Data and Signals

Data and Signals
An Introduction

Prof. David Bernstein
James Madison University

Computer Science Department

bernstdh@jmu.edu

Definitions

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

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)