LATHA MATHAVAN ENGINEERING COLLEGE Alagarkovil, Madurai

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1 UNIT I - SAMPLING & QUANTIZATION PART A 1. What is aliasing? (EC6501 June 2016) 2. What is Companding? Sketch the input-output characteristics of a compressor and an expander. (EC6501 June 2016) 3. An analog waveform with maximum frequency content of 3 khz is to be transmitted over an M-ary PCM system, where M=16. What is the minimum number of bits/sample that should be used in Digitizing the analog waveform? (The quantization error is specified not to exceed ± 1 % of the peak -to-peak analog signal) (EC2301 June 2016) 4. State Sampling theorem? (June 2011, 2015) 5. Define Non uniform quantization? (June 2015) 6. What is the need for non-uniform quantization? (June 2014) 7. What is difference between natural and flat top sampling (Nov 2014) 8. State any two non-uniform quantisation rules. (June2013) 9. What is natural sampling? (June, Nov 2013) 10. Write a law of compression? (Nov 2013) 11. What is quantization error? (June 2011) 12. Define quantization noise power. (Dec 2010) 13. A message has zero mean value and a peak value of 10V. It is to be quantized using a Step size of 0.1V with one level coinciding with 0V.Find the number of bits required for Encoding the quantized signal. (June 2007) 14. A signal x (t) = 5 Cos (1000πt) is sampled and quantized using 8 bit PCM system. Find the signal to quantization noise ratio. (Dec 2007) 15. Plot the magnitude spectrum of the ideally sampled version of the signal M (t) = 2 Cos (200πt) + 40 Sin (290πt).Assuming the sampling rate is 1 KHz. (June2008) PART B 1. (i) State the low pass sampling theorem and explain reconstruction of the signal from its samples.(9) (ii) The signal x(t) = 4 cos 400 Пt + 12 cos 360 Пt is ideally sampled at a frequency of 300 samples Per second. The sampled signal is passed through a unit gain low pass filter with a cut off frequency of 220 Hz. List the frequency components present at the output of the low pass filter? (7) (EC6501 June 2016) 2. (i) Explain the Pulse Code Modulation system with neat block diagram.(10) (ii) What is TDM? Explain the difference between analog TDM and digital TDM.(6)(EC6501 June 2016) 3. Explain Non - Uniform quantization technique. (8) (June 2011, 2014) 4. Explain the principal of quantization and obtain the expression for the signal to quantization noise for the case of uniform quantizer (16) (Dec 2014) 5. (i) Explain Nyquist sampling theorems and how the message can be reconstructed from its samples with an example. (Dec 2014) (ii) Explain the practical limitation in sampling and reconstruction. (Dec 2014) 6. Explain a PCM system. Derive the expression for quantization noise of a PCM system With uniform quantizer. (16) (June 2013) 7. Explain the process of quantization and obtain an expression for signal to quantization ratio in the case of a uniform quantizer. (16) (Dec 2013) 8. State the Nyquist sampling theorem. Demonstrate its validity for an analog signal x (t) having a Fourier transform x(f) which is zero outside the interval [-f m < f < +f m] (16) (Dec 2010) 9. Explain with a neat sketch Time Division Multiplexing (8) (June 2007) 10. Explain the process of quantization, encoding and decoding in PCM. In what way DPCM is Better than PCM? (16) (June 2007) 1

