Bandwidth Efficiency =
Thus bandwidth efficiency of a digital multiplexing system is only 11.77% which is extremely poor as compared to a much higher bandwidth efficiency of an analog multiplexing system (typically above 85%).
However this disadvantage of poor bandwidth efficiency is outweighed by the other advantages of digital transmission.
5.6.4. Advantages of Digital Multiplexing : Salient Features
(i) Hardware cost reduction due to the use of digital ICs.
(ii) Powder cost reduction due to use of regenerative repeaters.
(iii) More flexibility as compared to the analog multiplexers. This has been illustrated in figure 5.13 which shows a digital multiplexer which can multiplex voice signals, digital data, TV and videophone together.
DIAGRAM
FIGURE 5.13 A digital multiplexer used to multiplex different types of signals.
EXAMPLE 5.6. For CCIT hierarchy, assume that the first level multiplexer is a synchronous voice PCM bank with 30 input signals. The output bit rate of this multiplexer is 2.048 Mb/ sec. If bit robbing has not been implemented, calculate the number of framing plus signaling bits per frame.
Solution: One frame of transmitted signal is as shown in figure 5.14.
It consists of signal bits for all the 30 input signals plus one frame bit. Let us assume that there are “x” bits per frame.
DIAGRAM
FIGURE 5.14 Frame format for a CCIT digital multiplexer.
(i) Channels 1 to 30 each are 64 kb/s PCM encoded voice channels. Therefore, the minimum sampling rate required to multiplex them is,
f_{s(min)} = 64 x 10^{3} x 2 = 128 kHz …(i)
(ii) Number of frames transmitted per second = f_{s(min)} = 128 x 10^{3}
(iii) Number of bits per frame = x
(iv) Bit rate = Number of frames/sec x Number of bits/frame=128×10^{3}x
But it is given that bit rate = 2.048 Mb/sec
Hence. 128 x 10^{3}x = 2.048 x 10^{6}
or x = 16
Thus, number of bits per frame = 16. Ans.
5.7 NORTH AMERICAN HIERARCHY
As a matter of fact, the first digital signal in true sense is the PCM voice signal. A PCM voice signal represents 64 k bits/sec. i.e., 8000 samples per second x 8 bits per samples. Infact, such a signal is called as digital signal at level zero (DSO). Note that due to 8000 samples/sec, sampling rate. the time duration between adjacent samples will be (1/8000) i.e., 125 s. This digital signal at level zero (DSO) is the fundamental building block of all the digital communication systems. But, practically, the DSO signal is never transmitted because most of the telephone lines are analog. Hence, in a telephone central office, the subscribers analog line is passed through an antialiasing filter. The bandlimited signal is applied to a codec, which converts it into DSO signal. The generation of DSO signal is shown in figure 5.15.
DIAGRAM
FIGURE 5.15 Generation of DSO signal.
DO YOU KNOW? |
Digital telephone signals are time-division multiplexed with a data rate of 64 kb/s per voice channel. |
Now, 24 such DS0 lines are multiplexed into a DS1 (digital signal at level 1). Commonly this signal is called as T1 signal. The telephone companies implement TDM (time division multiplexing) through the hierarchy of digital signals. This is called as digital signal (DS) service. Figure 5.16 shows the DS hieararchy and the bit rates supported by various levels. The multiplexed signal is converted into a frame at the DS1 or T1 level.
diagram
FIGURE 5.16 D.S. hierarchy.
5.8 T LINES
DO YOU KNOW? |
The DS-1 signal and T1 carrier represent the lowest level in a hierarchy of TDM signals with higher bit rates. All of these signals contain PCM audio signals, each sampled 8000 times per second. |
DS0, DS1, DS2, …etc. are the names of the services. The telephone companies use the T lines (T — 0, T— 2) … etc.) to implement these services.
The T lines have capacities which precisely match with the bit rates of the corresponding services as shown in Table 5.3.
Table 5.3. Relation between DS and T lines
Service | Line | Rate (Mbps) | Number of voice channels |
DS-1
DS-2 DS-3 DS-4 |
T-1
T-2 T-3 T-4 |
1.544
6.312 44.736 274.176 |
24
96 672 4032 |
Thus, T-1 line implements DS-1 service, T-2 implements DS-2 service and so on. DS0 is defined as the basic service.
NOTE: T lines are digital lines which are designed to conveying digital data, audio or video.
But, the T lines can also be used or analog communication. For example T1 line can be used for the telephone applications.
A PCM-TDM SYSTEM : T1 CARRIER SYSTEM
- Block Diagram
When a large number of PCM signals are to be transmitted over a common channel, multiplexing of these PCM signals is required. Figure 5.17 shows the basic time division multiplexing scheme, called as the T1-digital system or T1 carrier system. This system is used to convey multiple signals over telephone lines using wideband coaxial cable.
diagram
FIGURE 5.17 Block diagram of a basic PCM-TDM system or T1 carrier system.
- Working Operation of the T1 Carrier System
The working operation of the PCM-TDM system shown in figure 5.17 can be explained in the form of few points as under:
(i) This system has been designed to accommodate 24 voice channels marked S_{1} to S_{24}. Each signal is bandlimited to 3.3 kHz, and the sampling is done at a standard rate of 8 kHz. This is higher than the Nyquist rate. The sampling is done by the commutator switch SW_{1}.
