency : 300Hz to 3400Hz
Sampling frequency : 8k samples/sec.
And each sample is represented by 8 bits. Then nd

(a) Bit rate, the rst null bandwidth and Signal power to quantization power ratio
(b) Minimum bandwidth required if

i. Sinc pulse is used to generate PCM
ii. Rectangular pulse shaping is used [16]

2. (a) Compare Delta modulation and PCM techniques in terms of bandwidth and
signal to noise ratio.
(b) A signal m(t) is to be encoded using either Delta modulation or PCM tech-
nique. The signal to quantization noise ratio ( O O) = 30dB. Find the ratio
bandwidth required for PCM to Delta Modulation. [8+8]

3. (a) Explain the signal space representation of QPSK.
(b) Compare QPSK with all other digital signaling schemes. [8+8]

4. (a) Derive an expression for error probability of coherent ASK scheme.
(b) Binary data has to be transmitted over a telephone link that has a usable
bandwidth of 3000Hz and a maximum achievable SNR of 6dB at its output
i. Determine the maximum singling rate and error probability if a coherent
ASK scheme is used for transmitting binary data through this channel.
ii. If the data rate is maintained at 300 bits/sec. calculate the error proba-
bility. [8+8]

5. Let X is a discrete random variable with equally probable outcomes x1=A, and x2=-
A and conditional probability pdf’s p(y/xi), i=1, 2 be the Gaussian with mean xi
and variance 2. Calculate average mutual information I(X; Y). [16]

6. A Binary Symmetric channel is shown in gure 6.


Code No: R05310404
Set No. 3

Figure 6
Find the rate of information transmission over this channel when p= 0.9, 0.8 and
0.6. Assume that the symbol rate (or bit) is 1000/sec. [16]

7. Explain about blo ck codes in which each block of k message bits enco ded into block
of n k bits with an example. [16]



Code No: R05310404
Set No. 4
Telematics)

1. A signal m(t) band limited to 4kHz is sampled at twice the Nyquist rate and the
samples transmitted by PCM. An output SNR of 47dB is required.

(a) Find N and minimum value of i if operation is to be above threshold.
(b) Calculate minimum system bandwidth required and nd signaling rate needed
to achieve the given output SNR. [4+4+4+4]

2. (a) What is Delta modulation and compare with PCM?
(b) Discuss di erent types of noise e ects in delta modulation. [8+8]

3. (a) Explain the signal space representation of QPSK.
(b) Compare QPSK with all other digital signaling schemes. [8+8]

4. (a) Derive an expression for error probability of non - coherent ASK scheme.
(b) Binary data is transmitted over an RF band pass channel with a usable band-
width of 10MHz at a rate of 4,8 × 106 bits/sec using an ASK singling method.
The carrier amplitude at the receiver antenna is 1mV and the noise power
spectral density at the receiver input is 10-15w/Hz.

i. Find the error probability of a coherent receiver.
ii. Find the error probability of a coherent receiver. [8+8]

5. Write short notes on the following:

(a) Mutual Information.
(b) Self Information.

(c) Logarithmic measure for information. [16]

6. (a) De ne the channel capacity in terms of average signal-power and noise power.
(b) Mention the two important implications of Shannon-Hartley theorem? [16]

7. Consider a (6, 3) generator matrix.
1 0 0| 0 1 1
= 0 1 0| 1 0 1
0 0 1| 1 1 0
Find


Code No: R05310404
Set No. 4
(b) the parity check matrix for this code.
(c) the minimum weight of this code. [16]


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