2 UNIT II - WAVEFORM CODING PART A 1. What are the advantages of Delta Modulator? (EC6501 June 2016) 2. What is a linear predictor? On what basis are the predictor coefficients determined? (EC6501 June 2016) 3. Differentiate the principles of temporal waveform coding and model based coding. (EC2301 June 2016) 4. Mention the merits of DPCM. 5. What is the main difference in DPCM and DM? 6. What is meant by Adaptive Delta Modulation? 7. What is the advantage of delta modulation and Disadvantages of Delta Modulation? (Nov2008) 8. What should be the minimum bandwidth required to transmit a PCM channel? (Dec 2007) 9. What is the advantage of delta modulation over PCM? (Dec 2007) 10. What are the two limitations of delta modulation? (May 2004) 11. How does Granular noise occurs? (May 2004) 12. A 64 kbps binary PCM polar NRZ signal is passed through a communication system with a raised Cosine filter with roll-off factor Find the bandwidth of a filtered PCM signal. (NOV2012) PART B 1. (i) Draw the block diagram of ADPCM system and explain its function.(10) (ii) A delta modulator with a fixed step size of 0.75 V, is given a sinusoidal message signal. If the sampling frequency is 30 times the Nyquest rate, determine the maximum permissible Amplitude of the message signal if slopes overload is to be avoided. (6) (EC6501 June 2016) 2. ( i) Draw the block diagram of an Adaptive Delta Modulator with continuously variable step size And explain. (10) (ii) Compare PCM system with delta Modulation system (6) (EC6501 June 2016) 3. Explain a DPCM system. Derive the expression for slope overload noise of the system. Show that SNR of DPCM is better than that of PCM. (EC2301 June 2016) 4. (i) Explain sub band coding. (8) (ii) Compare the performance of various speech encoding methods. (8) (EC2301 June 2016) 5. Describe the linear predictive coding technique in speech encoding (June 2014) 6. (i) Draw the block diagram of Adaptive Delta Modulation system and explain (Dec 2007) (ii) Explain the two types of quantization noise in Delta Modulation system (Dec 2007) 7. Explain the slope overload and granular noise in delta modulation 8. Explain with neat diagram of Delta Modulation system 9. Compare various Digital Modulation Techniques 10. Compare various speech encoding Techniques UNIT III - BASEBAND TRANSMISSION PART A 1. What are line codes? Name some popular line codes. (EC6501 June 2016) 2. What is ISI and what are the causes of ISI? (EC6501 June 2016) 3. What is the use of eye pattern? (EC2301 June 2016) 4. Give four applications of eye pattern? (June 2011, 2015) 5. What are requirement for line code? (June 2014) 6. What is ISI? (June, Nov 2014) 7. What is the function of the equalizing filter? (Nov 2014) 8. What is Manchester coding? What is its advantage? (Nov 2014) 9. Define transparency of a line code. Give two examples of line codes which are not transparent? (June2011, 2013) 10. ISI cannot be avoided justify the statement. (June 2013) 11. What is the use of eye pattern? (Nov 2013) 2

3 12. How does pulse shaping reduce inter symbol interference? (Dec 2010) 13. Draw the NRZ and RZ code for the digital data (Dec 2010) 14. What is the need for a demodulator in case of base band signalling when the received Waveforms are already pulse like form? 15. Define the principle of adaptive equalization? PART-B 1. (i) Draw the power spectra of (a) Polar NRZ and (b) bipolar RZ signals. (8) (ii) Compare the various line coding techniques and list their merits and demerits. (8) (EC6501 June 2016) 2. (i) Draw the block diagram of Duo binary signalling scheme without and with precoder and explain.(9) (ii) Explain the adaptive equalization with block diagram. (7) (EC6501 June 2016) 3. Explain the Nyquist first criterion for ISI elimination (June2015, 2016) 4. (i) Describe any one method for ISI control (June 2014) (ii) List the inference made from the eye pattern (June 2014) 5. Derive and draw the power spectra of a NRZ, (i) Polar coded waveform.(8) (June 2013) (ii) Bipolar coded waveform. (8) (June 2013) 6. (i) Describe with a diagram the functioning of a correlator type receiver. (Dec 2013) (ii) Explain the equivalence between correlator and matched filter receiver. (Dec 2013) 7. Draw the power spectra of polar codes and on-off codes. Discuss their characteristics (16) (June2011) 8. What does the term equalization refer to? Explain how it is carried out by using transverse filters. (16) (Dec 2010) 9. Draw the block diagram of adaptive equalization and explain (Dec 2007) 10. Discuss the following: (i) Adaptive equalization (ii) Base band M- ary PAM transmission (June 2007) UNIT IV - DIGITAL MODULATION SCHEME PART A 1. Distinguish between coherent and non coherent reception. (EC6501 June 2016) 2. What is QPSK? Write the expression for the signal set of QPSK. (EC6501 June 2016) 3. What are the draw backs of binary PSK system. (EC2301 June 2016) 4. What are coherent and non-coherent receivers? (June 2015, 2016) 5. What are the advantages of QPSK over PSK? (June 2014) 6. Draw the signal space diagram for QAM signal for M=8? (June 2014) 7. Draw constellation diagram of QAM? (Nov 2014) 8. Define QAM and draw its constellation diagram. (Dec 2010) 9. A binary frequency shift keying system employs two signalling frequencies f 1 and f 2. The lower frequency f 1 is 1200 Hz and signalling rate is 500 Baud. Calculate f 2. (Dec 2010) 10. Plot the power spectrum of a BPSK signal operated with a carrier frequency of 140MHz, Modulated by data bits at a rate of 2400 bits/sec. What is the bandwidth requirement? PART B 1. Explain the generation and detection of Coherent binary PSK signal and derive the Power Spectral density of binary PSK signal and plot it (16) (EC6501 June 2016) 2. Explain the non-coherent detection of FSK signal and derive the expression for probability of error.(16) (EC6501 June 2016) 3. (i) Derive the functional block diagram of modulator for QAM and explain its operation (ii) Draw the block diagram of QPSK transmitter and receiver. Explain the function of various block. (EC2301 June 2016) 4. (i) Draw the functional block diagram of Modulator for QAM and explain its operation.(8) (ii) Derive the expression for error probability of QAM system. (8) (EC2301 June 2016) 3

