(GRAC)Networking - Chapter 3
Discrete
(Applicable to digital signals) The signal abruptly changing levels
Period
(T) Amount of time it takes for one repitition T = 1 / f
Crosstalk
(when you're on phone and can hear another conversation) Is an unwanted coupling between signal paths Is typically of the same order of magnitude as thermal noise
Decibel (dB)
...
Duration of a pulse
1 / 2f So data rate is 2f bits per second (bps)
DC component
A component of zero frequency With no dc component, a signal has an average amplitude of 0 With a dc component, a signal has a frequency term at f = 0, and a nonzero average amplitude
Text
A familiar example of digital data. Convenient for humans but, in character form, can't be stored or transmitted by data processing and communication systems since they are designed for binary data
Point-to-point link
A guided transmission medium is point to point if it provides a direct link between two devices and they are the only two devices sharing the medium.
Aperiodic
A signal is aperiodic if it does not satisfy the equation s(t + T) = s(t), -infinity < t < infinity where constant T is the period of the signal
Interlacing
A technique to provide a flicker-free image without increasing the bandwidth requirement Odd numbered scan lines and even numbered scan lines are scanned separately, with odd and even fields alternating on successive scans
White noise
Also thermal noise - since it is uniformly distributed across the bandwidths typically used in communications systems
Relationship between data rate and bandwidth
Although a given waveform may contain frequencies over a very broad range, as a practical matter any transmission system (transmitter + receiver + medium) will be able to accomodate only a limited range of frequencies This limits the data rate that can be carried on the transmission medium Direct relationship - the higher the data rate of a signal, the greater is its effective bandwidth The greater the bandwidth of a transmission system, the higher is the data rate that can be transmitted over the system Figures 3.4, 3.7
Digital transmission
Assumes binary content to the signal - a digital signal can be transmitted only to a limited distance before attenuation, noise, and other impairments endanger the integrity of the data. To achieve greater distances, repeaters are used - which receives the digital signal, recovers the pattern of 1s and 0s, and retransmits a new signal (attenuation is overcome) Reasons for digital transmission over analog transmission: digital technology, data integrity, capacity utilization, security and privacy, and integration
Transmission impairments
Attenuation and attenuation distortion Delay distortion Noise
Attenuation distortion
Attenuation is greater at higher frequencies Particularly noticable for analog signals Since attenuation is different for different frequencies and the signal is made up of a number of components at different frequencies, the received signal is not only reduced in strength but also distorted Presents less of a problem with digital signals
Full duplex
Both stations may transmit simultaneously (two lane highway, going both directions) Medium is carrying signals in both directions at the same time
Half duplex
Both stations may transmit, but only one at a time (one lane highway, going both directions?)
Observations from Shannon's Capacity
C = Blog(base 2)(1 + SNR) For a given level of noise, it would appear that the data rate could be increased by increasing signal strength or bandwidth. But, as the signal strength increases, the effect of nonlinearities increase, leading to an increase in intermodulation noise. Since noise is assumed to be white, the wider the bandwidth, the more noise is admitted to the system. So, as B increases, SNR decreases
Nyquist bandwidth
Case of a channel that is noise free Limitation on data rate is simply the bandwidth of the signal - If the rate of signal transmission is 2B, then a signal with frequencies no greater than B is is sufficient to carry the signal rate - Converse is also true: Given a bandwidth of B, the highest signal rate that can be carried is 2B. (this limitation is due to the effect of intersymbol interference, such as is produced by delay distortion). If the signals to be transmitted are binary (2 voltage levels) then the data rate that can be supported by B Hz is 2B bps. Since signals with more than 2 levels can be used, each signal element can represent more than 1 bit. (if 4 possible voltage levels are used as signals, then each signal element can represent 2 bits) C = 2Blog(base2)M where M = the number of discrete signal or voltage levels
Codec
Coder-decoder How analog data can be represented by digital signals Takes an analog signal that directly represents the voice data and approximates that signal by a bit stream At the receiving end, the bit stream is used to reconstruct the analog data
IRA
Codes devised to represent characters as a sequence of bits International Reference Alphabet Each character in the code is represented by a unique 7-bit pattern IRA-encoded characters are almost always stored and transmitted using 8 bits per character - eighth bit is a parity bit used for error detection
Transmission
Communication of the data by the propagation and processing of signals
Digital signaling vs. analog signaling
Digital signaling is cheaper than analog signaling and less susceptible to noise interference But digital signals suffer more from attenuation than do analog signals
Thermal noise
Due to the thermal agitation of electrons and is present in all electronic devices and transmission media and is a function of temperature Uniformly distributed across the bandwidths typically used in communications sytems and is referred to as white noise Cannot be eliminated and places an upper bound on communications system performance
Harmonic frequency
Each multiple of the fundamental frequency
Data
Entities that convey meaning, or information
Conclusions from Nyquist bandwidth
For a given bandwidth, the data rate can be increased by increasing the number of different signal elements. But this places an increased burden on the receiver: instead of distinguishing one of two possible signal elements during each signal time, it must distinguish one of M possible signal elements. Noise and other impairments on the transmission line will limit the practical value of M. Indicates that doubling the bandwidth doubles the data rate
Noise
For any data transmission event - additional unwanted signals that are inserted somewhere between transmission and reception. Is the major limiting factor in comunications systems performance and can be divided into four categories: Thermal noise, intermodulation noise, crosstalk, impulse noise
Frequency v. Period
Frequency is how often something happens Period is the time is takes something to happen
Binary data
Generated by terminals, computers, and other data processing equipment and then converted into digital voltage pulses for transmission
How are data rate, bandwidth, noise, and error rate related?