(ii) These voice signals are selected one by one and connected to a PCM transmitter by the commutator switch SW_{1}.
(iii) Each sampled signal is then applied to the PCM transmitter which converts it into a digital signal by the process of A to D conversion and companding, as explained earlier.
(iv) The resulting digital waveform is transmitted over a co-axial cable.
(v) Periodically, after every 6000 ft, the PCM-TDM signal is regenerated by amplifiers called Repeaters. They eliminate the distortion introduced by the channel and remove the superimposed noise and regenerate a clean PCM-TDM signal at their output. This ensures that the received signal is free from the distortions and noise.
(vi) At the destination, the signal is companded, decoded and demultiplexed, using a PCM receiver. The PCM receiver output is connected to different low pass filters via the decommutator switch SW_{2}.
(vii) Synchronization between the transmitter and receiver commutators SW_{1} and SW_{2}, is essential in order to ensure proper communication.
- Important Terms Related to a T1 Carrier System
Now, let us discuss few important terms related to a T1 carrier system as under:
(i) Bits/Frame
The commutators sweep continuously from S_{1} to S_{24} and back to S_{1} at the rate of 8000 revolutions per second. This will generate 8000 samples per second of each signal (S_{1} to S_{21}). Erich sample, then encoded (converted) into an eight bit digital word.
Thus, the digital signal generated during one complete sweep (revolution) of the commutator is given by
1 Frame = 1 revolution = 24 channels = 24 x 8 bits = 192
One frame of T1 carrier system is shown in figure 5.18. Each voice signal from S_{1} to S_{2} is encoded into eight bits. One frame corresponds to the time corresponding transmission of each signal once. Hence 1-frame corresponds to one-revolution of the commutator.
DIAGRAM
FIGURE 5.18 One frame and bits per frame.
(ii) Frame Synchronization
DO YOU KNOW? |
The framing bits are used to enable the receiver to determine which sample and which bit in that sample are being received at a given time. |
As discussed earlier, the synchronization between the transmitter and receiver commutators is essential. Without such synchronization, the receiver cannot know which bits correspond to which of the original signals. To provide such synchronization, an extra bit is transmitted preceding the 192 bits carrying the information in each frame, as shown in figure 5.19. This bit is called as the frame synchronizing bit “F”. Thus, one frame synchronizing bit is transmitted per frame. This makes the total number of bits per frame to be 193. The time slots for the 24 signals and the extra frame synchronizing bit is as shown in figure 5.19.
DIAGRAM
FIGURE 5.19 The PCM T1 frame using frame synchronization and channel associated signaling.
Further, twelve successive F slots are used to transmit a 12 bit code. The code is 1101 1100 1000. This code is transmitted repeatedly once every 12 frames and it is used at the receiver to obtain synchronization.
(iii) Bit Rate
Bit rate means number of bits transmitted by a system per second.
In the T1 carrier system, each signal is sampled 8000 times per second, therefore, 1 frame (1 revolution of commutator) a 1/8000 = 125 sec.
But, 1 frame consists of 193 bits.
Hence, 193 bits are transmitted in 125 sec.
Also, number of bits in 1 sec. =
So, hit rate of T1 carrier system = 1.544 Mbits/sec.
(iv) Bandwidth of T1 Carrier System
Minimum bandwidth BW = (bit rate) = x (1.544 x 10^{6}) = 722 kHz
Duration of each bit can be found as follows:
Since 193 125
therefore, 1 bit (125/193) µs = 0.6476 s
(v) Channel Associated Signaling
When the PCM-TDM system is being used for the telephony, it is expected to transmit certain signaling and supervisory signals alongwith the
DO YOU KNOW? |
Twisted-pair lines can he specially conditioned for use as T1 and T2 carriers, but higher data rates require channels with greater bandwidth such as co-axial cable, microwave radio, or optical fiber. |
speech information. The signaling information consists of the signals such as a call.is being initiated or a call is being terminated, or the address of calling party etc. In analog system such a signaling information is transmitted over a separate channel other than the voice channel. But in the T1 carrier system which is a digital system, a separate channel is not used. In this system, the signaling information is sent using the sonic data bit slots which are used to send the voice information. The technique used is bit slot sharing. In the “bit slot sharing” method, for the first five frames, all the 24 channels are encoded into an 8 bit digital code. However in the sixth frame, all the channels are coded into a 7 bit code and the LSB (least significant bit) of each channel is used to transmit the signaling information. This is as shown in figure 5.19. This is called as channel associated signaling. This pattern is repeated after every six frames.
มาร์กาเร็ต ลิน เซเวียร์ | มาร์กาเร็ตหลินซาเวียร์ | แพทย์หญิงคนแรก Margaret Lin Xavier |
MODEL QUESTION PAPERS FOR PRACTICE
MODEL QUESTION PAPER 1
DIGITAL COMMUNICATIONS
Time : 3 hours Maximum Marks : 100
Note : Attempt all questions. Each carry equal marks.