4 5. (i) Explain Gram- Schmidt orthogonalisation procedure. (12) (ii) State and explain the dimensionality theorem. (4) (EC2301 June 2016) 6. Derive the bit error probability of QPSK receiver (16) (June 2013, 2015) 7. (i) Define basis set. How they are useful in representing a signal?(8) (June 2014) (ii) With an example, Explain how the basis set is determined by GSOP.(8) (June 2014) 8. (i) Describe the following modulation method (i) BPSK (ii) QAM (10) (June 2014) (ii) Compare the performance of various digital modulation schemes (6) (June 2014) 9. Discuss about the coherent detection of QPSK and non-coherent detection of DPSK (June 2014) 10. (i) Explain geometric representations of signals? (8) (Nov 2014) (ii) Explain different mathematical modes of a communication channels? (8) (Nov 2014) UNIT V - ERROR CONTROL CODING PART A 1. What is linear code? (EC6501 June 2016) 2. What is meant by constraint length of a convolutional encoder? (EC6501 June 2016) 3. Define Hamming distance and Hamming Weight? (EC2301 June 2016, 2015) 4. Define constraint length of a convolutional coder? (EC2301 June 2016, 2015) 5. What is need for error control codes? (Nov 2014) 6. Define code rate of a block code? (Nov2013) 7. State the significance of minimum distance of a block code. (June 2013) 8. State the principle of maximum likelihood detector. (June 2013) 9. Define Hamming distance and calculate its value for two code words and (Dec 2010) 10. Define the Channel coding 11. Differentiate Source coding from the Channel coding. 12. What is syndrome? 13. Define Code rate. 14. Define CRC. 15. Find the Hamming distance between and If the minimum Hamming distance of a (n,k) linear block code is 3, what is the minimum Hamming weight? PART B 1. Consider a linear block code with generator Matrix ( ) (i) Determine the parity check matrix. (ii) Determine the error detecting and capability of the code. (iii) Draw the encoder and syndrome calculation circuits. (iv) Calculate the syndrome for the received vector r = [ ]. (EC6501 June 2016) 2. (i) The generator polynomial of a (7,4) cyclic code is 1 + X + X 3. Develop encoder and Syndrome calculator for this code. (8) (ii) Explain the Viterbi decoding algorithm for convolutional code. (8) (EC6501 June 2016) 3. Explain the steps involved in the generation of linear block codes. Define and explain the Properties of syndrome. (16) (EC2301 June 2016) 4. (i) Explain how convolutional codes are generated? Illustrate with an example. (8) (ii) For a convolutional encoder of constraint length 3 and rate ½, obtain the encoded Output for the input message (8) (EC2301 June 2016) 5. Explain Viterbi algorithm to decode a convolutional coded message with an example? (June2013, 2015) 4

5 6. (i) Brief about any one decoding procedure of linear block codes (8) (June 2014) (ii) Find a generator for a (7,4) cyclic code hence find the code word for [ ] (8) (June 2014) 7. Describe coherent detection using maximum likelihood detector. (Dec 2013) 8. Assume a (2, 1) convolutional coder with constraint length 6. Draw the tree diagram, State diagram and Trellis diagram for the assumed coder. (16) (June 2011) 9. Find the (7, 4) linear systematic block code word corresponding to 1101.Assume a suitable Generator matrix. (16) (June 2011) 10. For (6, 3) systematic linear block code, the code word comprises I1, I 2, I 3, P 1, P 2, P 3 where the Three parity check bits P 1, P 2 and P 3 are formed from the information bits as follows: (16) P 1 = I 1 < I 2, P 2 = I 1 < I 3, P 3 = I 2 < I 3 Find (i) The parity check matrix (ii) The generator matrix (iii) All possible code words. (iv) Minimum weight and minimum distance and (v) The error detecting and correcting capability of the code.(vi) If the received Sequence is 10,000. Calculate the syndrome and decode the received sequence. (Dec 2010) Unit 1 Two Marks with Answer 1. What is meant by aliasing effect? Aliasing effect takes place.when sampling frequency is less than Nyquist rate under such condition, The spectrum of the sampled signal overlaps with itself. Hence higher frequencies take the form of lower frequencies. This interference of the frequency components is called as aliasing effect. 2. State Sampling theorem. (June 2011,2015) A band limited signal of finite energy, which has no frequency components higher than W Hz, may be completely recovered from the knowledge of its samples taken at the rate of 2W samples per second. 3. The signal to quantization noise ratio in a PCM system depends on what criteria? The signal to quantization noise ratio in PCM is given as, (S/N)db (4.8+6v) db. Here v is the number of bits used to represent samples in PCM. Hence signal to quantization noise ratio in PCM depends upon the number of bits or quantization levels 4. What is meant by quantization? (June 2012) While converting the signal value from analog to digital, quantization is performed. The.analog value is assigned to nearest digital value. This is called quantization. The Quantized value is then converted into equivalent binary value. The quantization levels are fixed depending upon the number of bits. Quantization is performed in every Analog to Digital Conversion. 5. What you mean by Non- uniform quantization? Step size is not uniform. Non uniform quantizer is characterized by a step size that increases as the separation from the origin of the transfer characteristics is increased. Non- uniform quantization is otherwise called as robust quantization 6. What is the disadvantage of Uniform quantization over the Non-uniform quantization? SNR decreases with decrease in input power level at the uniform quantizer but non-uniform quantization maintain a constant SNR for wide range of input power levels. This type of quantization is called as robust quantization. 7. What is Natural sampling? (June, Nov 2013) A band limited signal of finite energy, which has no frequency components higher than W Hz, may be completely recovered from the knowledge of its samples taken at the rate of 2W samples per second. 8. What is Quantization error? (June 2011) The difference between the message signal x(t) and quantized signal x q(t) is called as Quantization error or Quantization noise. e = x q (t) - x(t).where, x(t) message signal and x q(t) - quantized signal 9. Compare uniform and Non-uniform quantization (NOV 2011) S No UNIFORM QUANTIZATION NON QUANTIZATION 1. The quantization step size remains same throughout the dynamic range The quantization step size varies with the amplitude of the input signal of the signal 2. SNR ratio varies with input signal amplitude SNR ratio can be maintained constant 5

