pulse digital modulation scheme , Noise effect in PCM , digital communications , block diagram of DPCM

SUMMARY
■          The use of digital communications offers several important advantages as compared to analog communications.
■          Digital communications have become the dominant form of communication technology in our society.
■          To handle the transmission of analog message signals (i.e., voice and video signals) by digital means, the signal has to undergo an analog-to-digital conversion.
■          The simplest form of pulse digital modulation is called pulse code modulation (PCM).
■          In this system (PCM) the message signal is first sampled and then amplitude of each sample is rounded off to the nearest one of a finite set of allowable values known as quantization levels, so that both time and amplitude are in the discrete form. This means that in pulse code modulation both parameters i.e., time and amplitude are expressed in discrete form. This process is called discretization in time and amplitude.
■          We can improve the accuracy of the quantized signal to any desired degree simply by increasing the number of levels q.
■          Pulse-code modulation is known as a digital pulse modulation techniques. The pulse-code modulation (PCM) is quite complex compared to the Analog pulse modulation techniques (i.e., PAM, PWM and PPM) in the sense that the message signal is subjected to a great number of operations.
■          The essential operations in the receiver are regeneration of impaired signals, decoding and demodulation of the train of quantized samples.
■          Quantization refers to the use of a finite set of amplitude levels and the selection of a level nearest to a particular sample value of the message signal as the representation for it.
■          This operation combined with sampling, permits the use of coded pulses for representing the message signal.
■          It is the combined use of quantizing and coding that distinguishes pulse code modulation form analog modulation techniques.
■          Basically, the quantizers are of two types:
(i) Uniform quantizer
(ii) Non-uniform quantizer.
■          A uniform quantizer is that type of quantizer in which the ‘step size’ remains same through out the input range.
■          A non-uniform quantizer is that type of quantizer in which the ‘step-wise’ varies according to the input values.
■          Transmission bandwidth in PCM is given by
BW ³
But                                               r = vf_s
Therefore,                                    BW ³
Again, since                        f_s ³ 2f_m
Hence,                                BW ³ vf_m
■          Because of quantization, inherent errors are introduced in the signal. This error is called quantization error.
■          Normalized noise power
■          Thus, Signal to Quantization noise ratio for normalized values of power ‘P’ and amplitude of input x(t), will be
■          The compression of signal at transmitter and expansion at receiver is called combinely as companding.
■          The compression and expansion is obtained by passing the signal through the amplifier having non-linear transfer characteristic.
■          The combination of a compression and an expander is called a compander. Naturally, in an actual PCM system, the combination of compressor and uniform quantizer is located in the transmitter whereas the expander is located in the receiver.
■          In the -law companding, the compressor characteristic is continuous. It is described as
where m and v are the normalized input and output voltages, and  is a positive constant.

23. Another compression law that is used in practice is the so-called A-law. In the A-law companding, compressor characteristics is piecewise, made up of a linear segment for low-level inputs arid a logarithmic segment for high level inputs. It is described as

