Digital Communication - Theorems And Equations

• Digital communication systems, by definition, are communication systems
that use such a digital sequence as an interface between the source and
the channel input (and similarly between the channel output and final
destination)
• Placing a binary interface between source and channel. The source
encoder converts the source output to a binary sequence and the channel
encoder (often called a modulator) processes the binary sequence for
transmission over the channel. The channel decoder (demodulator)
recreates the incoming binary sequence (hopefully reliably), and the
source decoder recreates the source output.

1. DIGITAL COMMUNICATION

2. Digital communication

3. •Digital communication systems, by definition, are communication systems
that use such a digital sequence as an interface between the source and
the channel input (and similarly between the channel output and final
destination)
•Placing a binary interface between source and channel. The source
encoder converts the source output to a binary sequence and the channel
encoder (often called a modulator) processes the binary sequence for
transmission over the channel. The channel decoder (demodulator)
recreates the incoming binary sequence (hopefully reliably), and the
source decoder recreates the source output.

4. Need for digital communication
•Digital hardware has become so cheap, reliable, and miniaturized, that
digital interfaces are eminently practical.
•A standardized binary interface between source and channel simplifies
implementation and understanding, since source coding/decoding can be
done independently of the channel, and, similarly, channel
coding/decoding can be done independently of the source.
•A standardized binary interface between source and channel simplifies
networking, which now reduces to sending binary sequences through the
network.
• One of the most important of Shannon’s information theoretic results is
that if a source can be transmitted over a channel in any way at all, it can
be transmitted using a binary interface between source and channel. This
is known as the source/channel separation theorem.

5. Sampling theorem
•The sampling theorem states that, if the sampling
rate in any pulse modulation system exceeds twice
the maximum signal frequency, the original signal
can be reconstructed in the receiver with minimal
distortion.

15. PULSE MODULATION
•Pulse modulation may be used to transmit analog information, such as
continuous speech or data.
•It is a system in which continuous waveforms are sampled at regular
intervals.
•Information regarding the signal is transmitted only at the sampling times,
together with any synchronizing pulses that may be required.
•Pulse modulation may be subdivided broadly into two categories, analog
and digital.
•Pulse-amplitude and pulse-time modulation are both analog, while the
pulse-code and delta modulation systems are both digital.
•The two types of analog pulse modulation, pulse-amplitude and pulse-
time modulation, correspond roughly to amplitude and frequency
modulation.

16. Pulse-amplitude modulation (PAM)
•PAM is a pulse modulation system in which the signal is sampled at regular
intervals, and each sample is made proportional to the amplitude of the
signal at the instant of sampling.
•The pulses are then sent by either wire or cable, or else are used to
modulate a carrier.
•The two types are double-polarity PAM, which is self-explanatory, and
single-polarity PAM, in which a fixed dc level is added to the signal, to
ensure that the pulses are always positive.
•The ability to use constant-amplitude pulses is a major advantage of pulse
modulation, and since PAM does not utilize constant-amplitude pulses, it
is infrequently used. When it is used, the pulses frequency-modulate the
carrier.

18. •It is very easy to generate and demodulate PAM. In a generator, the signal
to be converted to PAM is fed to one input of an AND gate.
•Pulses at the sampling frequency are applied to the other input of the
AND gate to open it during the wanted time intervals.
•The output of the gate then consists of pulses at the sampling rate, equal
in amplitude to the signal voltage at each instant.
•The pulses are then passed through a pulse-shaping network, which gives
them flat tops.
•As mentioned above, frequency modulation is then employed, so that the
system becomes PAM-FM. In the receiver, the pulses are first recovered
with a standard FM demodulator.
•They are then fed to an ordinary diode detector which is followed by a
low-pass filter .
• If the cut off frequency of this filter is high enough to pass the highest
signal frequency, but low enough to remove the sampling frequency
ripple, an undistorted replica of the original signal is reproduced.

19. Pulse-Width Modulation
•A fixed amplitude and starting time of each pulse, but the width of each
pulse is made proportional to the amplitude of the signal at that instant.
•Pulse-width modulation may be generated by applying trigger pulses (at
the sampling rate) to control the starting time of pulses from a
monostable multivibrator, and feeding in the signal to be sampled to
control the duration of these pulses.
•The emitter-coupled monostable multivibrator makes an excellent
voltage-to-time converter, since its gate width is dependent on the voltage
to which the capacitor C is charged.
•If this voltage is varied in accordance with a signal voltage, a series of
rectangular pulses will be obtained, with widths varying as required.
•The circuit does the twin jobs of sampling and converting the samples into
PWM.