Greater the bandwidth, the greater the cost but all transmission channels of any practical interest are of limited bandwidth. The limitations arise from the physical properties of the transmission medium or from deliberate limitations at the transmitter on the bandwidth to prevent interference from other sources. So we want to make as efficient use as possible of a given bandwidth. For digital data, this means we want to get as high a data rate as possible at a particular limit of error rate for a given bandwidth. The main constraint on achieving this is noise The presence of noise can corrupt 1 or more bits. If the data rate is increased, then the bits become "shorter" so that more bits are affected by a given pattern of noise (look at figure 3.16) - If the data rate is increased, the more bits will occur during the interval of a noise spike, and more errors will occur The higher the data rate, the more damage that unwanted noise can do.
Impulse noise
Is annoying because it's the only type of noise that's not reasonably predictable and can have systems built to cope with it Is noncontinuous and consists of irregular pulses or noise spikes of short duration and of relatively high amplitude Generated from a variety of causes, like lightning, external electromagnetic disturbances, and faults and flaws in the communications system Only a minor annoyance for analog data but is the primary source of error in digital data communication
Frequency domain
Looking at signals in terms of frequency is better than looking at them in terms of time Since any electromagnetic signal can be shown to consist of a collection of sine waves at different amplitudes, frequencies, and phases For each signal, there is a frequency domain function S(f) that specifies the peak amplitude of the constituent frequencies of the signal
Intersymbol interference
Major limitation to maximum bit rate over a transmission channel Happens when some of the signal components of 1 bit position will spill over into other bit positions - happens because of delay distortion
Shannon's Capacity
Maximum channel capacity = C = Blog(base 2)(1 + SNR) C = capacity of the channel in bits per second B is the bandwidth of the channel in hertz Referred to as error-free capacity Represents the theoretical maximum that can be achieved, but in practice only much lower rates are achieved since formula assumes white noise but not impulse noise, attenuation distortion, and delay distortion
Channel capacity
Maximum rate at which data can be transmitted over a given communication path, or channel, under given conditions
Peak amplitude
Maximum value or strength of the signal over time Typically this is measured in volts
Analog transmission
Means of transmitting analog signals without regard to their content: signals may represent analog data or digital data. Either case, analog signal will attenuate after a certain distance. Fix this by introducing amplifiers that boost the energy in the signal. More of a problem for digital data than analog data
Phase
Measure of the relative position in time within a single period of a signal For a periodic signal f(t), phase is the fractional part t/T of the period T through which t has advanced relative to an arbitrary origin
Modem
Modulator/demodulator How digital data can be represented by analog signals Converts a series of binary voltage pulses into an analog signal by decoding the digital data onto a carrier frequency. The resulting signal occupies a certain spectrum of frequency centered about the carrier and may be propagated across a medium suitable for the carrier At the other end of the line, another modem demodulates the signal to recover the original data
Multipoint link
More than two devices share the same medium
Bandwidth
Mostly known as effective bandwidth The narrow band of frequencies that contains most of the energy of the signal Greater the bandwidth transmitted, the greater the cost But limiting the bandwidth creates distortions - the more limited the bandwidth, the greater the distortion, and the greater the potential for error by the receiver Greater the bandwidth of a signal, the more faithfully it approximates a digital pulse stream Infinite bandwidth - square wave (has frequency component and infinite other components) Less bandwidth - wave that approximates square wave (has frequency component and two harmonic components) Figure 3.8 on page 74, and Figure 3.7 on page 72
Data transmission
Occurs between transmitter and receiver over some transmission medium
Fundamental frequency
One big frequency that is a combination of littler frequencies Period of the total signal is equal to the period of the fundamental frequency
3 parameters of sine wave
Peak amplitude Frequency Phase
Delay distortion
Phenomenom that occurs in transmission cables and doesn't occur when signals are transmitted through the air by means of antennas Caused by the fact that the velocity of propagation of a signal through a cable is different for different frequencies. For a signal with a given bandwidth, the velocity tends to be highest near the center frequency of the signal and to fall off toward the two edges of the band. Various components of a signal will arrive at the receiver at different times Received signal is distorted due to varying delays experienced at its constituent frequencies
Signaling
Physical propagation of the signal along a suitable medium
Spectrum
Range of frequencies that a signal contains
Frequency
Rate (in cycles per hertz) at which the signal repeats
Eb/No