6 10. What is TDM? Time Division Multiplexing (TDM) is a type of digital multiplexing. In TDM each signal can occupy the entire bandwidth of the channel. i.e. the multiple signal take turns transmitting over the single channel. Each signal is allowed to use the channel for a fixed period of time one after the other. 11. What is frame? One byte of data may be transmitted during the time interval assigned to a particular channel. On transmission of each channel completes one cycle of operation called a frame. Sixteen Marks with Hints 1. Explain sampling theorem. Sampling process converts a continuous time varying signal to a discrete time varying signal. Sampling theorem states that a band limited signal of finite energy having the highest frequency component Fm Hz can be represented and removed completely from a set samples taken at a rate of Fs sampling per seconds provides that Fs 2Fm 2. Draw the block diagram of compander? Mention the types of companding? Block diagram: Input Compressor uniform quantizer expander output signal Transmitter receiver Types of companding: 1. μ law companding 2. A law companding 6

7 3. Explain PCM in detail. 7

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12 Unit 2 Two Marks with Answer 1. Mention the merits of DPCM. 1. Bandwidth requirement of DPCM is less compared to PCM. 2. Quantization error is reduced because of prediction filter 3. Numbers of bits used to represent one sample values are also reduced compared to PCM. 2. What is the main difference in DPCM and DM? DM encodes the input sample by one bit. It sends the information about + δ or -δ, ie step rise or fall. DPCM can have more than one bit of encoding the sample. It sends the information about difference Between actual sample value and the predicted sample value. 3. What is meant by Adaptive Delta Modulation? In adaptive delta modulation, the step size is adjusted as per the slope of the input signal. Step size is made high if slope of the input signal is high. This avoids slope overload distortion. 12