EQUATION
■          The signal to noise ratio of PCM remains almost constant with companding.
■          Delta modulation transmits only one bit per sample. Here, the present sample value is compared with the previous sample value and this result whether the amplitude is increased or decreased is transmitted.
■          The delta modulation has certain advantages over PCM as under:
(i)         Since, the delta modulation transmits only one bit for one sample, therefore the signaling rate and transmission channel bandwidth is quite small for delta modulation compared to PCM.
(ii)        The transmitter and receiver implementation is very much simple for delta modulation. There is no analog to digital converter required in delta modulation.
■          The delta modulation has two major drawbacks as under:
(i)         Slope overload distortion,
(ii)        Granular or idle noise.
■          To overcome the quantization errors due to slope overload and granular noise, the step size (A) is made adaptive to variations in the input signal x(t).
■          Adaptive delta modulation has certain advantages over delta modulation as under:
(i)         The signal to noise ratio becomes better than ordinary delta modulation because of the reduction in slope overload distortion and idle noise.
(ii)        Because of the variable step size, the dynamic range of ADM is wider than simple DM.
(iii)       Utilization of bandwidth is better than delta modulation.
■          If this redundancy is reduced, then overall bit rate will decrease and number of bits required to transmit one sample will also be reduced. This type of digital pulse modulation scheme is known as Differential Pulse Code Modulation.
SHORT QUESTIONS WITH ANSWERS
Q.1.     What is a pulse digital modulation scheme?
Ans.    It is the modulation in which the message and also the carrier are in discrete form. These are classified as:
Pulse code modulation and Delta modulation
Q.2.     What are the advantages of digital representation of analog signals?
Ans.    Some of the advantages of a digital signal over analog signal are:
(i)         Ruggedness to transmission noise and interference
(ii)        Efficient regeneration of the coded signal along the transmission path
(iii)       The possibility of a uniform format for different kinds of baseband signals.
Q.3. Draw the block diagram of PCM scheme showing the elements required for the transmission.
DIAGRAM
FIGURE 4.35.
Q.4.     Define Pulse Code Modulation.
Ans.    It is the process in which the message signal is sampled and the amplitude of each sample is rounded off to the nearest one of a finite sett of allowable values.
Q.5.     Discuss Noise effect in PCM.
Ans.    The performance of a PCM system is influenced by two major sources of noise.
(i)         Transmission Noise: Which is introduced anywhere transmitter output and the receiver input. It is also named as channel Noise.
(ii)        Quantizing Noise: This is introduced in the transmitter and is carried along to the receiver output.
Q.6.     Explain the importance (or) use of prediction in Differential pulse code modulation (DPCM).
Ans.    In standard PCM, each sample of the baseband signal is encoded independently of all others.
However sometimes, in some signals, when they are sampled at the Nyquist rate (or) faster exhibit significant correlation between successive samples i.e., the relative change in amplitude between the successive samples is very small.
Under these circumstances, if this highly correlated signal is encoded using PCM, then the resultant signal consists of redundant Information and results in a lower bit rate. The is because the symbols that are not essential to the transmission of information are generated as a result of the encoding process.
By removing this redundancy before encoding, we obtain a more efficient coded signal.
A relatively simple solution is to encode the difference between successive samples rather than the samples themselves.
Since the difference between the samples are expected to be smaller than the actual sampled amplitudes, fewer bits are required to represent the differences.
Thus, if a sufficient part of a redundant signal is known it is possible to make the most probable estimate of the rest i.e., if a small part of the sample is known, the other half can be estimated from the knowledge of previous sample.
This process is known as prediction.
Q.7.     Give the block diagram of DPCM.
Ans.                                                    DIAGRAM
FIGURE 4.36.
Q.8.     What is Delta Modulation and give the comparison between DM and DPCM.
Ans.    Delta Modulation is the one-bit (or) two-level version of DPCM.
They are similar except for two important differences namely, the use of a one-bit quantizer in delta modulator and the prediction filter is replaced by a single delay element.
Q.9.     Discuss the Noise effects in Delta Modulation.
Ans.    In Delta modulation we observe quantization noise. There are two major sources of quantizing error in DM systems. They are
(i)         Slope overload distortion
(ii)        Granular noise.
Q.10.   Write a short notes on slope overload Distortion.
Ans.    In general, the step size we choose to quantize, is fixed. So under maximum slope of the signal, step size becomes small to follow the steep of the input waveform. This condition is called slope-overload and the resulting quantizing error is called slop-overload distortion (noise). It is shown in figure 4.37.
DIAGRAM
FIGURE 4.37.
Q.11.   Write short notes on Granular noise.
Ans.    In contrast to the slope overload distortion, the granular noise occurs when the step size D is too large relative to the local slope characte-ristics of the input waveform, thereby causing the staircase approximation to hunt around a relatively flat segment of the input waveform.
This is also known as hunting process.
Q.12.   Compare Delta Modulation and Pulse code Modulation schemes.
Ans.    To compare the two modulation schemes, they should have some identical conditions.
Let us assume that both systems use approximately the same bandwidth for transmitting a baseband analog signal.
If                                 f_s denotes the sampling rate of an N-bit PCM
f_s‘ denotes the sampling rate of N-bit DM
Then the bit rate of PCM is Nf_s and f_s‘ for DM.
If the signal spectrum extends up to f_m Hz, then f_s = 2f_m and identical bandwidth requirements imply that
f’ s = 2/Vf_m

1. SNR

If the channel signal to noise ratio is high, then the performance of PCM and DM is limited by the quantization noise.
Then the signal-to-quantizing noise power ratio for the PCM system is given by
(S₀/N_q)_PCM = Q₂ = 2^2N 2 ≥ 2                                        …(i)
where Q = 2^N, the number of quantizer levels.
Similarly, for the DM system, the corresponding ratio is given by
(S₀/N_q)_DM =
From the above equations for a fixed bandwidth the performance of DM is always poorer than PCM.
For 8-bit PCM and DM, we have
(S₀/N_q)_PMC = 48 dB
(S₀/N_q)_DM = 22 dB
Thus the overall signal to noise ratio of a DM system is also lower than the overall signal-to-noise ratio of a PCM system using the same bandwidth.
QUESTIONS