Ratio of signal energy per bit to noise power density per hertz Eb/No = (S/R)/No = S/(kTR) where S = signal power, Tb is the time required to send 1 bit, R = data rate (1 / Tb) Eb = energy per bit in a signal = S*Tb As bit rate R increases, the transmitting signal power relative to noise (S) must increase to maintain the Eb/N0 Important since bit error rate for digital data is a (decreasing) function of this ratio Related to SNR but more convenient for determining digital data rates and error rates. Its advantage over SNR is that the latter quantity depends on bandwidth Standard quality measure for digital communication system performance
Signal-to-noise ratio (SNR)
Ratio of the power in a signal to the power contained in the noise that is present at a particular point in the transmission Typically measured at the receiver because it is at that point that an attempt is made to process the signal and recover the data. Reported in decibels SNR(sub dB) = 10log(base 10)(signal power / noise power) Expresses the amount, in decibels, that the intended signal exceeds the noise level. A high SNR means a high-quality signal and a low number of required intermediate repeaters For a given level of noise, we would expect that a greater signal strength would improve the ability to receive data correctly in the presence of noise
Attenuation
Reduction of signal strength Can lead rather quickly to the loss of the information contained in the propagated signal This reduction in strength is generally exponential (for guided media) and is typically expressed as a constant number of decibels per unit distance For unguided media, attenuation is a more complex function of distance and the makeup of the atmosphere N = -10log(base10)(P(sub)f/P(sub)1000)
Effective bandwidth
Relatively narrow band of frequencies that the energy of a signal is contained in Band within most of the signal energy is concentrated
Why is SNR important in the transmission of digital data?
Sets the upper bound on the achievable data rate
Analog signal
Signal intensity varies in a smooth, continuous fashion over time Continuously varying electromagnetic wave that may be propagated over a variety of media
Simplex
Signals are transmitted only in one direction; one station is transmitter, the other is receiver (one way road)
Periodic signal
Simplest form of a signal - same signal patterns repeats over time Periodic if it satisfies the equation: s(t + T) = s(t), -infinity < t < infinity where constant T is the period of the signal
Center frequency
Some frequency that the bandwidth of a signal is centered around The higher the central frequency, the higher the potential bandwidth and therefore the higher the potential data rate
Why does an increase in data rate increase the error rate?
Sometimes, noise is sufficient to alter a single bit. If data rate were doubled, the bits would be more tightly packed together, and the same passage of noise might destroy 2 bits.
Analog data
Take on continuous values in some interval (video and voice are continuously varying patterns of intensity) Most data collected by sensors, like temperature and pressure, are continuous valued Function of time and occupy a limited frequency spectrum (such data can be represented by an electromagnetic signal occupying the same spectrum)
Digital data
Take on discrete values - text and integers
Digital signal
The signal intensity maintains a constant level for some period of time and then abruptly changes to another constant level, in a discrete fashion Any digital waveform will have infinite bandwidth Sequence of voltage pulses that may be transmitted over a wire medium
Period
Time it takes to make one complete cycle Period = 1 / frequency
Direct link
Transmission path between two devices in which signals propagate directly from transmitter to receiver with no intermediate devices, other than amplifiers or repeaters used to increase signal strength.
Signal
Used to transmit data Generated by the transmitter and is transmitted over a medium Is a function of time, but can also be expressed as a function of frequency (consists of components of different frequencies) Electric or electromagnetic representations of data
Time domain
Viewing a signal as a function of time
Wavelength
Wavelength of a signal is the distance occupied by a single cycle Distance between two points of corresponding phase of two consecutive cycles Wavelength = v * T where signal is traveling with velocity v T is period
Guided media
Waves are guided along a physical path Examples: twisted pair, coaxial cable, optical fiber
Intermodulation noise
When signals at different frequencies share the same transmission medium Effect is to produce signals at a frequency that is the sum or difference of the two original frequencies or multiples of those frequencies Produced by nonlinearities in the transmitter, receiver, and/or intervening transmission medium. Ideally they behave as linear systems but they don't. Excessive nonlinearity can be caused by component malfunction or overload from excessive signal strength - it's under these circumstances that the sum and difference frequency terms occur
Absolute bandwidth
Width of the spectrum of a signal Many signals have an infinite bandwidth
Unguided media
Wireless Provides a means for transmitting electromagnetic waves but do not guide them
Sinusoid
s(t) = A sin(2*pi*f*t + theta) By adding together enough sinusoid signals, each with the appropriate amplitude, frequency, and phase, any electromagnetic signal can be constructed