13 4. What is the advantage of delta modulation over pulse modulation schemes? Delta modulation encodes one bit per samples. Hence signaling rate is reduced in DM 5. What should be the minimum bandwidth required to transmit a PCM channel? The minimum transmission bandwidth in PCM is given as, B T = vw, Here v is the number of bits used to represent one pulse. W is the maximum signal frequency. 6. What is the advantage of delta modulation over PCM? Delta modulation uses one bit to encode on sample. Hence it rate of delta modulation is low compared to PCM. 7. What are the two limitations of delta modulation? 1 Slope of overload distortion. 2. Granular noise. 8. What are the advantages and disadvantages of Delta Modulation? (Nov2008) Advantages: 1. One bit is transmitted per sample. So speed will be high.2.because of single bit per sample Bandwidth is small 3.Less complicated transmitter and receiver circuit when compared to PCM circuits. Disadvantages: 1.Two distortions are produced Slope overload distortion and Granular noise.2.slope overload Distortion will be much higher than that of PCM. 9. A 64 kbps binary PCM polar NRZ signal is passed through a communication system with a raised Cosine filter with roll-off factor Find the bandwidth of a filtered PCM signal. (NOV2012) Given, FB = 64 kpbs, B 0 = FB/2 = 32 kpbs, α = 0.25 The bandwidth of a filtered PCM signal, B = B 0 (1+α) = 32(1+0.25) = 40 khz 10. What are the two fold effects of quantizing process? The peak-to-peak range of input sample values subdivided into a finite set of decision levels or Decision thresholds. The output is assigned a discrete value selected from a finite set of representation Levels are reconstruction values that are aligned with the treads of the staircase. Sixteen Marks with Hints 1. Explain the slope overload and granular noise in delta modulation Slope-overhead distortion: If the slope of the signal x(t) is much higher than that of the approximate signal x (t) over will not follow x(t) at all as shown in figure. The difference between x(t) and x (t) is called the slope-overload distortion or the slope overload error. Thus, slope-overload error occurs when the slope of x(t) is much higher than x (t). The slope overload error can be reduced by increasing the step size δ or by increasing the sampling frequency. However with the bit rate and bandwidth requirement will increase. Granular noise: When the input signal x(t) is relatively constant in amplitude, the approximated signal x (t) will hunt above and below x(t). This leads to a noise called granular noise. It increases with in step size δ. To reduce granular slope-overload distortion. 2. Explain about DPCM DPCM is a combination between DM and PCM techniques. In DPCM scheme shown in, the input signal to the quantizer is defined by ( ) = ( ) ( ) the difference between the input sample m(nts) and a prediction of it, denoted by which is produced by using a prediction filter. The difference signal e(nts) is called the prediction error, since it is the amount by which the prediction filter fails to predict the incoming message signal exactly. By encoding the quantizer output, we obtain a variation of PCM, which is known as differential pulse-code modulation (DPCM). 13

14 3. Differentiate DM and ADM. S N Delta Modulation 1. Is a digital modulation in which one bit per sample is transmitted i.e. step size is constant. 2. Reduces the BW requirement to a great extent. 3. There are two types distortion in DM. Slope overload & granular Noise. 4. Wide dynamic range of analog signal cannot be used Adaptive Delta Modulation A system which uses variable step size is known as a adaptive data modulation. BW requirement is increased. In ADM there is reduction in slope overload and distortion. Wide dynamic range of analog signal can be used due to variable step size. 5. S/N ratio is high Improvement in S/N ratio 4. Explain with neat diagram of Delta Modulation system Delta modulation (DM) is implemented by applying a sampled version of the incoming message signal to a transmitter that consists of a comparator, quantizer, and accumulator connected together as shown in Figure 2 (a). The comparator computes the difference between its two inputs. The quantizer consists of a hard limiter with an input output characteristic that is a scaled version of the signum function. The accumulator operates on the quantizer output so as to Produce an approximation to the message signal. Fig.2 DM system (a) Transmitter (b) Receiver 14

15 5. Compare all the digital modulation techniques. Unit 3 Two Marks with Answer 1. What is linear code? A code is linear if the sum of any two code vectors produces another code vector. 2. What is ISI? (June, Nov 2014) The presence of outputs due to other bits interference with the output of required bit this effect is called inter symbol interference (ISI) 3. Differentiate Noise & fading Noise is an unwanted random addition to a wanted signal; it is called noise as a generalization of the audible noise heard when listening to a weak radio transmission Fading - random interference between multiple arriving image signals 4. Give the importance in calculating the spectral density of a signal. The spectral density of a signal characterizes the distribution of the signal s energy or power in the frequency domain. It is important when considering filtering communication system. It is used for evaluating the signal and noise at the filter. 5. State NRZ polar format? Binary 1 is represented by a positive pulse and binary 0 is represented by a Negative pulse. 15

16 6. Draw the NRZ and RZ code for the digital data State NRZ bipolar format? Binary 0 is represented by no pulse and binary one is represented by the alternative positive and negative pulse. 8. State Manchester format? (Nov 2014) Binary 0 -> The first half bit duration negative pulse and the second half bit duration positive pulse. Binary 1-> First half bit duration positive pulse and the second half bit duration negative pulse. 9. Define the principle of adaptive equalization? The filters adapt themselves to the dispersive effects of the channel that is the coefficients of the filters are changed continuously according to.the received.data. The filter coefficients are changed in such a way that the distortion in the data is reduced. 10.What is meant by prediction error? The difference between the actual sample of the process at the time of interest and the predictor output is called a prediction error. 11. What is the use of eye pattern? (Nov 2013) Eye pattern is used to study the effect of ISI in baseband transmission.1) Width of.eye.opening defines the.interval over.which the.received wave can be sampled without error from ISI.2) The sensitivity of the system to timing error is determined by the rate of closure of the eye as the sampling time is varied. 3) Height of the eye opening at sampling time is called margin over noise 12. Give two applications for eye pattern. (June 2011) 1. To determine an interval over which the received wave can be sampled without error due to ISI. 2. To determine the sensitivity of the system to timing error. 3. The margin over the noise is determined from eye pattern. 13. What you mean by correlative level coding Correlative level coding.allows the signal scaling rate of 2Bo in the channel of bandwidth Bo this is made physically possible by allowing ISI in the transmitted signal in controlled manner this ISI is known to the receiver 14. Draw the block diagram of base band binary data transmission system Input binary data Data encoding Transmitti ng filter Channel Receivi ng filter Design Device 15. Distinguish between baseband and band pass transmission. 16

