3. DIT
The Chapter includes:
• Pulse Amplitude
Modulation
• Pulse Width Modulation
• Pulse Position
Modulation
• Pulse Code Modulation
PULSE MODULATION
The process of transmitting signals in the form of
pulses (discontinuous signals) by using special
techniques.
4. DIT
Pulse Modulation
There are two types of Pulse Modulation which are analog pulse
modulation and digital pulse modulation
In analog pulse modulation
A periodic pulse train is used as the carrier wave, and some characteristic
feature of each pulse (e.g., amplitude, duration, or position) is varied in a
continuous manner in accordance with the corresponding sample value of
the message signal.
Thus in analog pulse modulation, information is transmitted basically in
analog form, but the transmission takes place at discrete times.
In digital pulse modulation
The message signal is represented in a form that is discrete in both time and
amplitude, thereby permitting its transmission in digital form as a sequence of
coded pulses; this form of signal transmission has no CW counterpart.
5. DIT
Analog Pulse Modulation Digital Pulse Modulation
Pulse Amplitude (PAM)
Pulse Width (PWM)
Pulse Position (PPM)
Pulse Code (PCM)
Delta (DM)
Pulse Modulation
Pulse Amplitude Modulation (PAM):
* The signal is sampled at regular intervals such that each sample
is proportional to the amplitude of the signal at that sampling
instant. This technique is called “sampling”.
* For minimum distortion, the sampling rate should be more than
twice the signal frequency.
6. DIT
Pulse Amplitude Modulation (PAM)
In pulse-amplitude modulation (PAM), the amplitudes
of regularly spaced pulses are varied in proportion to
the corresponding sample values of a continuous
message signal; the pulses can be of a rectangular
form or some other appropriate shape.
Pulse-amplitude modulation as defined here is
somewhat similar to natural sampling, where the
message signal is multiplied by a periodic train of
rectangular pulses. However, in natural sampling the
top of each modulated rectangular pulse varies with
the message signal, whereas in PAM it is maintained
flat;
8. DIT
* In this type, the amplitude is maintained constant but the duration
or length or width of each pulse is varied in accordance with
instantaneous value of the analog signal.
* The negative side of the signal is brought to the positive side by
adding a fixed d.c. voltage.
Analog Signal
Width Modulated Pulses
Pulse Width Modulation (PWM or PLM or PDM)
9. DIT
* In this type, the sampled waveform has fixed amplitude and
width whereas the position of each pulse is varied as per
instantaneous value of the analog signal.
* PPM signal is further modification of a PWM signal. It has
positive thin pulses (zero time or width) corresponding to the
starting edge of a PWM pulse and negative thin pulses
corresponding to the ending edge of a pulse.
* This wave can be
further amended
by eliminating the
whole positive
narrow pulses.
The remaining
pulse is called
clipped PPM.
PWM
PPM
Pulse Position Modulation (PPM)
10. DIT
PAM, PWM and PPM at a glance:
Analog Signal
Amplitude Modulated Pulses
Width Modulated Pulses
Position Modulated Pulses
11. DIT
* Analog signal is converted into digital signal by using a digital
code.
* Analog to digital converter employs two techniques:
1. Sampling: The process of generating pulses of zero width
and of amplitude equal to the instantaneous amplitude of the
analog signal. The no. of pulses per second is called
“sampling rate”.
2. Quantization: The process of dividing the maximum value
of the analog signal into a fixed no. of levels in order to
convert the PAM into a Binary Code.
The levels obtained are called “quanization levels”.
* A digital signal is described by its ‘bit rate’ whereas analog
signal is described by its ‘frequency range’.
* Bit rate = sampling rate x no. of bits / sample
Pulse Code Modulation (PCM)
12. DIT
Explanation of PCM
Pulse Code Modulation is the one of the basic form of digital pulse
modulation
The basic operations performed in the transmitter of a PCM system
are sampling, quantizing, and encoding
The low-pass filter prior to sampling is included to prevent aliasing
of the message signal.
The quantizing and encoding operations are usually performed in
the same circuit, which is called an analog-to-digital converter.
The basic operations in the receiver are regeneration of impaired
signals, decoding, and reconstruction of the train of quantized
samples.
Regeneration also occurs at intermediate points along the
transmission path as necessary.
When time-division multiplexing is used, it becomes necessary to
synchronize the receiver to the transmitter for the overall system to
operate satisfactorily.
14. DIT
Sampling
Analog signal is sampled every TS secs.
Ts is referred to as the sampling interval.
fs = 1/Ts is called the sampling rate or sampling
frequency.