- Attempt any four questions. (5 x 4 = 20)
(a) Explain the block diagram of digital communication system. (5)
(b) Explain source coding Theorem. What is the difference between fixed and variable length code words. (5)
(c) Consider a DMS X with two symbols x_{1} and x_{2} and p(x_{1}) = 0.9, P (x_{2}) = 0.1.Symbols x_{1} and x_{2} are encoded as follows:
x_{l} | P(x_{1}) | Code |
x_{1}
x_{2} |
0.9
0.1 |
0
1 |
find the efficiency h and redundancy γ of this code.
(d) An analog signal having 4-kHz bandwidth is sampled at 1.25 times the Nyquist rate, each sample is quantized into one of 256 equally likely levels. Assume that the successive samples are statistically independent.
(i) What is the information rate of this source ?
(ii) Can the output of this source be transmitted without error over an AWGN channel with a bandwidth of 10 kHz and an S/N ratio of 20 dB ? (5)
(e) Verify eqn. that I(x_{i} x_{j}) = I(x_{i}) + I(x_{j}) if x_{i} and x_{j} are independent.
(f) Write the Shannon-fano Algorithm. Write start note on Huffman Encoding. (5)
- Attempt any four questions. (5 x 4)
(a) Explain sampling theorem. (5)
(b) Differentiate between PAM, PWM and PPM. (5)
(c) The input to a Q-step uniform quantizer has a uniform PDF over the interval [—a, a]. Calculate the average signal to quantizer horse power ratio at the output. (5)
(d) Write short notes on inter-symbol interference (ISI). (5)
(e) Find the Nyquist rate and the Nyquist interval for the signal m(t) = 5 cos 100 πt cos 4000 πt. (5)
(f) Consider the binary sequence 0100101. Draw the waveforms for the following signaling formats.
(i) Unipolar NRZ signaling format.
(ii) Bipolar RZ signaling format.
(iii) AMI RZ signaling format. (5)
- Answer any two questions. (10 x 2)
(a) Explain the block diagram of a PCM system. Differentiate between DM and PCM. (10)
(b) A low pass filter with the cut-off frequency of about 3.4 kHz. The filtered voice signal is sampled at 8 kHz. In addition, a single bit is added at the end of the frame for the purpose of synchronization. Calculate
(i) the duration of each bit,
(ii) the resultant transmissior rate, and
(iii) the minimum required transmission bandwidth. (10)
(c) In a certain telemetry system, eight message signals having 2 kHz bandwidth each are time-division multiplexed using a binary PCM. The error in sampling amplitude cannot be greater than 1 per cent of the peak amplitude. Determine the minimum transmission bandwidth required if raised-consine pulses with roll off factor α = 0.2 are used. The sampling rate must be at least 25 per cent above the Nyquist rate.
- Answer any two questions. (10 x 2)
(a) A signal m_{1}(t) is band-limited to 3.6 kHz and three other signals m_{2}(t), m_{3}(t), and m_{4}(t) are band-limited to 1.2 kHz each. These signals are to be transmitted by means of time division multiplexing.
(i) Set up a scheme for accomplishing this multiplexing requirement, with each signal sampled at its Nyquist rate.
(ii) What must be speed of the commutator.
(b) If the commutator output is quantized with L = 1024 and the result is binary-coded, what is the output bit rate ?
(c) Determine the minimum transmission bandwidth of the channel.
(d) Write short notes on Error Free Communication over a noisy channel.
- Answer any two questions. (10 x 2)
(a) Write short notes on Hamming codes, Hamming sphere. Hamming distance, and Hamming band relation between minimum distance and error detecting and correcting capability
(b) A bandpass data transmission scheme uses a PSK signaling scheme with
s_{2}(t) = A cos w_{c}t. 0 £ t £ t_{b}, w_{c} = 10π/T_{b}
s_{1}(t) = – A cos w_{c} t, 0 £ t £ T_{b}, T_{b} = 0.2 m sec.
The carrier amplitude at the receiver input is 1m volt an the psd of the additive white Gaussion noise at the input is 10^{-11} Watt/Hz. Assume that an ideal correlation receiver is used. Calculate the average bit error rate of the receiver. (10)
(c) Prove that A linear block code with a minimum distance d_{min} can correct up to [(d_{min} – 1)/2] errors and detect up to d_{min} – 1 errors in each code used, where [d_{min} – 1)/2] denotes the largest integer no greater than [d_{min} – 1)/2]. (10)
MODEL QUESTION PAPER 2
DIGITAL COMMUNICATIONS
Time : 3 hours Maximum Marks : 100
Note : Attempt all questions. Each carry equal marks.
- Answer any four of the following. (5 x 4)
(a) Explain the block diagram of digital Communication System.
(b) Explain Source Coding theorem.
(c) Write short note on MPEG Coding.
(d) Verify equation I(x_{i} x_{j}) = I(x_{i}) + I(x_{j}) if x_{i} and x_{j} are independent.
(e) Write short note on Huffman encoding algorithm.
(f) Find Entropy, if P(x_{1}) = P(x_{2}) = and P(x_{3}) =
- Attempt any four questions. (5 x 4)
(a) Explain Sampling theorem.
(b) The input to a Q-step uniform quantizer has a uniform PDF over the interval [— a, a]. Calculate the average signal to quantizer noise power ratio at the output. (5)
(c) What is the ISI process. Describe zero ISI. (5)
(d) Find the Nyquist rate and the Nyquist interval for the signal m(t) = 5 cos 100π t cos 4000πt. (5)
(e) Consider the binary sequence 0100101. Draw the waveforms for the following signaling schemes.
