Dc Nov08

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Set No. 1

Code No: R05310404

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 ⋆⋆⋆⋆⋆

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

(b) Plot Pe Versus N, for N = 2, 4, 6 and 8.

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(a) Show that the threshold occurs when Pe ≈ 1/[16(22N )].

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

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2. (a) What is Delta modulation and compare with PCM? [8+8]

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(b) Discuss different types of noise effects in delta modulation.

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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.

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(b) What are the advantages and disadvantages of digital modulation schemes?

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(c) Discuss base band transmission of M-ary data.

[4+6+6]

4. (a) Explain how the residual effects of the channel are responsible for ISI?

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(b) What is the practical solution to obtain zero ISI? Explain.

[8+8]

5. (a) Define 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 i. C/B 1 of 2

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Set No. 1

Code No: R05310404

ii. Dt / B. where Dt is rate of information transmission over channel.

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7. Explain about block codes in which each block of k message bits encoded into block of n>k bits with an example. [16] 8. Explain various methods for describing Conventional Codes.

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Set No. 2

Code No: R05310404

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. (a) Derive the relation for signaling rate and transmission bandwidth in a PCM system.

[8+4+4]

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2. (a) Write short notes on

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i. Quantization noise in a PCM ii. Nyquist rate & Nyquist interval

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(b) Explain the terms:

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i. Granular Noise ii. Slope overload distortion.

[8+8]

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(b) Derive an expression for quantization noise in Delta modulation.

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3. (a) A binary base band is passed through a raised cosine roll - off filter with a 50% roll - off factor and is then modulated on to a carrier. The data rate is 64kbits/sec. Evaluate

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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.

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(b) Write the comparisons among binary modulated band pass signaling scheme (ASK, PSK and FSK). [10+6] 4. (a) What is meant by ISI? Explain how it differs 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. Define 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.

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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] 1 of 2

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Set No. 2

Code No: R05310404

7. Let H be the parity check matrix of (n-k) linear block code C with an odd minimum weight d. Construct a new code [16] C1 whose parity check matrix is |0 |0 |0 |. H |. H1 = |. |0 − − − − − |− − − 11....1 |1

(b) the minimum weight of C1 is d+1.

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(a) every code vector in C1 has not odd weight.

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Show that

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8. Explain various methods for describing Conventional Codes.

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Set No. 3

Code No: R05310404

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 specifications of a PCM signal of a digital telephone system is as follows: Sampling frequency : 8k samples/sec.

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And each sample is represented by 8 bits. Then find

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Audio voice frequency : 300Hz to 3400Hz

(a) Bit rate, the first null bandwidth and Signal power to quantization power ratio

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(b) Minimum bandwidth required if

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

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2. (a) Compare Delta modulation and PCM techniques in terms of bandwidth and signal to noise ratio.

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(b) A signal m(t) is to be encoded using either Delta modulation or PCM technique. The signal to quantization noise ratio (SO /NO ) ≥ 30dB. Find the ratio bandwidth required for PCM to Delta Modulation. [8+8]

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3. (a) Explain the signal space representation of QPSK. [8+8]

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(b) Compare QPSK with all other digital signaling schemes. 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 probability. [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 σ2. Calculate average mutual information I(X; Y). [16] 6. A Binary Symmetric channel is shown in figure 6.

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Set No. 3

Code No: R05310404

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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]

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7. Explain about block codes in which each block of k message bits encoded into block of n>k bits with an example. [16]

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8. Explain various methods for describing Conventional Codes.

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Set No. 4

Code No: R05310404

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. 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.

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(a) Find N and minimum value of Si /η if operation is to be above threshold.

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(b) Calculate minimum system bandwidth required and find signaling rate needed to achieve the given output SNR. [4+4+4+4] 2. (a) What is Delta modulation and compare with PCM?

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(b) Discuss different types of noise effects in delta modulation.

[8+8]

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3. (a) Explain the signal space representation of QPSK.

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(b) Compare QPSK with all other digital signaling schemes.

[8+8]

4. (a) Derive an expression for error probability of non - coherent ASK scheme.

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(b) Binary data is transmitted over an RF band pass channel with a usable bandwidth 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 10−15 w/Hz.

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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.

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6. (a) Define the channel capacity in terms of average signal-power and noise power. (b) Mention the two important implications of Shannon-Hartley theorem? 7. Consider 1 G = 0 0

a (6, 3) generator matrix. 0 0| 0 1 1 1 0| 1 0 1 0 1| 1 1 0

Find (a) all the code vectors of this data. 1 of 2

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Set No. 4

Code No: R05310404 (b) the parity check matrix for this code. (c) the minimum weight of this code.

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8. Explain various methods for describing Conventional Codes.

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