There are 3 sampling methods:
Ideal - an impulse at each sampling instant
Natural - a pulse of short width with varying amplitude
Flattop - sample and hold, like natural but with single
amplitude value
The process is referred to as pulse amplitude
modulation PAM and the outcome is a signal with
analog (non integer) values
16. DIT
Nyquist sampling rate for low-pass and
bandpass signals
According to the Nyquist theorem, the sampling rate must be at
least 2 times the highest frequency contained in the signal.
17. DIT
Example 1
A complex low-pass signal has a bandwidth of 200 kHz.
What is the minimum sampling rate for this signal?
Solution
The bandwidth of a low-pass signal is between 0 and f,
where f is the maximum frequency in the signal. Therefore,
we can sample this signal at 2 times the highest frequency
(200 kHz). The sampling rate is therefore 400,000 samples
per second.
19. DIT 5/21
Pulse Code Modulation (PCM) ExamplePulse Code Modulation (PCM) Example
The signal is assumed to be band-limited with bandwidth B
The PAM samples are taken at a rate of 2B, or once every Ts=1/(2B)
seconds
Each PAM sample
is quantized into
one of 16 levels
Each sample is
then represented
by 4 bits.
8 bits→256 level
→better quality
4000Hz voice→
(8000sample/s)*
8bits/sample=
64Kbps
20. DIT
Bit rate and bandwidth requirements of
PCM
The bit rate of a PCM signal can be calculated form the
number of bits per sample x the sampling rate
Bit rate = nb x fs
The bandwidth required to transmit this signal depends on
the type of line encoding used. Refer to previous section for
discussion and formulas.
A digitized signal will always need more bandwidth than the
original analog signal. Price we pay for robustness and other
features of digital transmission.
21. DIT
Example 2
We want to digitize the human voice. What is the bit rate,
assuming 8 bits per sample?
Solution
The human voice normally contains frequencies from 0 to
4000 Hz. So the sampling rate and bit rate are calculated
as follows:
22. DIT
PCM Decoder
To recover an analog signal from a
digitized signal we follow the following
steps:
We use a hold circuit that holds the amplitude
value of a pulse till the next pulse arrives.
We pass this signal through a low pass filter
with a cutoff frequency that is equal to the
highest frequency in the pre-sampled signal.
The higher the value of L, the less
distorted a signal is recovered.
24. DIT
Important advantages of PCM
Robustness to channel noise and interference.
Efficient regeneration of the coded signal along the
transmission path.
Efficient exchange of increased channel bandwidth for
improved signal-to-noise ratio, obeying an exponential
law.
A uniform format for the transmission of different kinds of
baseband signals, hence their integration with other
forms of digital data in a common network.
Comparative ease with which message sources may be
dropped or reinserted in a time-division multiplex system.
Secure communication through the use of special
modulation schemes or encryption
25. DIT
Limitations and modifications of PCM
PCM advantages, however, are attained at the cost of
increased system complexity and increased channel
bandwidth.
Although the use of PCM involves many complex
operations, today they can all be implemented in a cost-
effective fashion using commercially available and/or
custom-made very-large-scale integrated (VLSI) chips.
The requisite device technology for the implementation
of a PCM system is already in place. So improvements
in VLSI technology, we are likely to see an ever-
expanding use of PCM for the digital transmission of
analog signals.
If, however, the simplicity of implementation is a
necessary requirement, then may use Delta Modulation
(DM) as an alternative to pulse-code modulation.
26. DIT
Delta Modulation (DM)
In DM, an incoming message signal is oversampled to purposely increase
the correlation between adjacent samples of the signal.
An analog input is approximated by a staircase function that moves up
or down by one quantization level (δ) at each sampling interval (Ts).
A 1 is generated if the staircase function is to go up during the next
interval; a 0 is generated otherwise.
The staircase function tracks the original waveforms
27. DIT
Delta Modulation Operation
For transmission:
the analog input is compared to the most recent value of
the approximating staircase function.
If the value of the analog input exceeds that of the
staircase function, a 1 is generated; otherwise, a 0 is
generated.
Thus, the staircase is always changed in the direction of
the input signal.
For reception:
The output of the DM process is therefore a binary
sequence that can be used at the receiver to reconstruct
the staircase
function.
29. DIT
Pulse Code Modulation (PCM) versus Delta
Modulation (DM)
DM has simplicity compared to PCM
DM has worse SNR compared to PCM
PCM requires more bandwidth
e.g. for good voice reproduction with PCM
want 128 levels (7 bit) & voice bandwidth 4khz
need 8000 sample/s x 7bits/sample = 56kbps
PCM is more preferred than DM for analog signals
30. Merits of Digital Communication:
1. Digital signals are very easy to receive. The receiver has to just detect
whether the pulse is low or high.