(i) Unipolar NRZ signaling formats
(ii) Bipolar RZ signaling format.
(f) Write the properties of the different signaling schemes. (5)
- Attempt any two questions. (10 x 2)
(a) Explain the block diagram of a PCM system. Differential between DM and PCM.
(b) The T_{1} carrier system used in digital telephony multiplexes 24 voice channels based on 8-bit PCM. Each voice signal is usually put through a low pass filter with the cut-off frequency of about 3.4 kHz. The filtered voice signal is sampled at 8 kHz. In addition, a single bit is added at the end of the frame for the purpose of synchronization calculate
(i) The duration of each bit.
(ii) The resultant transmission rate.
(iii) The minimum required transmission bandwidth. (10)
(c) Differentiate between ASK, FSK and PSK. (10)
- Attempt any two question. (10 x 2)
(a) Write short note on raised filter. In a certain telemetry system eight message signals having 2 kHz bandwidth each are time division multiplexed using a binary PCM. The error a sampling amplitude can not be greater than 1 per if of the peak amplitude. Determine the minimum transmission bandwidth required if raised-consine pulses with roll-off factor α = 0.2 are used. The sampling rate must be at least 25 per cent above the Nyquist rate.
(b) How can generate PAM, PWM and PPM . Write short note on the detection technique of above (PAM, PWM, PPM) schemes.
(c) (i) Write short note on error free communication over a noisy channel.
(ii) What is the matched filter Receiver. (10)
- Attempt any two questions. (10 x 2)
(a) Write short note on Hamming codes, Hamming sphere, Hamming distance, and Hamming relation between minimum distance and error detecting and correcting capability. (10)
(b) Prove that a linear block code with a minimum distance d_{min} can correct up to [(d_{min} — 1)/2] errors and detect up to [d_{min} — 1] errors in each codeword, where [(d_{min} — 1)/2] denotes the largest integer no greater than [(d_{min} — 1)/2].
(c) A band pass transmission scheme uses PSK signaling scheme with
s_{2}(t) = A cos w_{c}t, 0 £ t £ T_{b}, w_{c} = π/T_{1}
s_{1}(t) = – A cos w_{c }t, 0 £ t £ T_{b}, T_{b} = 0.2 m sec
The carrieramplitude at the receiver input is 1m volt end the PSD of the additive white Caussion noise at the input is 10^{-11} Watt/Hz. Assume that an ideal correction receiver is used. Calculate the average bit error rate of the receiver. (10)
MODEL QUESTION PAPER 3
DIGITAL COMMUNICATIONS
Time : 3 hours Maximum Mark : 100
Note : Attempt all questions. Each carry equal marks. Marks
- Consider five messages given probabilities 1/2, 1/4, 1/8, 1/16, 1/16,
(a) Calculate H.
(b) Use Shannon fano algorithm to develop one efficient code and for that code calculate number of bits/message. Compare with H.
- Explain sampling theorem? What is the effect of under sampling?
- Explain in brief the methods of generation and detection of PWM, PPM and PCM ?
- What is quantinization? Explain signal to quantinization ratio?
- What is delta modulation and how it is different fro adoptive delta modulation ?
- Explain Time division multiplexing (TDM) ?
- Write short note on :
(i) Inter symbol interference (ISI)
(ii) Nyquist criterion for zero ISI
(iii) Raised consine spectrum.
- Explain the generation and detection of
(i) ASK
(ii) PSK
(iii) FSK
(iv) QPSK
(v) MSK, Also give the probabilities of error in them.
- Explain Hamming sphere, Hamming distance and Hamming bound?
- Explain Libear code, encoding and symbol decoding?
MODEL QUESTION PAPER 4
DIGITAL COMMUNICATIONS
Time : 3 hour Maximum Marks : 100
Note : Attempt all questions, Each carry equal Marks. (5 X 4)
- Attempt any four from the following :
(a) Explain the element of a digital communication system with neat block diagram.
(b) Explain the following
- Logarithmic measure of information
- Entropy
- Information rate
- Conditional entropy
- Redundancy
(c) What is the requirement of source coding ? Explain the Shannon’s coding theorem and the coding efficiency.
(d) Explain the prefix coding the Kraft McMillan inequality.
(e) What do you mean by modulation? Classify the various types of amplitude modulation scheme and explain it in brief. What is the advantages of modulation?
- Attempt any four from the following : (5 x 4)
(a) What is sampling ? Explain in detail for low pass signal. Also explain the two sampling theorems.
(b) What is the pulse modulation ? Explain the generation and detection of pulse amplitude modulation with neat block diagram.
(c) Explain the pulse position modulation generation and detection with neat block diagram.
(d) Explain the TDM and FDM Hierarchy.
(e) Explain .the line coding and its limitations.
- Attempt any two of the following : (10 x 2)
(a) What is the pulse code modulation ? Explain the DPCM and DM with neat block diagram.
(b) Explain time division multiplexing in detail. Also explain the various types of synchronization scheme.
(c) Explain the generation and detection of ASK, FSK and PSK with neat block diagram.
