An electric or electromagnetic representation of data
Analog and Digital Data
Analog Datum
Defined: An element of a continuum
Examples: audio
Digital Datum
Defined: An element of a discrete set
Examples: characters, integers
Analog and Digital Signals
Analog Signal
A continuously varying electric/electromagnetic wave
Digital Signal
A sequence of electric/electromagnetic pulses
The Four Possibilities
Analog Data/Analog Signal:
Analog signal occupies the same
spectrum as the data (called baseband
transmissions)
The input signal is combined with
a carrier (called amplitude modulation, frequency modulation or
phase modulation)
This is done either
because the baseband frequency isn't "practical" or to allow
frequency division multiplexing
Analog Data/Digital Signal:
A codec (code-decoder) is used for the analog-to-digital
conversion (e.g., pulse code modulation, delta modulation)
Digital Data/Analog Signal:
A modem (modulator-demodulator) is used (e.g.,
amplitude modulation/shift-keying,
frequency modulation/shift-keying, phase
modulation/shift-keying, or pulse modulation/shift-keying)
Digital Data/Digital Signal:
Signal consists of discrete values, one for each data value
(e.g., binary 0 is the lower voltage and binary 1 is the higher
voltage)
An encoding scheme based on transitions is used
(e.g., nonreturn to zero, bipolar alternate mark inversion,
differential Manchester)
Analog and Digital Transmission
Analog Transmission
The transmission of analog signals without regard to their
content (i.e., the signal may represent either analog data or
digital data)
Digital Transmission
The transmission of digital signals that represent
digital data
Transmission Impairments
Attenuation:
The strength of a signal falls over the distance
it travels
The fall-off varies with the frequency of the signal
(which is particularly problematic for
analog signals)
Delay Distortion:
The velocity of the propagation of a signal
through a guided medium varies with the frequency
(which is particularly problematic for digital data)
Noise:
Unwanted signals that are inserted somewhere between the
transmission and reception points
Important categories include thermal noise (due
to thermal agitation of electrons), intermodulation
noise (caused by nonlinearities in the system),
crosstalk (an unwanted coupling between signal paths),
and impulse noise (e.g., caused by electromagnetic
disturbances, flaws in the system)
Channel Capacity
The Question (Nyquist, 1924):
What is the transmission capacity of a perfect (i.e.,
noiseless) channel?
The Answer:
\(M = 2 H \log_2(V)\)
where
\(M\) is the maximum data rate (in bits per
second)
\(H\) is the bandwidth of the channel (in Hz)
\(V\) is the number of discrete levels in the
signal (in levels per cycle which means
\(\log_2(V)\) is measured in bits per cycle)
An Example:
Suppose \(H\) is 3 kHz and \(V\) is 2 (i.e., binary)
Then \(M = 2 \cdot 3000 \cdot \log_2(2) = 6000\)
Channel Capacity (cont.)
The Question (Shannon, 1948):
To what extend do impairments limit the digital data rate?
The Answer:
Depends on the details but it is possible to find bounds
(that do not depend on \(V\)) using the signal
to noise ratio, \(S/N\).
\(M = H \log_2(1 + S/N)\)
Data Integrity
The Question:
Can we detect and/or correct errors that are introduced
by impairments?
Modes of Operation:
The receiver can recognize than an error has occurred and
can correct it (e.g., Hamming codes, BCH codes)
The receiver can recognize that an error has occurred
(e.g., parity checks, redundancy checking) and
can signal the sender which can re-transmit
The receiver can recognize that an error has occurred
Direction of Information Flow
Simplex:
Information can flow in one direction only
(e.g., home security systems)
Half-Duplex:
Information can flow in both directions, but
only in one direction at a time (e.g., tin can telephone,
walkie-talkie)
Full-Duplex:
Information can flow in both directions simultaneously
(e.g., telephone)