1. With the help of neat diagrams, explain the transmitter and rceiver of pusle code modulation.
2. Explain what is uniform (linear) quantization?
3. Explain the quantization error and derive an expression for maximum signal to noise ratio in PCM system that uses Linear quantization.
4. Derive the relations for signaling rate and transmission bandwidth in PCM system.
5. Explain Delta modulation in detail with suitable diagram. Also, explain ADM and compare its performance with DM.
6. What is the slope overload distortion and granular noise in delta modulation and how it is removed in ADM.
7. Explain Differential pulse code modulation.
8. What is the necessity of non-uniform quantization and explain companding 2.
9. Compare PCM, DM, ADM & DPCM.

PROBLEMS

1. In the binary PCM system , find out the minimum number of bits required so that quantizing noise is less than ± k per cent of the analog level.

[Ans. V ≤ 1og2 (50/k)]

2. What is the maximum power that may be transmitted without slope overload distortion?

OBJECTIVE TYPE QUESTIONS

1. Fill up the Blanks
2. The essential operations in the transmitter of a PCM system are ___________and ___________.
3. The quantizing and encoding are performed in the circuit which is called ___________.
4. The existence of a finite number of ___________ is a basic condition of PCM.
5. The conversion of an analog sample of the signal into a digital (discrete) form is called the ___________ process.
6. The difference between two adjacent discrete values is called ___________ (or) ___________
7. The ___________ consists of difference between the input and output signals of the quantizer.
8. The use of a nonuniform quantizer is equivalent to passing the baseband signal through a ___________ and then applying the compressed signal to a ___________ quantizer.
9. The combination of a compressor and expander is called a ___________.
10. Any plan for representing each of the discrete set of values as particular arrangement of discrete events is called a ___________.
11. One of the discrete events in a code is called a ___________ (or) ___________.
12. A particular arrangement of symbols used in a code to represent a single value of the discrete set is called a ___________ (or) ___________.
13. In a ___________code, each symbol may be one of the three distinct values (or) kinds.
14. The process in which the information in a binary PCM is encoded in terms of signal transitions is referred to as___________ .
15. The capability of controlling the effects of distortion and noise produced by transmitting a PCM wave through a channel lies in reconstructing it by using ___________.
16. The___________ process involves generating a pulse the amplitude of which is the linear sum of all the pulses in the code word, with each pulse weighted by its place value (2⁰. 2¹, 2², 2³, ….) in the code.
17. The basic operations performed by___________ are equalization, timing and decision making.
18. If the spacing between received pulses deviates from its assigned value, a ___________ is introduced into the regenerated pulse position, thereby causing distortion.
19. ___________ noise may be introduced anywhere between the transmitter, output and the receiver input.
20. ___________ noise may be introduced in the transmitter and is carried along to the receiver output.
21. The average probability of error in a PCM receiver depends on the ratio of ___________ to ___________, measured at the decoder input in the receiver.
22. The important characteristic of a PCM system is its___________ to interference.
23. The___________ is the one bit version of DPCM.
24. A Delta modulator using a fixed step size is often referred to as ___________.
25. The___________ noise occurs when the step size is too large relative to the local slope characteristics of the input waveform.
26. The___________and___________ are the two noise effects in Delta modulation.
27. The method in which the step size is adapted to the level of the input signal is called ___________.
28. In terms of SNR performance, the adaptive delta modulation is ___________ to linear delta modulation by ___________dB at a bit rate of___________.
29. Multiple Choice Questions
30. Companding is used [ ]

(a)        to overcome quantizing noise in PCM
(b)        in PCM transmitters, to allow amplitude limiting in the receivers
(c)        to protect small signals in PCM from quantizing distortion.
(d)       in PCM receivers, to overcome impulse noise.

2. The biggest disadvantages of PCM is [ ]

(a)        its inability to handle analog signals
(b)        the high error rate which its quantizing noise introduces
(c)        its incompatibility with TDM
(d)       the large bandwidths that are required for it.