- Attempt any two of the following : (10 x 2)
(a) Explain the Shannon’s channel capacity theorem. Also explain the heartily Shannon’s law for the capacity of the white band limited guassian channel. A guassian channel has 1 MHz bandwidth. If the signal power to noise power is spectral density S/h = 10^{5} Hz. Calculate the channel capacity C and the maximum information transfer rate R.
(b) Consider 8 message signal given by probabilities 1/2, 1/8, 1/16, 1/16, 1/16, 1/32 and 1/ 32 respectively. Calculate
- Entropy, H
- Use the Shannon-Fanon Algorithm to develop an efficient code and for that code .calculate the average no. of bits per message. Compare with H.
- Calculate the efficiency of the code.
(c) Trellis diagram of a rate 1/2, constraint length 3 convolutional code is shown in Fig. the all zero sequence is transmitted and received sequence is 100010000… using the viterbi algorithm, compute the decode sequence.
- Attempt any two of the following. (10 x 2)
(a) A binary symmetric channel is shown in the Fig. below. Find the rate of information transmission over this channel when P = 0.9, 0.8 and 0.6 assume that the symbol (or bit rate is 1000/sec. Also calculate the channel capacity of this channel.
(b) Explain the type of noise generated in communication system what do you mean by noise figure. Consider two two-ports in cascade. Each with the same noise bandwidth but different available power gains and noise figure. Find the overall noise figure of the two circuits (assuming perfect impedance matching).
(c) Calculate channel capacity of a white guassian noise channel in which suppose 100V levels are employed to transmit 100 equally likely massages. Assume λ = 3.5 and system bandwidth = 10^{4} Hz.
MODEL QUESTION PAPER 5
DIGITAL COMMUNICATIONS
Time : 3 hours Maximum Marks : 100
Note : Attempt all questions. Each carry equal marks.
- Write briefly about following :
(a) Difference between source encoding and channel encoding?
(b) Advantage and disadvantage of Digital Communication over Analog Communication system?
(c) Describe type of channels used for Digital communication.
(d) What are the figure of merit for the performance of Analog and Digital Communication?
- (a) Describe sampling theorem for band-limited signals. Prove that a signal sampled twice it’s maximum frequency can be reconstructed.
(b) Compare Impulse sampling and natural sampling.
- (a) What is quantization error ? How does it depends on step size ?
(b) Consider an audio signal with spectral components limited to frequency band 300 – 3300 Hz (treat this one as a band limited signal). Assume a sampling rate of 8000 samples/sec will be used to generate PCM signal. Assume peak voltage to average quantization noise power at the output is 30 dB. Find
(i) What is the minimum number of quantization levels needed ? What is the minimum no of bits/sample needed ?
(ii) Calculate the system BW required for such PCM signal.
(Hint BW = 1/2 T_{b})
- Write briefly on :
(a) Aliasing and anti-aliasing.
(b) ‘Slope over load distortion’ and granular noise in delta modulation
(c) A-law and pt-Law
(d) DPCM.
- (a) Explain frequency shift keying. Describe coherent detection of FSK signal. What should be the relationship between bit rate and frequency shift better performance.
(b) What are optimum and matched filter ? Find transfer function.
- (a) Explain cyclic coding and Linear Block Codes.
(b) The generator matrix for a (7, 4) block code is
G =
Find all code words of the code.
- (a) Explain briefly Shannon-channel capacity tneorem ?
(b) Using Shannon-Fano algorithm, obtain code for a source emitting eight messa with probability 1/2, 1/8, 1/16, 1/16, 1/32 and 1/32. Calculate average information and efficiency.
- Derive necessary expression to establish that probability of error P_{e} of a matched filter of receiver with integrate and dump switching depends only on signal energy and not on the wave shape.
MODEL QUESTION PAPER 6
DIGITAL COMMUNICATIONS
Time : 3 hours Maximum Marks : 100
Note : Attempt all questions. Each carry equal marks.
- Attempt any Three questions :
(a) Explain Entropy and find its expression for discrete information source. Prove that Entropy is maximum when all the symbols emitted by the discrete information source are equally alike.
(b) Given the algorithms of Huffman code procedure used for Generating efficient code. Find the channel capacity of a white Guassian noise channel.
(c) Find Entropy, Information rate, Efficient code, Efficiency, Redundancy for a Discrete information source generate Symbols x_{l}, x_{2}, x_{3}, x_{4}, x_{5}, x_{6}, x_{7} with a n probability 0.4, 0.2, 0.12, 0.08, 0.04, 0.08, 0.08. Symbols are generated by the discrete information source at a rate one out of seven symbols per milliseconds.
(d) Explain Block diagram of an Communication system. Give advantages of the Digital communication System.
- Attempt any three questions.
(a) Explain Shannon’s first and second theorem for discrete information source.
(b) Explain Mutual information and Prove that
I(x;y) = H(x) + H(y) – H(x,y)
H(X), H(Y), H(X,Y) Are the corresponding entropy of discrete information source.
(c) Give the Statement of the sampling theorem. Prove it. Find the sampling frequency of the following signals.
(i) sin 200 πt (ii) sin 2 (200 πt)
(iii) sin 200 pt cos 100 πt
(iv) Explain all pulse modulation technique. Give their time spectra.
