Data and Signals

Definition of Terms

• Data must be transformed to electromagnetic signals to be transmitted.
• Data can be analog or digital. Analog data are continuous and take continuous
  values. Digital data have discrete states and take discrete values.
• Signals can be analog or digital. Analog signals can have an infinite number of
  values in a range; digital signals can have only a limited number of values.
• In data communications, we commonly use periodic analog signals and nonperiodic
  digital signals.
• A signal is periodic if it consists of a continuously repeating pattern.
• Frequency and period are the inverse of each other.
• Frequency is the rate of change with respect to time.
• Change in a short span of time means high frequency. Change over a long span of time means low frequency.
• If a signal does not change at all, its frequency is zero. If a signal changes instantaneously, its frequency is infinite.
• Phase describes the position of the waveform relative to time O.
• A time-domain graph plots amplitude as a function of time.
• A frequency-domain graph plots each sine wave’s peak amplitude against its frequency.
• A complete sine wave in the time domain can be represented by one single spike in
  the frequency domain.
• A single-frequency sine wave is not useful in data communications; we need to send a composite signal, a signal made of many simple sine waves.
• According to Fourier analysis, any composite signal is a combination of simple sine waves with different frequencies, amplitudes, and phases.
• The spectrum of a signal consists of the sine waves that make up the signal.
• If the composite signal is periodic, the decomposition gives a series of signals with discrete frequencies; if the composite signal is nonperiodic, the decomposition gives a combination of sine waves with continuous frequencies.
• The bandwidth of a composite signal is the difference between the highest and the lowest frequencies contained in that signal.
• Bit rate (number of bits per second) and bit interval (duration of 1 bit) are terms used to describe digital signals.
• A digital signal is a composite analog signal with an infinite bandwidth.
• Bit rate and bandwidth are proportional to each other.
• Baseband transmission of a digital signal that preserves the shape of the digital
  signal is possible only if we have a low-pass channel with an infinite or very wide bandwidth.
• Baseband transmission means sending a digital or an analog signal without modulation
  using a low-pass channel.
• Broadband transmission means modulating a digital or an analog signal using a band-pass channel.
• If the available channel is a bandpass channel, we cannot send a digital signal
  directly to the channel; we need to convert the digital signal to an analog signalbefore transmission.
• For a noiseless channel, the Nyquist bit rate formula defines the theoretical maximum bit rate. For a noisy channel, we need to use the Shannon capacity to find the maximum bit rate.
• The Shannon capacity gives us the upper limit; the Nyquist formula tells us how many signal levels we need.
• Optical signals have very high frequencies. A high frequency means a short wave length because the wave length is inversely proportional to the frequency (λ = v/f), where v is the propagation speed in the media.
• Attenuation is the loss of a signal's energy due to the resistance of the medium.
• The decibel measures the relative strength of two signals or a signal at two different points.
• Distortion is the alteration of a signal due to the differing propagation speeds of each of the frequencies that make up a signal.
• Noise is the external energy that corrupts a signal.
• The bandwidth-delay product defines the number of bits that can fill the link.
• The wavelength of a frequency is defined as the propagation speed divided by the frequency.
• If a signal does not change at all, its frequency is zero. If a signal changes instantaneously, its frequency is infinite.
• The Shannon capacity gives us the upper limit; the Nyquist formula tells us how many signal levels we need.
• The bandwidth-delay product defines the number of bits that can fill the link.

Data can be

• Analog
• Digital

Comparison of analog and digital signals

Units of period and frequency

Characteristics of a Sine Wave

• Amplitude
• Frequency
• Phase

Can Impair a Signal

• Attenuation
• Distortion
• Noise

We can evaluate transmission media by

• Throughput - a measure of how fast we can actually send data through a network. An actual measurement of how fast we can send data.
• Propagation speed - depends on the medium and on the frequency of the signal. In a vacuum, light is propagated with a speed of 3 x 10⁸ m/s. It is lower in air and  it is much lower in cable.
• Propagation time - measures the time required for a bit to travel from the source to the destination. The propagation time is calculated by dividing the distance by the propagation
  speed.

In networking, we use the term bandwidth in two contexts.

• The first, bandwidth in hertz, refers to the range of frequencies in a composite signal or the range of frequencies that a channel can pass.
• The second, bandwidth in bits per second, refers to the speed of bit transmission in a channel or link.

Formulas

• Frequency and Period

• Number of bits of each Level

• Decibel
, dB = 20 log₁₀(V₂/V₁)
• Noiseless Channel: Nyquist Bit Rate

• Noisy Channel: Shannon Capacity

• Signal-to-Noise Ratio (SNR)
SNR = Average Signla Power/Average Noise Power
SNR_db = 10log₁₀SNR

Note: You can proceed to take the multiple choice exam regarding this topic. Data and Signals - Set 1 MCQs

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credit: Behrouz A. Forouzan©2013 www.FroydWess.com

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