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```1. In general digital waveforms have an infinite bandwidth as shown in the
following frequency domain representation. Elaborate on this.
“One easy means of representing binary data in a signal is to use a square wave. A positive
voltage V will be a 1, and a negative voltage V will be a 0.
A square wave is composed of the sum of an infinite number of sinusoidal waves, its Fourier
series.
A square wave with frequency f has a positive pulse and a negative pulse in each period. So
each pulse lasts 1/2f seconds long (since each is 1/2 the period). Since each pulse can
represent a bit, 2f bits are being transmitted per second on this waveform.
To get a square wave from sinusoids, we add sinusoids of frequencies f and 3f. This gives us
a crude approximation. Note that the amplitude of the frequency components is not
constant. The higher frequencies contribute less to the signal than does the main frequency.
If we keep adding frequencies, we get a better and better square wave. We need an infinite
number of them for a perfect square wave. But this gives us infinite bandwidth.”
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Each signal, there is a time-domain function s(t) that specifies the amplitude of the
signal at each instant in time.
There’s also the frequency-domain function S(f) that specifies the peak amplitude
of the constituent of the signal.
Thus, the frequency-domain function for a single square pulse that has the value 1
between –X/2 and X/2 and is 0 elsewhere.
In this case, S(f) is continuous and that is has non-zero values indefinitely, although
the magnitude of the frequency components becomes smaller for a larger f.
NOTE: S(f) is symmetric around f=0, thus it has values for negative frequencies.
2. The velocity of propagation of a signal through a guided media varies with
frequency. What are the implications of this on bandlimited signals?
Effective bandwidth is where MOST of the signal energy is concentrated. However, any
waveform may contain frequencies over a very broad range as a practical matter any
transmission system that is utilized can accommodate a limited band of frequencies. So, this
limits the data rate that can be carried on the transmission medium.
----TO REFER TO STALLINGS, DATA ENCODING CHAPTER, PAGE 130-131
(SIXTH EDITION)-----
3. Data bits are mapped to signal elements for transmission using an encoding scheme.
What is the significance of the encoding technique for synchronization of data
transmitted?
Like Positive volt = Binary bit 1, Negative volt = Binary bit 0
Definition of Synchronisation:
1) The attaining of synchronism between the frequencies or between the frequencies
and phases of two or more signals.
2) A state of simultaneous occurrences of significant instants among two or more signals.
Website link: http://www.rhyshaden.com/encoding.htm
In order to transport digital bits of data across carrier waves, encoding
techniques have been developed each with their own pros and cons. This
document briefly describes some of the more common techniques.
Manchester Phase Encoding (MPE)
802.3 Ethernet uses Manchester Phase Encoding (MPE). A data bit '1' from the
level-encoded signal (i.e. that from the digital circuitry in the host machine
sending data) is represented by a full cycle of the inverted signal from the master
clock which matches with the '0' to '1' rise of the phase-encoded signal (linked to
the phase of the carrier signal which goes out on the wire). i.e. -V in the first half
of the signal and +V in the second half.
The data bit '0' from the level-encoded signal is represented by a full normal
cycle of the master clock which gives the '1' to '0' fall of the phase-encoded
signal. i.e. +V in the first half of the signal and -V in the second half.
The above diagram shows graphically how MPE operates. The example at the
bottom of the diagram indicates how the digital bit stream 10110 is encoded.
A transition in the middle of each bit makes it possible to synchronize the sender
and receiver. At any instant the ether can be in one of three states: transmitting a
0 bit (-0.85v), transmitting a 1 bit (0.85v) or idle (0 volts). Having a normal clock
signal as well as an inverted clock signal leads to regular transitions which
means that synchronisation of clocks is easily achieved even if there are a series
of '0's or '1's. This results in highly reliable data transmission. The master clock
speed for Manchester encoding always matches the data speed and this
determines the carrier signal frequency, so for 10Mbps Ethernet the carrier is
10MHz.
Differential Manchester Encoding (DME)
A '1' bit is indicated by making the first half of the signal, equal to the last half of
the previous bit's signal i.e. no transition at the start of the bit-time. A '0' bit is
indicated by making the first half of the signal opposite to the last half of the
previous bit's signal i.e. a zero bit is indicated by a transition at the beginning of
the bit-time. In the middle of the bit-time there is always a transition, whether
from high to low, or low to high. Each bit transmitted means a voltage change
always occurs in the middle of the bit-time to ensure clock synchronisation.
