1. Introduction to Analog And Digital Communications
Second Edition
Simon Haykin, Michael Moher

2. Chapter 5 Pulse Modulation : Transition from Analog to Digital Communications
5.1 Sampling Process
5.2 Pulse-Amplitude Modulation
5.3 Pulse-Position Modulation
5.4 Completing the Transition from Analog and Digital
5.5 Quantization Process
5.6 Pulse-Code Modulation
5.7 Delta Modulation
5.8 Differential Pulse-Code Modulation
5.9 Line Codes
5.10 Theme Examples
5.11 Summary and Discussion

3. Analog pulse modulation
Some parameter of a pulse train is varied in accordance with the message signal
Analog pulse modulation
A periodic pulse train is used as the carrier wave
Some characteristic feature of each pulse is varied in a continuous manner in accordance with the corresponding sample value of the message signal
Digital pulse modulation
The message signal is represented in a form that is discrete in both time and amplitude
Its transmission in digital form as a sequence of coded pulse
Lesson1 : Given a strictly band-limited message signal, the sampling theorem embodies the conditions for a uniformly sampled version of the signal to preserve its information content
Lesson2 : Analog pulse-modulation systems rely on the sampling process to maintain continuous amplitude representation of the message signal. In contrast, digital pulse-modulation system use not only the sampling process but also the quantization process. Digital modulation makes it possible to exploit the full power of digital signal-processing techniques.

4. 5.1 Sampling Process
Instantaneous Sampling and Frequency-Domain Consequences
Sample the signal g(t) instantaneously and at a uniform rate,
Instantaneously (ideal) sampled signal
The signal obtained by individually weighting the elements of a periodic sequence of Dirac delta functions :
Reproduce the relationships listed at the bottom of the right-hand side of the table 5.1
The process of uniformly sampling a continuous time signal of finite energy results in a periodic spectrum with a repetition frequency equal to the sampling rate.
Fig. 5.1
Table. 5.1

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Fig.5.1

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table.5.1

7. Sampling Theorem A discrete-time Fourier transform of the sequence
For a strictly band-limited signal, under the two conditions
Fig. 5.2

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Fig.5.2

9. The sequence {g(n/2W)} has all the information contained in g(t).
Reconstructing the signal g(t) from the sequence of sample values.
The interpolation formula for reconstructing the original signal g(t) from the sequence of sample values {g(n/2W)} .

10. The sampling theorem for strictly band-limited signals of finite energy in two equivalent parts
Analysis : A band-limited signal of finite energy that has no frequency components higher than W hertz is completely described by specifying the values of the signal at instants of time separated by 1/2W seconds.
Synthesis : A band-limited signal of finite energy that has no frequency components higher than W hertz is completely recovered form knowledge of its samples taken at the rate of 2W samples per second.
Nyquist rate
The sampling rate of 2W samples per second for a signal bandwidth of W hertz
Nyquist interval
1/2W (measured in seconds)

11. Aliasing Phenomenon
The phenomenon of a high-frequency component in the spectrum of the signal seemingly taking on the identify of a lower frequency in the spectrum of its sampled version.
To combat the effects of aliasing in practices
Prior to sampling : a low-pass anti-alias filter is used to attenuate those high-frequency components of a message signal that are not essential to the information being conveyed by the signal
The filtered signal is sampled at a rate slightly higher than the Nyquist rate.
Physically realizable reconstruction filter
The reconstruction filter is of a low-pass kind with a passband extending from –W to W
The filter has a non-zero transition band extending form W to fs-W
Fig. 5.3
Fig. 5.4

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Fig.5.3

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Fig.5.4

14. 5.2 Pulse-Amplitude Modulation
Pulse-Amplitude Modulation (PAM)
The amplitude of regularly spaced pulses are varied in proportion to the corresponding sample values of a continuous message signal.
Two operations involved in the generation of the PAM signal
Instantaneous sampling of the message signal m(t) every Ts seconds,
Lengthening the duration of each sample, so that it occupies some finite value T.