- Attempt any three question.
(a) Explain the need of Quantization. What is Non-uniform Quantization?
(b) Explain block diagram of Pulse code modulation system. Give its advantages. How a signal to noise ration is improved in PCM system?
(c) A television Signal (video and audio) has BW of 4.5 MHz. Signal is sampled, Quantized and binary coded to obtain PCM system.
(i) Determine the sampling rate if the signal it to be sampled at a rate 20% above the Nyquist rate.
(ii) If signal is sample are quantized at into 1024 level, determine Number of binary pulses required to encode each sample.
(iii) Determine the binary pulse rate (bit per second) of the binary coded signal and the minimum BW required to transmit this signal.
(d) Explain Delta modulation. Give its advantages and disadvantages. Explain slope overload distortion.
- Attempt any three questions.
(a) Compare Various type of Digital Modulation technique Such as ASK, PSK FSK.
(b) Prove that error probability depends only on Signal Energy not on Signal Wave Shape.
(c) The generator matrix for a block code is given below. Find all code vectors of this code.
G =
(d) Consider (7, 4) block code generated by
G =
Explain how the errors syndrome S helps in correcting a single errors.
- Write short note on following :
(a) MPEG Audio coding standard.
(b) EYE Pattern and Pulse Stuffing.
(c) Inter Symbol Interference.
(d) Convolution code.
(e) Nyquist Criteria for Zero intersymbol interference (ISI).
MODEL QUESTION PAPER 7
DIGITAL COMMUNICATIONS
Time : 3 hour Maximum Marks : 100
Note : Attempt all questions. Each carry equal marks.
- Attempt any Four of the following : (5 x 4) = 20
(a) Define Entropy and conditional Entropy. Explain properties of conditional entropy.
(b) Apply the Shannon-Fano coding procedure for the given message ensemble:
[X] = [x_{1} x_{2} x_{3} x_{4} x_{5} x_{6} x_{7} x_{8}]
[P] =[1/4 1/8 1/16 1/16 1/4 1/16 1/8]
Assume M = 2.
(c) Apply the Huffman coding method for the given message ensemble :
[X] = [x_{1} x_{2} x_{3} x_{4} x_{5} x_{6} x_{7}]
[P] = [0.4 0.2 0.12 0.08 0.08 0.08 0.04]
Assume M = 2.
(d) Explain Shannon-Hartely theorem.
(e) State and Prove sampling theorem.
(f) How PWM signal can be generated and detected, explain ?
- Attempt any Four of the following : (5 x 4) = 20
(a) Explain A-law and of commanding.
(b) Derive an expression for bandwidth requirement of PCM system.
(c) For a PCM signal, determine L if the compression parameter µ = 100 and the minimum SNR required is 45 dB. Determine the output SNR with this value of L. Remember that L must be a power of 2, that is L = 2^{n} for PCM.
(d) Explain Delta modulation scheme.
(e) Explain M12 Multiplexer system.
(f) Explain CCITT recommended TDM PCM hierarchy.
- Attempt any Two of the following : (10×2) = 20
(a) Explain the following :
(i) Intersymbol Interference (ISI)
(ii) Eye Pattern.
(b) Explain the following :
(i) High-Density Bipolar (HDB) Signaling.
(ii) Binary with 8 Zero Substitution (B8ZS) Signaling.
(c) (i) Show that for a matched filter the maximum signal component curs at t = T (i.e., sampling interval) and has magnitude equal to E, i.e., energy of the signal x(t).
(ii) Polar binary pulses are received with peak amplitude A_{p} = 1mV. The channel noise amplitude is 192.3 mV. Threshold detection is used, and 1 and 0 are equally likely. Find the detection error probability.
- Attempt any Two of the following : (10×2) =20
(a) Explain generation and detection of BPSK.
(b) It is required to transmit 2.08 x 10^{6} binary digits per second with P_{b} £ 10^{-6}. Two possible schemes are considered:
(i) 16-ary ASK
(ii) 16-ary PSK
The channel noise PSD is S_{n}(w) = 10^{-8}. Determine the transmission bandwidth and the signal power required at the receiver input in each case.
(c) Derive the expression for bandwidth efficiency of M-ary PSK and M-ary FSK signals.
- Attempt any Two of the following : (10×2=20)
(a) Explain encoding and decoding of Linear Block Codes.
(b) Find a generator polynomial g(x) for a (7, 4) cyclic code, and find code vectors for the following data vectors : 1010, 1111, 0001, and 1000. Also construct a systematic (7, 4) cyclic code using a generator polynomial you have find and above data vectors.
(c) Explain encoding and decoding of Convolution Codes.
MODEL QUESTION PAPER 8
DIGITAL COMMUNICATIONS
Time : 3 hours Maximum Marks : 100
Note : Attempt all questions. Each carry equal marks.
- Attempt any Four of the following : (4 x 5) = 20
(a) Draw the block diagram of a digital communication system and explain the functions of a source encoder and channel encoder.
(b) Define information and entropy and show that 9 £ H £ log_{2} n.
(c) Find out the Shannon-Fano algorithm for the following DMS.
Message A B C D E F G H
Prob. 1/100 1/2 3/20 2/25 1/50 2/25 1/100 3/30
and determine whether the generated code sequence satisfies the kraft’s inequality.