17 Sixteen Marks with Hints 1. List and explain the properties of line codes (Dec 2011) DC Component Self-synchronization Error detection Band width compression Differential Encoding Noise Immunity Spectral Compatability With Channel 2. Explain with neat diagram diagram of M-ary FSK transmitter and receiver. Unit 4 Two Marks with Answer 3. Derive and draw the power spectra of a NRZ, (i) Polar coded waveform.(8) (June 2013) (ii) Bipolar coded waveform. (8) (June 2013) Line coding: Line coding refers to the process of representing the bit stream (1 s and 0 s) in the form of voltage or current variations optimally tuned for the specific properties of the physical channel being used. Unipolar (Unipolar NRZ and Unipolar RZ): Unipolar is the simplest line coding scheme possible. It has the advantage of being compatible with TTL logic. Unipolar coding uses a positive rectangular pulse p(t) to represent binary 1, and the absence of a pulse (i.e., zero voltage) to represent a binary 0. Two possibilities for the pulse p(t) exist Non-Return-to-Zero (NRZ) rectangular pulse and Return-to-Zero (RZ) rectangular pulse. The difference between Unipolar NRZ and Unipolar RZ codes is that the rectangular pulse in NRZ stays at a positive value (e.g., +5V) for the full duration of the logic 1 bit, while the pule in RZ drops from +5V to 0V in the middle of the bit time. A drawback of unipolar (RZ and NRZ) is that its average value is not zero, which means it creates a significant DC-component at the receiver (see the impulse at zero frequency in the corresponding power spectral density (PSD) of this line code. Polar (Polar NRZ and Polar RZ): 17

18 In Polar NRZ line coding binary 1 s are represented by a pulse p(t) and binary 0 s are represented by the negative of this pulse -p(t) (e.g., -5V). Polar (NRZ and RZ) signals.using the assumption that in a regular bitstream a logic 0 is just as likely as a logic 1,polar signals (whether RZ or NRZ) have the advantage that the resulting Dccomponent is very close to zero when a long sequence of 0 s or 1 s is transmitted Manchester encoding: In Manchester code each bit of data is signified by at least one transition. Manchester encoding is therefore considered to be self-clocking, which means that accurate clock recovery from a data stream is possible. In addition, the DC component of the encoded signal is zero. Although transitions allow the signal to be selfclocking, it carries significant overhead as there is a need for essentially twice the bandwidth of a simple NRZ or NRZI encoding. POWER SPECTRA OF LINE CODES: Unipolar most of signal power is centered around origin and there is waste of power due to 18

19 DC component that is present. Polar format most of signal power is centered around origin and they are simple to implement. Bipolar format does not have DC component and does not demand more bandwidth, but power requirement is double than other formats. Manchester format does not have DC component but provides proper clocking. Unit 4 Two Marks with Answer 1. Why do we go for Gram-Schmidt Orthogonalization procedure? Consider a message signal m. The task of transforming an incoming message m i i=1,2,..m, into a modulated wave S i (t) may be divided into separate discrete time & continuous time operations. The justification for this separation lies in the Gram-Schmidt orthogonalization procedure which permits the representation of any set of M energy signals, {S i (t)}, as linear combinations of N orthonormal basis functions, where N<M. 2. What are Coherent and Non Coherent Receivers? (June 2013) Receivers in which the carrier used in the receiver is of same frequency and phase of transmitted one is called Coherent Receivers. Receivers in which the carrier used in the receiver is of different frequency and phase of transmitted one is called Coherent Receivers. 3. Define: BER BER: Bit Error Rate. It is a measure of the performance of a communication system. The number of bits received in error divided by the total number of bits. 4. Distinguish between Coherent and Non coherent detection. In coherent detection the local carrier generated at the receiver is phase locked with the carrier at the transmitter. Hence it is also called synchronous detection. In non-coherent detection the local carrier generated at the receiver not be phase locked with the carrier at the transmitter. It is simple, but it has higher probability of error. 5. Explain how QPSK differs from PSK in term of transmission bandwidth and bit information it carries? For a given bit rate 1/Tb, a QPSK wave requires half the transmission bandwidth of the corresponding binary PSK wave. Equivalently for a given transmission bandwidth, a QPSK wave carries twice as many bits of information as the corresponding binary PSK wave 6. Define QPSK. QPSK is Quadrature phase shift keying. In QPSK the phase of the carrier takes on one of the four equally spaced values Such as π/4, 3π/4, 5π/4 and 7π/4. 7. Draw the signal space diagram for QAM signal for M=8? (June 2014) 8. Draw constellation diagram of QAM? (Nov 2014) 19