15. Sample-and-Hold Filter : Analysis
The PAM signal is
The h(t) is a standard rectangular pulse of unit amplitude and duration
The instantaneously sampled version of m(t) is
Fig. 5.5

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Fig.5.5

17. To modify mδ(t) so as to assume the same form as the PAM signal
The PAM signal s(t) is mathematically equivalent to the convolution of mδ(t) , the instantaneously sampled version of m(t), and the pulse h(t)

18. Aperture Effect and its Equalization
Fig. 5.6
Aperture Effect and its Equalization
Aperture effect
The distortion caused by the use of pulse-amplitude modulation to transmit an analog information-bearing signal
Equalizer
Decreasing the in-band loss of the reconstruction filter as the frequency increases
The amplitude response of the equalizer is
The noise performance of a PAM system can never be better than direct transmission of the message signal
For transmission over long distances, PAM would be used only as a means of message processing for time-division multiplexing.
Fig. 5.7

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Fig.5.6

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Fig.5.7

21. 5.3 Pulse-Position Modulation
PDM (Pulse-duration modulation)
Pulse-width or Pulse-length modulation.
The samples of the message signal are used to vary the duration of the individual pulses.
PDM is wasteful of power
PPM (Pulse-position modulation)
The position of a pulse relative to its unmodulated time of occurrence is varied in accordance with the message signal.
Fig. 5.8

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Fig.5.8

23. 5.4 Completing the Transition from Analog to Digital
The advantages offered by digital pulse modulation
Performance
Digital pulse modulation permits the use of regenerative repeaters, when placed along the transmission path at short enough distances, can practically eliminate the degrading effects of channel noise and signal distortion.
Ruggedness
A digital communication system can be designed to withstand the effects of channel noise and signal distortion
Reliability
Can be made highly reliable by exploiting powerful error-control coding techniques.
Security
Can be made highly secure by exploiting powerful encryption algorithms
Efficiency
Inherently more efficient than analog communication system in the tradeoff between transmission bandwidth and signal-to-noise ratio
System integration
To integrate digitized analog signals with digital computer data

24. 5.5 Quantization Process Amplitude quantization
The process of transforming the sample amplitude m(nTs) of a baseband signal m(t) at time t=nTs into a discrete amplitude v(nTs) taken from a finite set of possible levels.
Representation level (or Reconstruction level)
The amplitudes vk , k=1,2,3,……,L
Quantum (or step-size)
The spacing between two adjacent representation levels
Fig. 5.9
Fig. 5.10

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Fig.5.9

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Fig.5.10

27. 5.6 Pulse-Code Modulation
PCM (Pulse-Code Modulation)
A message signal is represented by a sequence of coded pulses, which is accomplished by representing the signal in discrete form in both time and amplitude
The basic operation
Transmitter : sampling, quantization, encoding
Receiver : regeneration, decoding, reconstruction
Operation in the Transmitter
Sampling
The incoming message signal is sampled with a train of rectangular pulses
The reduction of the continuously varying message signal to a limited number of discrete values per second
Nonuniform Quantization
The step size increases as the separation from the origin of the input-output amplitude characteristic is increased, the large end-step of the quantizer can take care of possible excursions of the voice signal into the large amplitude ranges that occur relatively infrequently.

28. Compressor Fig. 5.11 A particular form of compression law : μ-law
μ-law is neither strictly linear nor strictly logarithmic
A-law :
Fig. 5.11

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Fig.5.11

30. Fig. 5.12
Encoding
To translate the discrete set of sample vales to a more appropriate form of signal
A binary code
The maximum advantage over the effects of noise in a transmission medium is obtained by using a binary code, because a binary symbol withstands a relatively high level of noise.
The binary code is easy to generate and regenerate
Table. 5.2

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Fig.5.12

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table.5.2

33. Regeneration Along the Transmission Path
The ability to control the effects of distortion and noise produced by transmitting a PCM signal over a channel
Equalizer
Shapes the received pulses so as to compensate for the effects of amplitude and phase distortions produced by the transmission
Timing circuitry
Provides a periodic pulse train, derived from the received pulses
Renewed sampling of the equalized pulses
Decision-making device
The sample so extracted is compared o a predetermined threshold
ideally, except for delay, the regenerated signal is exactly the same as the information-bearing signal
The unavoidable presence of channel noise and interference causes the repeater to make wrong decisions occasionally, thereby introducing bit errors into the regenerated signal
If the spacing between received pulses deviates from its assigned value, a jitter is introduced into the regenerated pulse position, thereby causing distortion.
Fig. 5.13

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Fig.5.13

35. Operations in the Receivers
Decoding and expanding
Decoding : regenerating a pulse whose amplitude is the linear sum of all the pulses in the code word
Expander : a subsystem in the receiver with a characteristic complementary to the compressor
The combination of a compressor and an expander is a compander
Reconstruction
Recover the message signal : passing the expander output through a low-pass reconstruction filter

36. 5.7 Delta Modulation Basic Consideration DM (Delta Modulation)
An incoming message signal is oversampled to purposely increase the correlation between adjacent samples of the signal
The difference between the input signal and its approximation is quantized into only two levels - corresponding to positive and negative differences
Fig. 5.14