2. AM FM signals become corrupted over much short distances as compared
to digital signals. In digital signals, the original signal can be reproduced
accurately.
3. The signals lose power as they travel, which is called attenuation. When
AM and FM signals are amplified, the noise also get amplified. But the
digital signals can be cleaned up to restore the quality and amplified by
the regenerators.
4. The noise may change the shape of the pulses but not the pattern of the
pulses.
5. AM and FM signals can be received by any one by suitable receiver. But
digital signals can be coded so that only the person, who is intended for,
can receive them.
6. AM and FM transmitters are ‘real time systems’. I.e. they can be received
only at the time of transmission. But digital signals can be stored at the
receiving end.
7. The digital signals can be stored, or used to produce a display on a
computer monitor or converted back into analog signal to drive a loud
speaker. END
Hinweis der Redaktion
1)In analog pulse modulation,
-A periodic pulse train is used as the carrier wave, and some characteristic feature of each pulse (e.g., amplitude, duration,
or position) is varied in a continuous manner in accordance with the corresponding sample value of the message signal.
-Thus in analog pulse modulation, information is transmitted basically in analog form, but the transmission takes place at discrete times.
2) In digital pulse modulation,
-The message signal is represented in a form that is discrete in both time and amplitude, thereby permitting its transmission in digital form as a sequence
of coded pulses; this form of signal transmission has no CW counterpart.
-In pulse-amplitude modulation (PAM), the amplitudes of regularly spaced pulses are varied in proportion to the corresponding sample values of a continuous
message signal; the pulses can be of a rectangular form or some other appropriate shape.
-Pulse-amplitude modulation as defined here is somewhat similar to natural sampling, where the message signal is multiplied by a periodic train of rectangular pulses. However, in natural sampling the top of each modulated rectangular pulse varies with the message signal, whereas in PAM it is maintained flat;
Pulse-duration modulation (PDM), also referred to as pulse-width modulation,
where samples of the message signal are used to vary the duration of the individual
pulses in the carrier.
Pulse-position modulation (PPM), where the position of a pulse relative to its ., modulated time of occurrence is varied in accordance with the message signal.
-In pulse-code modulation (PCM), 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 operations performed in the transmitter of a PCM system are sampling, quantizing, and encoding -the low-pass filter prior to sampling is included to prevent aliasing of the message signal.
-The quantizing and encoding operations are usually performed in the same circuit, which is called an analog-to-digital converter.
-The basic operations in the receiver are regeneration of impaired signals, decoding, and reconstruction of the train of quantized samples.
- Regeneration also occurs at intermediate points along the transmission path as necessary. When time-division multiplexing
is used, it becomes necessary to synchronize the receiver to the transmitter for the overall system to operate satisfactorily.
SAMPLING
The incoming message signal is sampled with a train of narrow rectangular pulses so as to closely approximate the instantaneous sampling process. To ensure perfect reconstruction of the message signal at the receiver, the sampling rate must be greater than twice the highest frequency component W of the message signal in accordance with the sampling theorem. In practice, a low-pass anti-aliasing filter is used at the front end of the sampler to exclude frequencies greater than W before sampling. Thus the application of sampling permits the reduction of the continuously varying message signal (of some finite duration) to a limited number of discrete values per second.
QUANTIZATION
The sampled version of the message signal is then quantized, thereby providing a new representation of the signal that is discrete in both time and amplitude. The quantization process may follow a uniform law. In telephonic communication, however, it is preferable to use a variable separation between the representation levels.
For example, the range of voltages covered by voice signals, from the peaks of loud talk to the weak passages of weak talk, is on the order of 1000 to 1. By using a non-unifom qwntizer with the feature that the step-size increases as the separation from the origin of the input-output amplitude characteristic is increased, the large end steps of the quantizer can take care of possible excursions of the voice signal into the large amplitude ranges that occur relatively infrequently. In other words, the weak passages, which need more protection, are favored at the expense of the loud passages. In this way, a nearly uniform percentage precision is achieved throughout the greater part of the amplitude range of the input signal, with the result that fewer steps are needed than would be the case if a uniform
quantizer were used.
ENCODING
In combining the processes of sampling and quantization, the specification of a continuous message (baseband) signal becomes limited to a discrete set of values, but not in the form best suited to transmission over a telephone line or radio path. To exploit the advantages of sampling and quantizing for the purpose of making the transmitted signal more robust to noise, interference and other channel impairments, we require the use of an encoding process to translate the discrete set of sample values to a more appropriate form of signal.