22. •It will be recalled that the stable state for this type of multivibrator
is with T1 OFF and T2 ON.
•The applied trigger pulse switches T1 ON, where upon the voltage at
C1 falls as T1 now begins to draw collector current; the voltage at
B2 follows suit and T2 is switched oFF by regenerative action.
•As soon as this happens, however, C begins to charge up to the
collector supply potential through R.
•After a time determined by the supply voltage and the RC time
constant of the charging network, B2 becomes sufficiently positive
to switch T2 ON.
•T1 is simultaneously switched OFF by regenerative action and stays
OFF until the arrival of the next trigger pulse.
•The voltage that the base of T2 must reach to allow T2 to turn on is
slightly more positive than the voltage across the common emitter
resistor R
k.

23. •This voltage depends on the current flowing through the circuit, which at
the time is the collector current of T1 (which is then ON).
•The collector current depends on the 'base-bias, which is governed by the
instantaneous changes in the applied signal voltage.
• The applied modulation voltage controls the voltage to which B2 must rise
to switch T2 ON. Since this voltage rise is linear, the modulation voltage is
seen to control the period of time during which T2 is OFF, that is, the pulse
duration.
• It should be noted that this pulse duration is very short compared to even
the highest signal frequencies, so that no real distortion arises through
changes in signal amplitude while T2 is OFF.
•The demodulation of pulse-width modulation is quite a simple process.
•PWM is merely fed to an integrating circuit from which a signal emerges
whose amplitude at any time is proportional to the pulse width at that
time.
•This principle is also employed in the very efficient so-called class D
amplifiers.
• The integrating circuit most often used there is the loudspeaker itself.

24. Pulse-Position Modulation (PPM)
•The amplitude and width of the pulses is kept constant in this system,
while the position of each pulse, in relation to the position of a recurrent
reference pulse is varied by each instantaneous sampled value of the
modulating wave.
•This means that the transmitter must send synchronizing pulses to
operate timing circuits in the receiver.
•pulse-position modulation has the advantage of requiring constant
transmitter power output, but the disadvantage of depending on
transmitter receiver synchronization.

25. Generation And Demodulation Of
PPM
•Pulse-position modulation may be obtained very simply from PWM.
•Considering PWM and its generation again, it is seen that each such
pulse has a leading edge and trailing edge (like any other pulse, of
course).
•However, in PWM the locations of the leading edges are fixed,
whereas those of the trailing edges are not.
•Their position depends on pulse width, which is determined by the
signal amplitude at that instant.
•Thus, it may be said that the trailing edges of PWM pulses are, in
fact, position-modulated.
•The method of obtaining PPM from PWM is thus accomplished by
"getting rid of" the leading edges and bodies of the PWM pulses.

27. •Figure 13-7a and b shows, once again, PWM corresponding to a given
signal.
•If the train of pulses thus obtained is differentiated, then, as shown in
Figure 13-7c,another pulse train results.
•This has positive-going narrow pulses corresponding to leading edges and
negative-going pulses corresponding to trailing edges.
•If the position corresponding to the trailing edge of an unmodulated pulse
is counted as zero displacement, then the other trailing edges will arrive
earlier or later.
•An unmodulated PWM pulse is one that is obtained when the
instantaneous signal value is zero.
•These pulses are appropriately labeled in Figure 13-7b, They will therefore
have a time displacement other than zero; this time displacement is
proportional to the instantaneous value of the signal voltage.
• The differentiated pulses corresponding to the leading edges are removed
with a diode clipper or rectifier, and the remaining pulses, as shown in
Figure 13-7d, are position-modulated.

28. •When PPM is demodulated in the receiver, it is again first converted into
PWM. This is done with a flip-flop, or bistable multivibrator.
• One input of the multivibrator receives trigger pulses from a local
generator which is synchronized by trigger pulses received from the
transmitter, and these triggers are used to switch OFF one of the stages of
the flip-flop.
•The PPM pulses are fed to the other base of the flip-flop and switch that
stage ON (actually by switching the other one OFF).
•The period of time during which this particular stage is OFF depends on
the time difference between the two triggers, so that the resulting pulse
has a width that depends on the time displacement of each individual
PPM pulse.
•The resulting PWM pulse train is then demodulated.

29. Pulse-Code Modulation (PCM)
•Pulse-code modulation is just as different from the ,forms of pulse
modulation so far studied as they were from AM or FM.
•PAM and PTM differed from AM and FM because, unlike in those two
continuous forms of modulation, the signal was sampled and sent in pulse
form.
•Like AM and FM, they were forms of analog communication in all these
forms a signal is sent which has a characteristic that is infinitely variable
and proportional to the modulating voltage.
•PCM also uses the sampling technique, but it differs from the others in
that it is a digital process. That is, instead of sending a pulse train capable
of continuously varying one of the parameters, the PCM generator
produces a series of numbers, or digits (hence the name digital process).
•Each one of these digits, almost always in binary code, represents the
approximate amplitude of the signal sample at that instant.

