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BANDWIDTH DEFINITION
Bandwidth, in general, represents a range of
frequencies
Bandwidth is 400 MHz
300 MHz 700 MHz
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USAGE OF THE TERM BANDWIDTH
To specify the • A medium such as a
communication coaxial cable is associated
capacity with a bandwidth
To indicate the • Voice grade circuits have
bandwidth of a a bandwidth of 4 KHz (0-
technology 4000 Hz)
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MODULE 3:
Analog And Digital Systems
Case Study: Telephone Channel
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Analog or Digital Systems
Specify whether a system is digital or analog
by reference to the possible amplitudes of
voltage (and/or current) waveforms.
Analog Information Source produces values
defined on a continuum e.g., human voice.
Digital Information Source produces a finite
set of possible symbols e.g., computer
keyboard
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AREAS OF APPLICATION (ANALOG)
Old telephone networks
Most analog television broadcasting systems are turning into
digital ones.
Radio broadcasting
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ANALOG TO DIGITAL CONVERSION
1 0 1 1 0 1 0 0
A to D Converters, Digital
Signal Processors (DSP) etc.
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DATA TRANSMISSION USING ANALOG TECHNOLOGY
Computer Modem
Digital Analog
0s and 1s 0s and 1s
Digital-to-Analog Modulation
and vice versa
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Case Study: Telephone Channel
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Telephone Transmission
A baseband voice signal where the frequency
range optimized for voice signals
300Hz 3400 Hz
Direct transmission of digital data not possible
Long sequences of 1's or 0's look like a signal with zero Frequency.
Frequency for 9600bps sequences of alternating 0's and 1's > 3400Hz.
Modulate an audio-frequency carrier signal with digital data
Carrier always above low cutoff. To get high data rates at <3400Hz,
squeeze multiple bits into a signal element.
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Baud Rate
Each signal element is a “baud” (after its inventor Baudot (1845-1903)
Number of signal elements /s is called the baud rate.
Theoretical Limitations on Transmission Rate, Nyquist Theorem:
Max Bit Rate = 2 x carrier bandwidth x log2(possible values/signal element)
no of bits encoded by a signaling element
e.g., for an 8 levels for signal element (i.e., 3 bit/signal element) in a voice
channel;
Max bit rate = 2 x 3000 x log2(8) = 18000bps
Fixed by legacy for voice grade lines and 8
technology possible values per baud
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Shannon-Hartley Law
This law takes noise into account;
Max bit rate = bandwidth x log2(1 + S/N)
Where S/N is the signal to noise ratio.
S/N for analogue PSTN with multiple exchanges is ~1000
(It depends on complexity of connection)
Max bit rate = 3000 x log2(1000) = 30000bps
33.3kbps modems reached this limit
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Why Use The Narrowest Bandwidth?
Narrower signal bandwidth permits “packing” more
individual channels into a fixed total bandwidth.
Engineers are usually required to build the most
economical system which meets quality requirements.
Systems with higher quality requirements use
greater audio bandwidth:
AM Broadcasting: 5 kHz (4.5 kHz in some countries)*
FM Broadcasting: at least 15 kHz audio bandwidth
Hi-Fi audio: 20 Hz lows and 20 kHz highs (Compact Disks)
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Module 4
Frequency and Time Division Multiplexing
With Case Study: DSL
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Examples Of Multiplexing Schemes:
Frequency Division Multiplexing Using Analog Carrier Systems
The standard telephony voice channel [300 – 3400 Hz] is
stacked on high frequency carriers by single sideband
amplitude modulation. This is the most bandwidth efficient
scheme possible.
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The analog voice channels are pre-grouped into threes and
heterodyned on carriers at 12, 16, and 20 kHz. The
resulting upper sidebands of four such pre-groups are then
heterodyned on carriers at 84, 96, 108, and 120 kHz to
form a 12-channel group.
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Time Division Multiplexing
Nyquist Sampling Theorem
A band-limited waveform can be accurately reconstructed if
sampled at a rate greater than twice its bandwidth.
Example: a 4 kHz bandwidth signal must be sampled slightly more than
8000 samples per second
Exactly 8000 samples/sec would sample each 4000 Hz sine wave
component exactly twice per cycle.
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Digital Multiplexer Processes
Measure the voice waveform voltage to obtain 8000 samples
per second
Digitally encode this voltage into a binary code value of 8 bits
Serially transmit 8 bits consecutively for each such coded
sample
Insert extra” bit(s) in the transmitted bit stream for
synchronizing purposes
De-multiplexer operations are substantially the reverse of
those listed here
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Example Of TDM , The E-1 Frame
125 s or 1/8000 second
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
32 8-bit time slots per frame,
normally 30 used for subscriber
PCM, two for synch and signals one time slot
Slot zero contains Slot 16 contains
synchronizing common channel
bit label: 1 2 3 4 5 6 7 8
bit pattern and some signaling, either 3.9 s/slot
trouble-shooting channel associated
bit patterns. condition bits, or
CCS7
8000 frames/s
256 bits/frame
2.048 Mbit/s bit rate
0.488 µs/bit
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Digital Multiplexing Hierarchy
In the European system, the E1 signal constitutes the first level
of a hierarchy of signals that are each formed by successively
carrying out the TDM multiplexing of 4 lower level signals.
This way we obtain signals with the following formats:
E2 (8.448 Mbit/s),
E3 (34.368 Mbit/s) and
E4 (139.264 Mbit/s).
A fifth level, E5 (565.148 Mbit/s) was also defined but in the
end was not standardized.
This digital multiplexing hierarchy is the European version of
what is known as Plesiochronous Digital Hierarchy or PDH.
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E1 Multiplexing Scheme
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Worldwide Plesiochronous Digital
Hierarchy (PDH)
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