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Code No: RR310405 Set No. 1

III B.Tech I Semester Supplimentary Examinations, February 2008DIGITAL COMMUNICATIONS

( Common to Electronics & Communication Engineering and Electronics &Telematics)

Time: 3 hours Max Marks: 80Answer any FIVE Questions

All Questions carry equal marks⋆ ⋆ ⋆ ⋆ ⋆

1. (a) Define the Sampling theorem and establish the same for band pass signals,using neat schematics. [12]

(b) For the modulating signal m(t) = 2 Cos (100 t) + 18 Cos (2000 πt), determinethe allowable sampling rates and sampling intervals. [4]

2. (a) What are the different types of pulse modulation? [4]

(b) Prove that PWM requires a greater average power a PAM system? [12]

3. (a) Define and explain different pulse modulation schemes. [8]

(b) For the data stream 101101, find the duo-binary encoding output sequence.The data sequence to be transmitted is bk. The pre-coded sequence ak = bk

⊕ ak−1. The first bit of ak is selected arbitrarily as 0. ck = ak + ak−1 isduo-binary coder sequence. [8]

4. (a) Why equalization is necessary is Base band transmission? Give the blockdiagram of adaptive filter and explain about each element. [8]

(b) The unequalized pulse in a PAM system has the following values at samplingtimes:

pr (kTb) = pr (k) =

0.2 k = 10.8 k = 00.2 k = −1

pr(k) = 0 for |k| > 1

i. Design a three-tap zero forcing equalizer so that the equalizer output is 1at k = 0 and 0 at k = ±1

ii. Calculate Peq (k) for k = ±2,±3. [8]

5. (a) Draw the block diagram of PCM Generator and explain each block.

(b) Determine the Transmission Bandwidth in PCM. [8+8]

6. (a) The ramp signal m(t) = at is applied to a DM which operates with a samplingperiod Ts and step size δ.

i. Show that the slope over load distortion occurs in δ <a Ts.

ii. Sketch the modulator output for the following three values of step size:

A. δ=0.75a Ts

B. δ=a Ts

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C. δ=1.25a Ts [8]

(b) Consider a speech signal with maximum frequency of 3.4 kHz and maximumamplitude of 1v. This speech signal is applied to a DM whose bit rate is setat 20kbps. Discuss the choice of appropriate step size for the modulator. [8]

7. (a) In the on-off keying version of an ASK system, symbol 1 is represented byTramsmitting a sinusoidal carier of amplitude

√2Eb / Tb, where Eb is the

signal energy per bit and Tb is the bit duration. Symbol ‘0’ is represented byswitching off the carrier. Assume that 1 and 0 occur with equal probability.For an AWGN channel determine the average probability of error for this ASKsystem, assuming

i. Coherent reception

ii. Noncoherent reception, operating with a large value of a bit energy-to-noise density ratio.

Note: For large value of xI0(x) ≈ exp (x) / (

√2 Πx)

(b) A high frequency transmitter used in a binary communication system is peakPower limited to 1 kw. The power loss in the channel is 60 dB and thenoise power at the receiver input (ηrb) is 10−4 Watts. Assuming maximumsignaling rate and equiprobable message bits, find Pe for non coherent ASKand coherent PSK signaling schemes. [8+8]

8. (a) What are the different methods of correcting errors? Discuss about the differ-ent types of transmission errors in a communication system? [8]

(b) Show a generic circuit to decode a block code. [8]

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1. (a) Define the Sampling theorem and establish the same for band pass signals,using neat schematics. [12]

(b) For the modulating signal m(t) = 2 Cos (100 t) + 18 Cos (2000 πt), determinethe allowable sampling rates and sampling intervals. [4]

2. (a) Sketch and explain the typical waveforms of PWM signals, for leading edge,trailing edge and symmetrical cases.

(b) Compare the analog pulse modulation schemes with CW modulation systems.

(c) Show that a PAM signal can be expressed as the convolution of an instanta-neously sampled signal, and a rectangular pulse p(t) of the form

p (t) =

{

1, |t| ≤ τ/20 elsewhere

[5+5+6]

3. (a) Explain the base band transmission of M-ary data with suitable diagrams. [8]

(b) A certain telephone line bandwidth is 4 KHz. Calculate the data rate in bpsthat can be transmitted if we use binary signaling with raised cosine pulsesand a roll-off factor α = 0.25. [8]

4. (a) Explain how eye patterns are used for monitoring the performance of baseband PAM system. [8]

(b) What is the necessity of shaping transmitted signal spectrum. [8]

5. (a) A PCM system is to have a Signal to Noise Ratio of 40dB.The signals arespeech and an RMS to peak ratio of -10dB is allowed for. Find the number ofbits per code word required.

(b) A telephone signal with a cutoff frequency of 4kHz is digitized into 8-bit sam-ples at Nyquist rate Assume raised cosine filtering is used with roll-off factorof unity. Calculate

i. The baseband transmission Bandwidth.

ii. The quantization SNR. [8+8]

6. In a single-integration DM system, the voice signal is sampled at a rate of 64kHz.Themaximum signal amplitude is Amax=1.

(a) Determine the minimum value of the step size σ to avoid slope over load error.

(b) Determine the granular noise power if the voice signals bandwidth is 3.5 kHz.

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(c) Assuming that the voice signal is sinusoidal, determine output signal powerand SNR

(d) Determine the minimum transmission bandwidth. [4+4+4+4]

7. (a) What are power spectra? Explain power spectra of binary PSK and FSKsignals along with graphs. [8]

(b) Give the comparison of M-ary digital modulation techniques. [8]

8. Consider a (7,4) linear code whose generator matrix is

G =

1 0 0 0 1 0 10 1 0 0 1 1 10 0 1 0 1 1 10 0 0 1 0 1 1

(a) Find all the code vectors of this code.