(d) A DMS has an alphabet of five symbols with their probabilities:
Symbol : S_{0 }S_{1 }S_{2 }S_{3 }S_{4}
Prob. : 0.55 0.15 0.15 0.10 0.05
Compute two different Huffman codes for this source and determine for each of the two :
- The average code word length
- The variance
(e) Show that the channel capacity of an ideal AWGN channel with infinite band width is given by
C_{0} = 1.44 P/N bits /sec.
Where P-Signal power N-Noise power
- Attempt any Two of the following : (2 x 10) = 20
(a) (i) State and prove sampling theorem for the low pass signals.
(ii) Find the Nyquist rate and Nyquist interval for each of the following signals.
- m(t) = 5 cos 1000 πt cos 4000 πt
- m(t) = sin 200 πt/πt
- m(t) = (sin 200 πt/πt)^{2}
(b) (i) Explain the term aliasing. How can it be removed in sampling state clearly.
(ii) Explain the sampling of band signals.
(c) Define the different types of pulse modulate systems. Explain the generation and detection of PWM system with proper waveforms and neat circuit diagrams.
- Attempt any Four parts : (4 x 5) = 20
(a) (i) Find out the expression for signal to quantization noise ratio for a sinusoidal modulating signal.
(ii) Consider a sinusoidal signal given by m(t) = 3 cos (100πt). Find the out the minimum no of bits needed to achieve a signal to noise ratio of at least 40 dB.
(b) Define non-uniform quantization, why is it required ? Explain µ -law and A – law commanding.
(c) Explain DPCM with suitable diagrams of transmitter and receiver.
(d) Explain the different types of distortions in a delta modulated system. How avoid them ?
(e) (i) Compare PCM and DM.
(ii) Write a short note on MPEG audio coding standard.
- Attempt any Four parts : (4 x 5) = 20
(a) Discuss the fundamentals of time division multiplexing.
(b) Explain different types of signaling formats for digital base band transmission with proper wave forms.
(c) Derive the impulse response for a matched filter receiver.
(d) Discuss different types of digital modulation techniques with suitable waveforms.
(e) Estimate the bandwidth of binary coherent DPSK waveforms.
- Attempt any Two of the following : (2 X 10) = 20
(a) What are linear block code ? Explain their encoding and syndrome decoding by taking proper examples.
(b) Discuss the cyclic codes and explain encoding and decoding for systematic cyclic codes.
(c) Explain viterbi algorithm and sequential decoding.
MODEL QUESTION PAPER 9
DIGITAL COMMUNICATIONS
Time : 3 hours Maximum Marks : 100
Note : Attempt all questions. Each carry equal marks.
- Attempt any Four of the following :
(a) Find the information received from each symbol with probability as P_{1}-1/2, P_{2} = 1/2, P_{3} = 1/8, P_{4} = P_{5} = 1/16
(b) What is aliasing error in sampling?
(c) What is slope overload error?
(d) What is difference between coherent and non-coherent receiver ?
(e) Explain the term hamming distance.
(f) What is a correlation detector ?
- Attempt any Four of the following :
(a) A signal is having maximum frequency as 4 KHz. This signal is sampled at Nyquist rate. If the PCM system uses 128 levels them find the bit rate data.
(b) Find the signal to quantization noise ration.
(c) What is ISI ?
(d) Explain the method of generation and detection of PSK.
(e) Write a note trellis diagram.
(f) Find the entropy of a source having symbol probabilities as p_{1} = 0.3, p_{2} = 0.25, p_{3} = 0.20, p_{4} = 0.15, p_{5} 0.1.
- Attempt any Four of the following :
(a) Calculate the capacity of a Gaussian channel with the bandwidth of 1 MHz. And S/N ratio of 20 dB.
(b) Write a note on adaptive delta modulation.
(c) What is the error in flat top sampling ? How is it removed ?
(d) Explain the synchronization scheme of T1 carrier system.
(e) Write a note on matched filter receiver.
(f) What is quadrature sampling ?
- Attempt any Two of the following :
(a) Find the Huffman code for six massages occurring with the probabilities. 1/3, 1/3, 1/6, 1/2, 1/24, and 1/24.
(b) Describe the method of generation and detection of PWM.
(c) Explain of QPSK modulation and demodulation.
- Attempt any Two of the following :
(a) Find the probability of error in PSK.
(b) Consider the (7,4) Hamming code defined by the generator polynomial.
The code word 0111001 is sent over a noisy channel, producing the received word 010111001. Determine the syndrome polynomial s(X) for the received word.
(c) Write a note on DPCM. Why is it not used for speech coding ?
MODEL QUESTION PAPER 10
DIGITAL COMMUNICATIONS
Time : 3 hours Maximum Marks : 100
Note : Attempt all questions. Each carry equal marks.
- Attempt any Three parts
(a) A discrete memoryless source with source alphabet S = {S_{0}, S_{1}, S_{2}, S_{3}} has their respective probabilities as {1/3, 1/6, 1/4, 1/4}. The successive symbols emitted by the source are satistically independent. Calculate the Entropy of the source and also the Entropy of the second-order extenstion of the source.