Token Ring uses DME and this is why a preamble is not required in Token Ring,
compared to Ethernet which uses Manchester encoding.
Non Return to Zero (NRZ)
NRZ encoding uses 0 volts for a data bit of '0' and a +V volts for a data bit of '1'.
The problem with this is that it is difficult to distinguish a series of '1's or '0's due
to clock synchronisation issues. Also, the average DC voltage is 1/2V so there is
high power output. In addition, the bandwidth is large i.e. from 0Hz to half the
data rate because for every full signal wave, two bits of data can be transmitted
(remember that with MPE the data rate equals the bit rate which is even more
inefficient!) i.e. two bits of information are transmitted for every cycle (or hertz).
After 50m of cable attenuation the signal amplitude may have been reduced to
100mV giving an induced noise tolerance of 100mV.
Return to Zero (RZ)
With RZ a '0' bit is represented by 0 volts whereas a '1' data bit is represented by
+V volts for half the cycle and 0 volts for the second half of the cycle. This means
that the average DC voltage is reduced to 1/4V plus there is the added benefit of
there always being a voltage change even if there are a series of '1's.
Unfortunately, the efficiency of bandwidth usage decreases if there are a series
of '1's since now a '1' uses a whole cycle.
Non Return to Zero Invertive (NRZ-I)
With NRZ-I a '1' bit is represented by 0 volts or +V volts depending on the
previous level. If the previous voltage was 0 volts then the '1' bit will be
represented by +V volts, however if the previous voltage was +V volts then the '1'
bit will be represented by 0 volts. A '0' bit is represented by whatever voltage
level was used previously. This means that only a '1' bit can 'invert' the voltage, a
'0' bit has no effect on the voltage, it remains the same as the previous bit
whatever that voltage was.
This can be demonstrated in the following examples for the binary patterns
10110 and 11111:
Note how that a '1' inverts the voltage whilst a '0' leaves it where it is. This means
that the encoding is different for the same binary pattern depending on the
voltage starting point.
The bandwidth usage is minimised with NRZ-I, plus there are frequent voltage
changes required for clock synchronisation.
With fibre there are no issues with power output so a higher clock frequency is
fine whereas with copper NRZ-I would not be acceptable.
4. a. Give an example of encoding digital data as analog signals.
Shift Keying
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ASK - V amplitude levels can encode lg V bits per signal unit
FSK - V frequency levels can encode lg V bits per signal unit
PSK/QPSK - V phases can encode lg V bits per signal unit. QPSK uses four phases
offset 90 degrees.
QAM - Mixed PSK and ASK, use pairs (p,a) to describe signal units, where p is the
phase and a is the amplitude. This can keep power requirements lower and
discrimination better than either technique alone.
PPM - pulse position modulation, May be used with either analog or digital
transmission to encode digital signals Signal is divided into frames, each frame has N
slots (plus some synchronization overhead every so often) In each frame, exactly one
slot has a pulse in it, A<>0; the other slots have A = 0 (no pulse). This allows lg N
bits/frame to be encoded. It is useful when power requirements must be kept low
and the transmission medium may be pulsed easily (e.g., lasers in deep-space
communication)
----MANUALLY DRAW THE DIAGRAMS FOR ASK/FSK/PSK---
5. b. A voice grade line will pass frequencies in the approximate range 300-3400 Hz
and signals are transmitted in both directions (full-duplex). Use the following
diagram to explain how binary frequency shift keying (BFSK) overcomes
interference of signals.
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
To achieve FULL DUPLEX, the bandwidth is SPLIT. 1 direction (either
transmit or receive), the frequencies used to represent 1 and 0 are centered
on 1170Hz, with a shift of 100Hz on either side. (TO THE LEFT)
Effect of alternating between two frequencies is to produce a signal whose
spectrum is indicated as the shaded area on the left (depicted in the diagram).
Thus, in the other direction (either receive or transmit) the modem utilizes
frequencies shifted 100Hz to each side of a center frequency of 2125Hz. (TO
THE RIGHT).
FSK less susceptible to error than ASK.
Commonly used for HIGH FREQUENCY (3-30Mhz) radio transmission.
6. In PSK, the phase of the carrier signal is shifted to represent data. Elaborate on the
case where two phases are used to represent the two binary digits (BFSK).
