# Bandwidth

Bandwidth is the physical property fo the transmission medium

Baseband
The signal that runs from 0 to a maximum frequency. Has very narrow and near-zero frequency range. Used in wires
Passband
Signals that occupy the higher range of frequency and pass through frequency filter(s). Used in wireless spectrum

## Signal Bandwidth

Bandwidth of analogue and digital signals are measured differently:

• Analogue signal bandwidth is measured in terms of its frequency (Hz)

• Digital signal bandwidth is measured in terms of bit rate (bps)

# Digital Modulation

Digital signals (0,1) are encoded by low and high voltage

There are many digital encoding schemes ## NRZ Encoding (Non-Return-to-Zero)

NRZ Encoding
• A high voltage represents a 1 and a low voltage represents a 0
• The voltage does not return to zero, it changes only when the bit value changes
• Problem: having long runs of consecutive bits with the same value (no changes in voltage) the constant signal values can’t synchronize the communicating devices

• Especially with long runs of either 0 or 1, there is no change to resynchronise so it is likely that the clocks would get out of sync

## NRZI Encoding

• NRZI attempts to alleviate the problem in NRZ scheme
NRZI encoding
• 0 is encoded as no change in the level. 1 is encoded depending on the current state of the line
• 1 is encoded as an inverting of the current state
• This fixes the problem of sending consecutive 1s but not consecutive 0s

## Bipolar Encoding

Bipolar Encoding
• 0 is represented by a zero voltage, neither high nor low
• 1 is represented by either positive voltage or negative voltage
• It is inverted based on the last transmission of 1
• It is represented by a negative voltage if it was represented by a positive voltage when it was last transmitted, and vice versa

For this, over a long enough message, the sum of the voltages is zero, this is called a “balanced encoding” and is desirable in some applications

## Manchester Encoding

Manchester Encoding
• A high to low voltage represents a 1 and a low to high voltage represents a 0
• Uses signal changes to transmit a bit and achieves synchronisation
• This is equivalent to an XOR of the clock signal and the NRZ encoding. The clock is at twice the frequency of the NRZ
• Twice the bandwidth of NRZ is required

# Multiplexing

• Channels are often shared by multiple signals

• Different ways to accomplish multiplexing:

## Frequency Division Multiplexing

• Refactor the signals to start at different frequencies

• Sit them side by side on the frequency spectrum on the same channel, so they don’t interfere with each other

• Put a small region in-between adjacent frequency bands to avoid interference 1. The original bandwidths

2. The bandwidths raised in frequency

3. The multiplexed channel

## Wavelength Division Multiplexing

• The same as FDM but for optical fibres instead of wireless signals ## Time division multiplexing

• Intersperse the channels in some sequence, leave a guard time to be able to separate out information ## Code Division Multiple Access

• Nice and clean mathematical method allows every transmitter to use the entire channel all the time

• The individual transmissions are blended (or extracted by a receiver) using coding theory

• Imagine that we have four transmitters called, from now on, stations

• Each station has a chip (i.e. a code), which is a four bit vector

• These codes are chosen so that the dot product of any of these codes with any other of the codes is 0 i.e. they are orthogonal to each other

• Transmitting the stations chip sequence a 1

• Transmitting the negation of a stations chip sequence is a 0