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Fig.5.14

38. System Details Comparator Quantizer Accumulator Fig. 5.15
Computes the difference between its two inpus
Quantizer
Consists of a hard limiter with an input-output characteristic that is a scaled version of the signum function
Accumulator
Operates on the quantizer output so as to produce an approximation to the message signal.
Fig. 5.15

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Fig.5.15

40. Quantization Errors Slope-overload distortion Granular noise
The step size is too small for the staircase approximation to follow a steep segment of the original message signal
The result that the approximation signal falls behind the message signal
Granular noise
When the step size is too large relative to the local slope characteristic of the original message signal
The staircase approximation to hunt around a relatively flat segment of the message signal.
Fig. 5.16

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Fig.5.16

42. Delta-Sigma Modulation (Sigma-delta modulation)
A delta modulation system that incorporates integration at its input
Benefit of the integration
The low-frequency content of the input signal is pre-emphasized
Correlation between adjacent samples of the delta modulator input is increased
Design of the receiver is simplified
Fig. 5.17

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Fig.5.17

44. 5.8 Differential Pulse-Code Modulation
Prediction
If we know the past behavior of a signal up to a certain point in time, it is possible to make some inference about its future values
Tapped-delay-line filter (discrete-time filter)
A simple and yet effective approach to implement the prediction filter
With the basic delay set equal to the sampling period
The quantizer output may be expressed as
Fig. 5.18
Fig. 5.19

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Fig.5.18

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Fig.5.19

47. Comparing the DPCM with DM system,
The use of a one-bit (two-level) quantizer in the DM system
Replacement of the prediction filter in the DPCM by a single delay element
Noise is concerned
DPCM, like DM, is subject to slope-overload distortion whenever the input signal changes too rapidly for the prediction filter to track it
Like PCM, DPCM suffers from quantization noise

48. 5.9 Line Codes Several line codes On-off signaling
Nonreturn-to-zero (NRZ)
Return-to-zero
Bipolar return-to-zero (BRZ)
Split-phase (Manchester code)
Differential encoding
Fig. 5.20

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Fig.5.20

50. 5.10 Theme Examples Time-division Multiplexing Synchronization
Enables the joint utilization of a common communication channel by a plurality of independent message sources without mutual interference among them
Highly sensitive to dispersion in the common channel – a non-constant magnitude response of the channel and a nonlinear phase response.
Synchronization
Keep the same time as a distant standard clock at the transmitter
One possible procedure to synchronize the transmitter and receiver clocks is to set aside a code element or pulse at the end of a frame and to transmit this pulse every other frame only
Fig. 5.21

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Fig.5.21

53. Impulse Radio
Information is sent by means of very narrow pulses that are widely separated in time
A form of a ultra-wideband (UWB) radio transmission
Gaussian monocycle
One type of pulse used for impulse radio
PPM is one method for digitally modulating such an impulse wave
Fig. 5.22
Fig. 5.23
Fig. 5.24

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Fig.5.22

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Fig.5.23

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Fig.5.24

57. Due to the limitation on transmit power,
Good aspect
The signal power is spread over a large bandwidth, the amount of power that falls in any particular narrowband channel is small
Bad aspect
The power falls in all such narrowband channel
Due to the limitation on transmit power,
Ultra-wideband radio is restricted to short-range applications ( less than a few hundred meters )

58. 5.11 Summary and Discussion
Sampling : which operates in the time domain ;
The sampling process is the link between an analog waveform and its discrete-time representation
quantization : which operates in the amplitude domain;
The quantization process is the link between an analog waveform and its discrete-amplitude representation
Sampling theorem
A strictly band-limited signal with no frequency components higher than W Hz is represented uniquely by a 2W samples per second.
The sampling process is basic to the operation of all pulse modulation systems
Analog pulse modulation results from varying some parameter of the transmitted pulses
Digital pulse modulation systems transmit analog message signals as a sequence of coded pulses

59. The advantage of DM (delta modulation) is simplified circuitry
Differential pulse-code modulation employs increased circuit complexity to improve system performance
Adaptivity
Is used in delta modulation to improve noise performance
Is used in differential pulse-code modulation to reduce bandwidth requirement
Pulse modulation
lossy in the sense that some information is lost as a result of the signal representation that they perform
Source-encoding strategies (PCM, DM, and DPCM)
Whose purpose is to convert analog signals into digital form

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Fig.5.25
Fig. 5.25

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Fig.5.26
Fig. 5.26

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Fig.5.27
Fig. 5.27

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Fig.5.28
Fig. 5.28

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Fig.5.29
Fig. 5.29