----REFER TO PDF FILE: BFSK WRITEUP----
7. Pulse Code Modulation (PCM) is a technique used to transform analog data to
digital data. The following figure shows how Pulse Amplitude Modulation (PAM)
samples are taken at a rate 2B (once every 1/2B seconds) for a signal with
bandwidth B. Each PAM sample is approximately by being quantized into one of
16 different values. Reflect on the fact that is impossible to recover the original
signal exactly. What changes can you make to overcome this problem?
QUANTIZED WAVES are indicated by a series of coded pulses. (Codes may be in
binary)
PULSE MODULATION SYSTEMS provide methods of converting analog wave
shapes to digital wave shapes.
The entire range of AMPLITUDE (FREQUENCY or PHASE) values of the analog
wave can be arbitrarily divided into a series of standard values.
Each PULSE of a PULSE TRAIN (View Diagram B) takes the standard value nearest its
actual value when modulated. The modulating wave can be faithfully reproduced as
shown in views C and D.
The amplitude range has been divided into 5 standard values in view C. Each PULSE is
given whatever standard value is nearest its actual instantaneous value.
In view D, the same amplitude range has been divided into 10 standard levels. The curve
of view D is a much closer approximation of the modulating wave, view A. than is the 5level quantized curve in view C. BECAUSE GREATER number of standard levels are
used and more closely the quantized wave approximates the original.
So, in ACTUAL practice the levels are usually established at some exponential value of 2,
such as 4(22), 8(23), 16(24), 32(25), 64(26), 128(27), 256 (28)…..N(2n). Quantization is used
mostly in amplitude and frequency modulated pulse systems.
----REFER TO: http://www.tpub.com/neets/book12/49l.htm (elaborate on
Figure 2.50 and 2.51)----
8. One of the principal reasons for modulation of analog data to analog signals is to
permit frequency division multiplexing. Reflect on this.
Frequency division multiplexing (fdm), unlike tdm, transmits and receives for the full 360 degrees of a sine
wave. Fdm used presently by the Navy may be divided into two categories. One category is used for voice
communications and the other for tty communications. The normal voice speaking range is from 100 to
3,500 hertz. During single channel AM voice communications, the audio frequency amplitude modulates a
single rf (carrier frequency). However, in voice fdm, each voice frequency modulates a separate frequency
lower than the carrier frequency (subcarrier frequency). If these subcarrier frequencies are separated by
3,500 hertz or more, they may be combined in a composite signal. This signal modulates the carrier
frequency without causing excessive interference. In figure 3-30, the output of channel one is the voice
frequency range of 100 to 3,500 hertz. The output of channel two is the combination of a different voice
frequency with a subcarrier frequency of 4,000 hertz. The output of channel three is another voice
frequency. This voice frequency combined with a subcarrier frequency of 8,000 hertz gives you an output
frequency range of 8,100 to 11,500 hertz. The overall bw for the composite modulation package shown is
100 to 15,500 hertz. Each separate channel occupies its own band of frequencies. The composite signal is
used to modulate the carrier frequency of the transmitter.
Figure 3-30.—Block diagram of a frequency-division multiplexing system.
9. In PSK, the phase of the carrier signal is shifted to represent data. Elaborate on the
case where two phases are used to represent the two binary digits (BFSK).
8. One of the principal reasons for modulation of analog data to analog signals is to
permit frequency division multiplexing. Reflect on this.
Frequency division multiplexing (fdm), unlike tdm, transmits and receives for the full 360
degrees of a sine wave. Fdm used presently by the Navy may be divided into two
categories. One category is used for voice communications and the other for tty
communications.
The normal voice speaking range is from 100 to 3,500 hertz. During single channel AM
voice communications, the audio frequency amplitude modulates a single rf (carrier
frequency). However, in voice fdm, each voice frequency modulates a separate
frequency lower than the carrier frequency (subcarrier frequency). If these subcarrier
frequencies are separated by 3,500 hertz or more, they may be combined in a
composite signal. This signal modulates the carrier frequency without causing excessive
interference.
In figure 3-30, the output of channel one is the voice frequency range of 100 to 3,500
hertz. The output of channel two is the combination of a different voice frequency with a
subcarrier frequency of 4,000 hertz. The output of channel three is another voice
frequency. This voice frequency combined with a subcarrier frequency of 8,000 hertz
gives you an output frequency range of 8,100 to 11,500 hertz. The overall bw for the
composite modulation package shown is 100 to 15,500 hertz. Each separate channel
occupies its own band of frequencies. The composite signal is used to modulate the
carrier frequency of the transmitter.
Figure 3-30.—Block diagram of a frequency-division multiplexing system.
```