20 9. What is QAM? (June 2013) Quadrature amplitude modulation (QAM) is both an analog and a digital modulation scheme. It conveys two analog message signals, or two digital bit streams, by changing (modulating) the amplitudes of two carrier waves, using the amplitude-shift keying (ASK) digital modulation scheme or amplitude modulation (AM) analog modulation scheme. 10. What are coherent systems? (Nov2013) In coherent detection, the local carrier generated at the receiver is phase locked with the carrier at the transmitter. The detection is done by correlating received noisy signal and locally generated carrier. The coherent detection is a synchronous detection. 11. What is a non-coherent detection system? (June 2011) Non coherent detection: In this method, the receiver carrier need not be phase locked with transmitter carrier. Hence it is called envelope detection. 12. What is meant by DPSK? In DPSK, the input sequence is modified. Let input sequence be d(t) and output sequence be b(t). Sequence b(t) changes level at the beginning of each interval in which d(t)=1 and it does not changes level when d(t)=0. When b(t) changes level, phase of the carrier is changed. And as stated above, b(t) changes t=its level only when d(t) =1. This means phase of the carrier is changed only if d(t)=1. Hence the technique is called Differential PSK 13. A binary frequency shift keying system employs two signalling frequencies f 1 and f 2. The lower frequency f 1 is 1200 Hz and signalling rate is 500 Baud. Calculate f 2. (Dec 2010) Given, For binary FSK baud=fb,fb=500hz, Fs=f 1 =1200HZ Consider the FN modulation index(h) of 1 in FSK Wkt, Fm-Fs/ Fb = h=1, Fm-Fs=Fb, Fm-1200Hz=500Hz Fm=1700Hz, f 2 =fm=1700hz Sixteen Marks with Hints 1. Explain geometric representations of signals? (8) (Nov 2014) Analog signal: If the magnitudes of a real signal s(t) over its range of definition, T1 t T2, are real numbers (there are infinite such values) within a finite range, say, Smin S(t) Smax, the signal is analog. A digital signal s(t), on the contrary, can assume only any of a finite number of values. Orthogonally and Signal spaces To show that signals sharing the same channel don t interfere with each other, we need to show that they are orthogonal. This means, in short, that a receiver can uniquely separate them. Signals in different frequency bands are orthogonal. We will study orthogonal signals, and learn an algorithm to take an arbitrary set of signals and output a set of orthogonal signals with which to represent them. Orthonormal Two signals x(t) and y(t) are orthonormal if they are orthogonal and they both have norm 1, i.e., x(t) = 1 y(t) = 1 Orthonormal Signal Representations We consider how to take a set of arbitrary signals and represent them as vectors in an orthonormal basis. We refer to the set of arbitrary signals as: S = {s 0 (t), s 1 (t),..., s M 1 (t)} A transmitter may be allowed to send any one of these M signals in order to convey information to a receiver. We re going to introduce another set called an orthonormal basis: B = {φ 0 (t), φ 1 (t),..., φ N 1 (t)} Each function in B is called a basis function. Let B as an unambiguous & useful to represent the signals from the set S. 2. Describe the following modulation method (i) BPSK (ii) QAM (10) (June 2014) (i) BPSK: In BPSK the distance d between signals is 2 PsTb = 2 Eb Where Eb is PsTb is the energy Contained in a bit duration. The distance d is inversely proportional to the probability that we make an error, in the presentation noise. At end of receiver b(t) is being received. 20