Any plan for representing each of this discrete set of values as a particular arrangement of discrete events is called a code. One of the discrete events in a code is called a code element or symbol. For example, the presence or absence of a pulse is a symbol. A particular arrangement of symbols used in a code to represent a single value of the discrete set is called a code word or character.
Stallings DCC8e Figure 5.16 shows an example in which the original signal is assumed to be bandlimited with a bandwidth of B. PAM samples are taken at a rate of 2B, or once every Ts = 1/2B seconds. Each PAM sample is approximated by being quantized into one of 16 different levels. Each sample can then be represented by 4 bits. But because the quantized values are only approximations, it is impossible to recover the original signal exactly. By using an 8-bit sample, which allows 256 quantizing levels, the quality of the recovered voice signal is comparable with that achieved via analog transmission. Note that this implies that a data rate of 8000 samples per second 8 bits per sample = 64 kbps is needed for a single voice signal.
In a generic sense, pulse-code modulation (PCM) has emerged as the most favored modulation scheme for the transmission of analog information-bearing signals such as voice and video signals. The advantages of PCM may all be traced to the use of coded pulses for the digital representation of analog signals, a feature that distinguishes it from all other analog methods of modulation.
A variety of techniques have been used to improve the performance of PCM or to reduce its complexity. One of the most popular alternatives to PCM is delta modulation (DM). With delta modulation, an analog input is approximated by a staircase function that moves up or down by one quantization level () at each sampling interval (Ts). The important characteristic of this staircase function is that its behavior is binary: At each sampling time, the function moves up or down a constant amount . Thus, the output of the delta modulation process can be represented as a single binary digit for each sample. In essence, a bit stream is produced by approximating the derivative of an analog signal rather than its amplitude: A 1 is generated if the staircase function is to go up during the next interval; a 0 is generated otherwise.
Stallings DCC8e Figure 5.20 shows an example where the staircase function is overlaid on the original analog waveform. A 1 is generated if the staircase function is to go up during the next interval; a 0 is generated otherwise. The transition (up or down) that occurs at each sampling interval is chosen so that the staircase function tracks the original analog waveform as closely as possible.
There are two important parameters in a DM scheme: the size of the step assigned to each binary digit, , and the sampling rate. As the above figure illustrates, must be chosen to produce a balance between two types of errors or noise. When the analog waveform is changing very slowly, there will be quantizing noise. This noise increases as is increased. On the other hand, when the analog waveform is changing more rapidly than the staircase can follow, there is slope overload noise. This noise increases as is decreased. It should be clear that the accuracy of the scheme can be improved by increasing the sampling rate. However, this increases the data rate of the output signal.
The Figure illustrates the logic of the process, which is essentially a feedback mechanism. For transmission, the following occurs: At each sampling time, the analog input is compared to the most recent value of the approximating staircase function. If the value of the sampled waveform exceeds that of the staircase function, a 1 is generated; otherwise, a 0 is generated. Thus, the staircase is always changed in the direction of the input signal. The output of the DM process is therefore a binary sequence that can be used at the receiver to reconstruct the staircase function. The staircase function can then be smoothed by some type of integration process or by passing it through a lowpass filter to produce an analog approximation of the analog input signal.
The principal advantage of DM over PCM is the simplicity of its implementation. In general, PCM exhibits better SNR characteristics at the same data rate. Good voice reproduction via PCM can be achieved with 128 quantization levels, or 7-bit coding (27 = 128). A voice signal, conservatively, occupies a bandwidth of 4 kHz. Thus, according to the sampling theorem, samples should be taken at a rate of 8000 samples per second. This implies a data rate of 8000 7 = 56 kbps for the PCM-encoded digital data. But using the Nyquist criterion from Chapter 3, this digital signal could require on the order of 28 kHz of bandwidth. Even more severe differences are seen with higher bandwidth signals. For example, a common PCM scheme for color television uses 10-bit codes, which works out to 92 Mbps for a 4.6-MHz bandwidth signal. In spite of these numbers, digital techniques continue to grow in popularity for transmitting analog data. The principal reasons for this are
• Because repeaters are used instead of amplifiers, there is no cumulative noise.
• use time division multiplexing (TDM) for digital signals with no intermodulation noise, verses of the frequency division multiplexing (FDM) used for analog signals.
• The conversion to digital signaling allows the use of the more efficient digital switching techniques.
Furthermore, techniques have been developed to provide more efficient codes.
Studies also show that PCM-related techniques are preferable to DM-related techniques for digitizing analog signals that represent digital data.