(b) Find the parity check matrix for this code.

(c) Find the minimum weight of this code

(d) Show the error correction capability of this code. [16]

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1. (a) Define the band pass sampling theorem. Verify the signal recovery for thespectrum X(f) of an ideally sampled signal shown in Figure1a, for the twocases, when

i. fs = 20 KHz,

ii. f s = 30 KHz

Figure 1aSketch and explain the spectrum, bringing out the aliasing effects if any, ineach case. [10]

(b) Two signals 10 Cos (1000 πt) and 10 Cos (50 πt) are both sampled at 75 Hz.Find and compare the sampled frequencies in both cases. [6]

2. (a) What are the advantages and limitations of PAM systems. [4]

(b) List out the applications, merits and demerits of PPM signals. [4]

(c) Explain the process of generation and recovery of PWM signals, with neatschematics. [8]

3. (a) Derive the probability of error in base band PAM transmission? [8]

(b) Design a binary base band PAM system to transmit data at a rate of 9600bps with a bit error probability Pe < 10−5. The channel available is an ideallowpass channel with a bandwidth of 9,600Hz. The noise can be assumed to bewhite, Gaussian with a two-sided psd η/2 = 10−13 Watt/Hz. Sketch the shapeof |HT (f)| , |HR(f)| , |Pg(f)| and find the Transmitter power requirements.

[8]

4. (a) With the help of block diagram explain how clock waveform is derived fromthe received waveform? [8]

(b) Extended Binary-coded Decimal Interchange code (EBCDIC) has 256 charac-ters which are binary coded. If a computer generates 200000 characters persecond, determine,

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i. The number of bits required per character,

ii. The data rate Rb required to transmit the computer output. [8]

5. (a) Draw the block diagram of PCM Generator and explain each block.

(b) Determine the Transmission Bandwidth in PCM. [8+8]

6. (a) The ramp signal m(t) = at is applied to a DM which operates with a samplingperiod Ts and step size δ.

i. Show that the slope over load distortion occurs in δ <a Ts.

ii. Sketch the modulator output for the following three values of step size:

A. δ=0.75a Ts

B. δ=a Ts

C. δ=1.25a Ts [8]

(b) Consider a speech signal with maximum frequency of 3.4 kHz and maximumamplitude of 1v. This speech signal is applied to a DM whose bit rate is setat 20kbps. Discuss the choice of appropriate step size for the modulator. [8]

7. (a) Explain in detail a correlation receiver and integrate and dump correlationreceiver. [8]

(b) A band pass data Transmission scheme uses a PSK signaling scheme withs2(t) = A cosωct , 0<=t<=Tb, ωc=10π/Tb

s1(t) = -A cosωc t , 0<=t<=Tb, Tb=0.2msecThe carrier amplitude at the receiver input is 1 mvolt and the psd of theadditive white gaussian noise at the input is 10 −11 W/Hz.assume that anideal correlation receiver is used. Calculate the average bit error rate of thereceiver. [8]

8. (a) Show that if g(x) is a polynomial of degree (n-k) and is a factor of xn+1, theng(x) generates an (n,k) cyclic code in which the code polynomial for a datavector D is generated by v(x) = D(x)g(x). [8]

(b) What are the hardware components required to implement a cyclic code en-coder? [8]

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1. (a) State and prove Sampling Theorem as applicable to band limited signals.

(b) Find the minimum sampling rate and Nyquist interval for the signals repre-sented by

i. m(t) and

ii. m2(t) where m(t) = Sin(300πt)πt

[12+4]

2. (a) Sketch and explain the typical waveforms of PWM signals, for leading edge,trailing edge and symmetrical cases.

(b) Compare the analog pulse modulation schemes with CW modulation systems.

(c) Show that a PAM signal can be expressed as the convolution of an instanta-neously sampled signal, and a rectangular pulse p(t) of the form

p (t) =

{

1, |t| ≤ τ/20 elsewhere

[5+5+6]

3. (a) Suggest a method to transmit data at the rate of rb bits/sec. over channelwith a bandwidth of rb/2 Hz and explain it. [8]

(b) A base band binary PAM system uses a signaling waveform Pg(t) = Sin π rbt

π rbt

to transmit binary data at a bit rate of rb bps. The amplitude levels at thepulse generator out put are + 1V or – 1V, +1 if the in put bit is 1 and -1 ifthe input bit is 0. Sketch the waveform of the pulse generator output whenthe input bit string is 1001101. [8]

4. (a) Give the block diagram of a system used to derive a clock-signal from thereceived waveform and explain its operation. [8]

(b) Compare the performance of bi-polar coding, twinned binary coding in termsof d.c component, bandwidth required and clock recovery? [8]

5. (a) Explain the working of DPCM system with neat block diagram.

(b) Compare PCM & DPCM system. [10+6]

6. In a single-integration DM system, the voice signal is sampled at a rate of 64kHz.Themaximum signal amplitude is Amax=1.

(a) Determine the minimum value of the step size σ to avoid slope over load error.

(b) Determine the granular noise power if the voice signals bandwidth is 3.5 kHz.

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(c) Assuming that the voice signal is sinusoidal, determine output signal powerand SNR

(d) Determine the minimum transmission bandwidth. [4+4+4+4]

7. Why FSK is preferred over ASK ? Give reasons. How FSK is generated and obtainthe expression for its bandwidth .Briefly discuss regarding its frequency spectrum.

[16]

8. (a) Describe Exhaustive search method of decoding for convolutional code. [8]

(b) What is an interlaced code? Explain about its capability for correcting errorswith suitable example. [8]

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