31. Basic Elements of PCM

•The transmitter section of a Pulse Code Modulator circuit consists
of Sampling, Quantizing and Encoding, which are performed in the analog-
to-digital converter section. The low pass filter prior to sampling prevents
aliasing of the message signal.
•The basic operations in the receiver section are regeneration of impaired
signals, decoding, and reconstruction of the quantized pulse train.
Following is the block diagram of PCM which represents the basic
elements of both the transmitter and the receiver sections.

33. •Low Pass Filter : This filter eliminates the high frequency
components present in the input analog signal which is greater than
the highest frequency of the message signal, to avoid aliasing of the
message signal.
•Sampler: This is the technique which helps to collect the sample
data at instantaneous values of message signal, so as to reconstruct
the original signal. The sampling rate must be greater than twice
the highest frequency component W of the message signal, in
accordance with the sampling theorem.
•Quantizer: Quantizing is a process of reducing the excessive bits
and confining the data. The sampled output when given to
Quantizer, reduces the redundant bits and compresses the value.

34. •Encoder: The digitization of analog signal is done by the encoder. It
designates each quantized level by a binary code. The sampling
done here is the sample-and-hold process. These three sections
(LPF, Sampler, and Quantizer) will act as an analog to digital
converter. Encoding minimizes the bandwidth used.
•Regenerative Repeater :This section increases the signal strength.
The output of the channel also has one regenerative repeater
circuit, to compensate the signal loss and reconstruct the signal,
and also to increase its strength.
•Decoder: The decoder circuit decodes the pulse coded waveform to
reproduce the original signal. This circuit acts as the demodulator.

35. •Reconstruction Filter: After the digital-to-analog conversion is done by the
regenerative circuit and the decoder, a low-pass filter is employed, called
as the reconstruction filter to get back the original signal. Hence, the Pulse
Code Modulator circuit digitizes the given analog signal, codes it and
samples it, and then transmits it in an analog form. This whole process is
repeated in a reverse pattern to obtain the original signal.

36. Principles of PCM
•In PCM, the total amplitude range which the signal may occupy is divided
into a number of standard levels, as shown in Figure 13-8.
• Since these levels are transmitted in a binary code, the actual number of
levels is a power of 2,
•16 levels are shown here for simplicity, but practical systems use as many
as 128.
•By a process called quantizing, the level actually sent at any sampling time
is the nearest standard (or quantum) level.
•As shown in Figure 13-8, should the signal amplitude be 6.8 V at any time,
it is not sent as a 6.8-V pulse, as it might have been in PAM, nor as a 6.8
micro second-wide pulse as in PWM, but simply as the digit because 7 V is
the standard amplitude nearest to 6.8 V.
•Furthermore, the digit 7 is sent at that instant of time as a series of pulses
corresponding to the number 7.

38. •Since there are 16 Ievels (2^4), 4 binary places are required; the number
becomes 0111, and could be sent as OPPP, where P = pulse and O = no-pulse.
•Actually, it is often sent as a binary number back-to front, i.e., as 1110, or
PPPO, to make demodulation easier.
•As shown in Figure 13-8, the signal is continuously sampled, quantized, coded
and sent, as each sample amplitude is converted to the nearest standard
amplitude and into the corresponding back-to-front binary number.
•Provided sufficient quantizing levels are used, the result cannot be
distinguished from that of analog transmission.
•A supervisory or signaling bit is generally added to each code group
representing a quantized sample.
•Hence each group of pulses denoting a sample, here called a word, is
expressed by means of n + 1 bits, where 2^n is the chosen number of standard
levels.

39. Generation and Demodulation of
PCM
•The signal is sampled and converted to PAM, the PAM is quantized and
encoded, and supervisory signals are added.
•The signal is then sent directly via cable, or modulated and transmitted.
•Because PCM is highly immune to noise, amplitude modulation may be
used, so that PCM-AM is quite common.
•At the receiver, the signaling information is extracted, and PCM is
translated into corresponding PAM pulses which are then demodulated in
the usual way.
•In fact, the "quantized wave" of Figure 13-8 would be the output for that
signal from an ideal PCM receiver. One of the methods of reconverting
PCM is most ingenious and simple.

40. Applications of data communication
1.Used in military application for secure communication and
missile guidance.
2.Used in image processing for pattern recognition, robotic
vision and image enhancement, video compression and
speech processing.
3.In digital signal processing.
4.The digital communication systems in telephony for text
messaging .
5.In space communication where spacecraft transmits signals
to earth.
6.used in digital audio transmission and also in data
compression.