3. Indicate which of the following pulse modulation systems is analog [ ]

(a)        PCM                            (b)        Differential PCM
(c)        PWM               (d)       Delta modulation

4. Quantizing noise occurs in [ ]

(a)        time-division multiplexing
(b)        FDM
(c)        PCM                            (d)       PWM

5. Quantizing noise can be reduced by increasing the number of samples per second. It is true,

(a)        yes, it is                       (b)        no, it is not
(c)        not necessarily             (d)       none of these

6. In PCM a system, the quantization noise depends upon (IETE, 1998)

(a)        the number of quantization levels only
(b)        the sampling rate only
(c)        both the sampling rate and the number of quantization levels
(d)       none of the above is correct

7. The signal-to quantization noise ratio in PCM system depends upon (IETE, 1997)

(a)        sampling rate
(b)        number of quantization levels
(c)        message signal bandwidth
(d)       none of the above

8. Indicate which of the following systems is digital?

(a)        Pulse-position modulation
(b)        Pulse-code modulation
(c)        Pulse-width modulation
(d)       Pulse-frequency modulation

9. Quantizing noise occurs in

(a)        time-division multiplex
(b)        frequency-division multiplex
(c)        pulse-code modulation
(d)       pulse-width modulation

10. In order to reduce quantizing noise. one must

(a)        increase the number of standard amplitudes
(b)        send pulses whose sides are more nearly vertical
(c)        use an R.F. amplifier in the receiver
(d)       increase the number of samples per second

11. The biggest disadvantages of PCM is

(a)        its inability to handle analog signals
(b)        the high error rate which its quantizing noise reduces
(c)        its incompatibility with TDM
(d)       the large bandwidth that are required for it

12. Companding is used

(a)        to overcome quantizing noise in PCM
(b)        in PCM transmitters, to allow amplitude limiting in the receivers
(c)        to protect small signals in PCM from quantizing distortion
(d)       In PCM receiver, to overcome impulse noise

13. The main advantage of PCM system is

(a)        lower bandwidth
(b)        lower power
(c)        lower noise

14. Quantization noise is produced in

(a)        all pulse modulation system
(b)        PCM
(c)        all modulation system

15. One of the following systems is analog

(a)        PCM
(b)        delta
(c)        differential PCM
(d)       PAM

16. For an efficient communication in PCM system number of samples per second must at least be equal to twice the highest modulating frequency. Comment

(a)        Not necessary
(b)        A very important consideration
(c)        Who cares
(d)       80 – 50, true

17. In PCM system, output SIN increases

(a)        linearly with bandwidth
(b)        exponentially with bandwidth
(c)        inversely with bandwidth
(d)       none of these

18. The transmitted pulse in PCM system usually occur at a uniform rate for minimum bandwidth

(a)        true                                          (b)        false

19. In a DM system, the granular (idling) noise occurs when the modulating signal                                                        (IETE, 1998)

(a)        increase rapidly
(b)        remains constant
(c)        decreases rapidly
(d)       the nature of modulating signal has nothing to do with this noise

20. Quantization noise is produced in        (IETE, 1997)

(a)        all pulse modulation system
(b)        PCM
(c)        all modulation system

21. The main advantage of PCM signal is (IETE, 1997)

(a)        lower bandwidth
(b)        higher bandwidth
(c)        lower noise

22. For transmission of normal speech signal the PCM channel needs a bandwidth of (IETE, 1998)

(a)        64 kHz                                    (b)        8 kHz
(c)        4 kHz

23. The non-uniform quantization leads to        (IETE, 1998)

(a)        reduction in transmission bandwidth
(b)        increase in maximum SNR
(c)        increase in SNR for low level signals
(d)       simplification of quantization process

24. The equipment needed either at the transmitter or at the receiver is

(IETE, 1998)
(a)        simpler
(b)        more complicated
(c)        of simple complexity, when delta modulation is used in the case of PCM

25. PCM systems use non-uniform quantization in order to

(a)        raise SNR for low level signals
(b)        cut down the required bandwidth of transmission
(c)        increases the maximum SNR

26. The use of non-uniform quantization leads to

(a)        reduction in transmission bandwidth
(b)        increase in maximum SNR
(c)        Increase in SNR for low level signals
(d)       Simplification of quantizations process

27. In QAM, both identities are varied.

(a)        amplitude and phase
(b)        frequency and phase
(c)        bit rate and phase
(d)       baud rate and phase

28. Signal-to-quantization noise ratio of a PCM system using 8-bit words for the analog signal that does not exceed its quantization boundary is

(a)        48 dB                          (b)        54 dB
(c)        52.7 dB                                   (d)       64 dB