(b) State and Proved “Shanno’s Information capacity theorem” for a continuous channel of Bandwidth ‘B’ Hz. Perturbed by white Gaussian Noise. of psd No/2
C = B log2 bits/s
where P is the average transmitted power.
(c) Explain the difference between PAM, PWM and PPM. Sketch the waveforms and show the method of generation of PPM and PWM.
(d) State and Expalin “Sampling theorem” for Low Pass Signals. Explain how will you recover the original signal from the samples.
Draw the block diagram of a Digital Communication system and Explain the function of each block.
- Attempt any Three parts
(a) The fire source symbols of the alphabet of a discrete memoryless source and their respective probabilities are given as
Symbol | Probabilities |
S_{0} | 0.4 |
S_{1} | 0.2 |
S_{2} | 0.2 |
S_{3} | 0.1 |
S_{4} | 0.1 |
Find the Huffman code for the source. Also find the average code-word Length of the source code.
(b) Consider an AWGN channel with 4kHz bandwidth and the Noise power spectral density h/2 = 10^{-12} W/Hz. The signal power required at the receiver is 0.1 mw. Calculate the capacity of this channel.
(c) Explain the following types of sampling and discuss their applications
(i) Instantaneous sampling
(ii) Natural sampling
(iii) Flat-Top sampling.
- Attempt any Three parts
(i) Explain Non-uniform Quantization and discuss its applications.
(ii) What is Delta Modulation ? Compare DM with pulse code Modulation.
(iii) With the help of Block Diagram explain Time Division Multiplexingand discuss its usefulness.
(iv) In a binary PCM system, the output signal-to-quantizing ratio is to beheld to a minimum for 40 dB. Determine the number of requiredlevels and find the corresponding output signal-to-Noise ratio.
OR
(i) Draw the block diagram of a PCM system and explain the function of each block.
(ii) Explain Idling Noise and slope overload in Delta Modulation and How it can be avoided.
(iii) Find the mean square value of quantization error for a uniform quantizer.
(iv) What is T-1 carrier system ?
Give the Signaling Format.
Also explain the Digital Hierarcly developed by AT and T (Bell system).
- Attempt any Three
(i) What is Line coding ? List the desirable features of a Line code.
(ii) Explain how ISI can be used in a controlled manner to achieve signaling rate higher than the Bandwidth of the channel.
(iii) Find the transmission Bandwidth requirement of a raised consine pulse.
(iv) Find the unipulse response of the matched filter receiver . Show how it can be implemented in a correlation detector.
OR
(i) Draw the waveforms for the following Line codes, explain them and gire there relative merits and demerits.
(a) ON-OF (RZ) (d) ON-OFF (NRZ)
(b) Polar (RZ) (e) Polar (NRZ)
(c) Bipolar (RZ)
(ii) What is Intersymbol? State Nyquist criteria for zero ISI.
(iii) Explain partial response signaling ?
(iv) What is detection Error Probability? Is the performance of the bipolar signals same as that of the ON-OFF signals from the point of view of P(t). Discuss.
- Answer any Two parts
(i) What is minimum shift keying ? Explain for any given input binary sequence. Draw the waveforms for MSK signal;
Explain the MSK transmitter and receiver using Block Diagram.
(ii) Binary data is transmitted over an RF band pass channel with a usable bandwidth of 10 Mz at a rate of 4.8 x 10^{6} bits /sec using on ASK signaling method.
The carrier amplitude at the receiver atenna is 1 my and the noise Power spectral density at receiver input 10^{-15} watt/Hz. Find the probability of error of a coherent receiver.
(iii) What is FSK ? Explain the generation and its coherent and Non coherent detection.
OR
(i) What is the difference between ASK, FSK and PSK modulation technique? Explain with waveforms.
Compare them on the basis of power requirements. Bandwidth requirements, immunity to channel impairments and prob. of error.
(ii) Binary data has to be transmitted over a telephone link that has a usable bandwidth of 3000 Hz and a maximum achievable signal to nose power ratio of 8 dB at its output.
(a) Determine the maximum signaling rate and P_{e} if a coherent binary ASK scheme is used for transmitting binary dats through this channel.
(b) If the dats rate is maintained at 300bit/s calculate the error probability.
(iii) What is differential phase shift keying ? Explain the technique and the generation and detection of DPSK signals.
- Answer any Two parts
(i) The generator polynomial of a (7,4) cyclic code is
g(x) = 1 + x + x^{3}
Find the 16 codewords of this code by
(a) By forming the code polynomials where D(x) is the anuned message polynomial.
(b) By using the systematic form.
(ii) Write short Notes on any Two :
(a) BCH codes
(b) Reed-solomon codes
(c) Maximum Likelihood decoding of convolution codes.
(iii) What are convolution codes. Explain the method of sequential decoding using proper figure
OR
(i) Design and Decoder for the (7, 4) binary cyclic code generated by
g(x) = 1 + x + x^{3}
and verify its operation using the message vector (0101).
(ii) A parity-check code has the parity-check matrix
H =
(a) Determine the generator matrix G.
(b) Find the codes
(c) Suppose that the received word is 110110. Decode this received word.
(iii) Write short noted on any Two
(a) Hamming codes
(b) Convolution codes ; sequential decoding
(c) Burst error correction.