21 (ii) QAM QAM is a form of digital modulation where the digital information is contained in both the amplitude and phase of the transmitted carrier signal. Noise immunity of the system can be improved by allowing the signal to differ not only in phase but also in amplitude is called as QAM. The bit stream b(t) is applied to the series to parallel converter, operating on a clock which has a period of Ts, which is the symbol duration. The bits b (t) are stored by the converter and then presented in the parallel form. The four bit symbols are bk+3, bk+2, bk+1, bk. Out of these four bits, the first two bits are applied to a D/A converter and the other two bits are applied to the second D/A convertor. The output of the first converter is Ae(t), which is modulated by the carrier 2Pscosωct whereas the output of the second D/A converter, A0(t) is modulated by the carrier 2Pssinωct in the balanced modulators.the balanced modulator output are added together to get the QASK output signal Which is expressed as, Diagram of QAM Modulator 3. Draw and explain the DPSK receiver. Here the received signal and the received signal delayed by the bit time Tb are applied to a balanced modulator. The balanced modulator output is given by, b (t) b (t-tb) (2Ps) cos ωc (t+θ) cos [ωc(t-tb) + θ] = b(t)b(t-tb)ps{ cosωctb + cos [2ωc(t-Tb/2) + 2 θ] } The output of the balanced modulator is applied to the integrator which suppressed the double frequency term. The first term [b(t)b(t-tb)ps cosωctb ] is the required signal and ωctb is selected in such a way so that ωctb = 2nπ (where n is integer) so that cosωctb = +1 and the signal output will be as large as possible. Further with this selection, the bit duration encompasses an integer number of clock cycle of the double frequency term is exactly zero. The transmitted data bit d(t) can be determined from the product b(t)b(t-tb). If there is no phase change between b(t) and b(t-tb) then d(t) = 0. In this case, b(t)b(t-tb) = -1. Then d(t) = 1. 21

22 4. Explain in detail about BPSK and obtain an expression for its probability of error. i. Block Diagram of Transmitter and Receiver. ii. Explanation of Transmitter and receiver. iii. Signal Space Diagram iv. Calculation of Probability of Error 5. Explain in detail about QPSK and obtain an expression for its probability of error. i. Block Diagram of Transmitter and Receiver. ii. Explanation of Transmitter and receiver. iii. Signal Space Diagram iv. Calculation of Probability of Error Unit 5 Two Marks with Answer 1. State Shannon s Channel Coding Theorem. Shannon's channel coding theorem states that "the error rate of data transmitted over a bandwidth limited Noisy channel can be reduced to an arbitrary small amount if the information rate is lower than the Channel capacity." 2. What are Golay codes? Golay code is the (23,12) cyclic code whose generating polynomial is, G(p) = p11+p9+p7+p6+p5+p+1 This code has minimum distance of d min = 7. This code can correct upto 3 errors. But Golay code cannot be generalized to other combinations of n and k. 3. What is meant by systematic and non-systematic codes? In a Systematic block code, message bits appear first and then check bits. In the non-systematic code, message and check bits cannot be identified in the code vector. 4. What is meant by linear code? A code is linear if modulo-2 sum of any two code vectors produces another code vector. This means any Code vector can be expressed as linear combination of other code vectors. 5. What are the error detection and correction capabilities of hamming codes? The minimum distance (d min ) of hamming codes is 3. Hence it can be used to detect double errors or Correct single errors. Hamming codes are basically linear block codes with d min =3. 6. What is code rate? Code rate is the ratio of message bits (k) and the encoder output bits (n).it is defined by r. (i.e.) r = k/n 7. What is meant by cyclic codes? Cyclic codes are the subclasses of linear block codes. They have the property that a cyclic shift of one code word Produces another code word. 8. What is hamming distance? The hamming distance between two code vectors is equal to the number of elements in which they differ. For example, let the two code words be, X = (101) and Y= (110). These two code words differ in second and third bits. Therefore, the hamming distance between X and Y is two. 9. How syndrome is calculated in Hamming codes and cyclic codes? In hamming codes the syndrome is calculated as, S=YH T. Here Y is the received and H T is the transpose of parity check matrix. 10. What is convolution code? What are its advantages? Fixed number of input bits is stored in the shift register & they are combined with the help of mod 2 adders. This operation is equivalent to binary convolution coding. Advantages: 1.The decoding delay is small in Convolutional codes since they operate o smaller blocks of data.2..the storage hardware required by Convolutional decoder is less since the block sizes are smaller. 22

23 1. Explain in detail about Shannon Coding Theorem. Sixteen Marks with Hints i. Statement of Theorem. ii. Discussion of theory. iii. Derivation of the Theorem. 2. Explain the construction of Block Code and explain how error syndrome is calculated i. Representation of Block Code. ii. Generator Matrix. iii. Generation of Code words. iv. Generation of Parity Check Matrix. v. Calculation OF Error Syndrome. 3. Explain in detail about Golay Codes, Reed Solomon Codes and BCH Codes. i. Definition of Golay Codes, Reed Solomon Codes and BCH Codes. ii. Explanation of Golay Codes iii Explanation of Reed Solomon Codes iv Explanation of BCH Codes. 4. Draw the code tree of a Convolutional code of code rate r=1/2 and Constraint length of K=3 starting from the state table and state diagram for an encoder which is commonly used. a. Draw the state Diagram. b. Draw the state Table. c. Draw the code Tree 5. Decode the given sequence of a convolutional code with a code rate of r=1/2 and Constraint length K=3, using viterbi decoding algorithm. a. Draw the state Diagram. b. Draw the state Table. c. Draw the code Tree d. Decode the given sequence using trellis diagram 23