29. Granular noise is associated with

(a)        PCM                                        (b)        DPCM
(c)        DM                                          (d)       QAM

30. The signal to quantization noise ratio in a PCM system depends upon
31. sampling rate
32. number of quantization levels
33. message signal bandwidth

(a)        1, 2 and 3                                (b)        2 and 3 only
(c)        2 only                          (d)       3 only

31. In PCM, if the transmission path is very long

(a)        repeater stations are used
(b)        pulsewidth may be increased
(c)        pulse amplitude is increased
(d)       pulse spacing is reduced

32. A signal having uniformly distributed amplitude in the interval (-V, + V) is to be encoded using PCM with uniform quanti-zation. The (SNR)_q is determined by

(a)        dynamic range of the signal
(b)        sampling rate
(c)        no. of quantizing levels
(d)       power spectrum of signal

33. In PCM the biggest disadvantage compared to analog modulation is

(a)        large bandwidth
(b)        larger noise
(c)        inability to handle analog signals
(d)       incompatability with TDM system

34. In an ADM system, the output signal amplitudes for 1’s and 0’s are

(a)        fixed and the repetition rate is also fixed
(b)        fixed but the repetition rate is variable
(c)        variable and the repetion rates is also variable
(d)       variable but the repetition rate is fixed

35. The use of non-uniform quantization leads to

(a)        reduction in transmission BW
(b)        increase in max. SNR
(c)        increase in SNR for low level signals
(d)       simplification of quantization process

36. Consider the following statements comparing DM and PCM systems, DM requires
37. a lower sampling rate
38. a higher sampling rate
39. a larger BW
40. simple harware

Which of these statements are correct?
(a)        1, 2 and 4                                (b)        1, 2 and 3
(c)        1, 3 and 4                                (d)       2, 3 and 4

37. For uniform quantization with 32 levels, the qunantized output can be represented by n binary digits where n is

(a)        5                                              (c)        6
(b)        8                                              (d)       4

38. In a PCM system, the number of quantiza-tion levels are 16 and the maximum signal frequency is 4 kHz, the bit transmission rate is

(a)        64 bps                          (b)        16 kbps
(c)        32 kpbs                                    (d)       32 bps

39. PCM systems require regenerative repeaters over long distances. The correct sequence of the operations which such a repeater performs is

(a)        Timing, equalisation and decision making
(b)        Equalisation timing and decision making
(c)        Timing, theresholding and equalisation
(d)       Thresholding, timing and equali-sation

40. In a DM system, the granular noise occurs when the

(a)        modulating signal increases rapidly
(b)        pulse rate decreases
(c)        modulating signal remains constant
(d)       pulse amplitude increases

41. In a PCM system, the amplitude levels are transmitted in a 7 unit code. The sampling is done at the rate of 10 kHz. The BW should be

(a)        5 kHz                                      (b)        35 kHz
(c)        70 kHz                                                (d)       5 MHz
Answers

1. Fill up the Blanks
2. Sampling, quantizing and encoding; 2. Analog-to-Digital converter; 3. discrete amplitude levels; 4. Quantizing ; 5. quantum, step size ; 6. Quantizing error ; 7. Compressor, uniform ; 8. compander ; 9. code ; 10. code element, symbol ; 11. codeword, character ; 12. ternary code ; 13. Differential encoding; 14. regenerative repeaters ; 15. decoding ; 16. Regenerative repeater ; 17. jitter ; 18. Transmission noise ; 19. Quantizing noise ; 20. Peak pulse power to the average noise power ; 21. Ruggedness ; 22. Delta modulation ; 23. linear delta modulator ; 24. Granular noise ; 25. slope over load, granular noise ; 26. Adaptive delta modulator ; 27. superior, 8 dB, 20 kilobits/sec.
3. Multiple Choice Questions
4. (b) 2.         (d)                   3.         (c)                    4.         (c)
5. (d) 6.         (c)                   7.         (b)                    8.         (b)
6. (c) 10.       (a)                    11.       (d)                   12.       (a)
7. (c) 14.       (b)                    15.       (d)                   16.       (b)
8. (a) 18.       (a)                    19.       (b)                    20.       (b)
9. (v) 22.       (a)                    23.       (c)                    24.       (c)
10. (a) 26.       (c)                    27.       (a)                    28.       (a)
11. (c) 30.       (c)                    31.       (a)                    32.       (c)
12. (a)            34.       (a)                    35.       (c)                    36.       (a)
13. (a) 38.       (c)                    39.       (b)                    40.       (d)

41.       (b)