1 signals signals are electric or electromagnetic encoding of data
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Signals
Signals are electric or electromagnetic encoding of data
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Information, Data and SignalsData - A representation of facts,
concepts, or instructions in a formalized manner suitable for communication, interpretation, or processing by human beings or by automatic means
Information - The meaning that is currently assigned to data by means of the conventions applied to those data
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Information, Data and Signals
Information Data Signal
001011101
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Computers Use Signals for CommuncationComputers transmit data using digital
signals, sequences of specified voltage levels. Graphically they are often represented as a square wave.
Computers sometimes communicate over telephone line using analog signals, which are formed by continuously varying voltage levels.
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Signal = Function of TimeThe signal is a function of time.
Horizontal axis represents time and the vertical axis represents the voltage level.
Signal represents data OR Data is encoded by means of a signal
Signal is what travels on a communication medium
An understanding of signals is required so that suitable signal may be chosen to represent data
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Continuous and Discrete Signal
Continuous or Analog signals take on all possible values of amplitude
Digital or Discrete Signals take on finite set of voltage levels
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Analog and Digital Signal
Continuous/Analog signals take on all possible values of amplitude
Digital or Discrete Signals take on finite set of voltage levels
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Analog and Digital DataAnalog data take on all possible
values. Voice and video are continuously varying patterns of intensity
Digital data take on finite (countable) number of values. Example, ASCII characters, integers
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Periodic SignalsSome signals repeat themselves over
fixed intervals of time. Such signals are said to be periodic
A signal s(t) is periodic if and only if:s(t+T) = s(t) - < t < +
where the constant T is the periodic of the signal, otherwise a signal is aperiodic (or non- periodic).
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Periodic Signal PropertiesThree important characteristics of a
periodic signal are : Amplitude (A): the instantaneous value of a
signal at any time measured in volts. Frequency (f): the number of repetitions of
the period per second or the inverse of the period; it is expressed in cycles per second or Hertz (Hz). T=1/f
Phase (): a measure of the relative position in time within a single period of a signal, measured in degrees
Wavelength (): distance occupied by a signal in one period
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Spectrum and BandwidthSpectrum of a signal - the range of
frequencies it containsAbsolute bandwidth - the width of the
spectrumEffective bandwidth or just bandwidth
- the band of frequencies which contains most of the energy of the signal - half-power bandwidth
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Bandwidth and Data RateWidth of the spectrum of frequencies
that can be transmittedif spectrum=300 to 3400Hz,
bandwidth=3100HzGreater bandwidth leads to greater
costsLimited bandwidth leads to distortionAnalog measured in Hertz, digital
measured in baud
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General Observations about SignalsFor a signal with multiple frequencies, energy is
in the first few frequency componentsIncreasing the bandwidth increases data rateThe transmission medium limits the bandwidthGreater the bandwidth, the greater the costFor a given data rate, limiting the bandwidth,
increases distortion, and hence the error rate
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Transmission ImpairmentsAttenuationDelayNoise
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AttenuationLoss of signal strength over distanceUse of amplifiers to boost analog
signals; entire signal (including noise or distortion) is amplified
Use of repeaters for digital data; data recovered and then transmitted
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Attenuation DistortionAnalog signal is made up of several
frequenciesAttenuation is different for different
frequencies; Different losses at different frequencies
More of a problem for analog signals than digital
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AttenuationAttenuation– the strength of a signal falls off with
distanceAttenuation Distortion – attenuation varies as a function of
frequency
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Attenuation is measured in deciBels - dB
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dB CalculationExample
Input power is 1 Watt Output power is 1 mW dB Attenuation is 10 * log (1 W/1 mW) = 10 * (3) = 30 dB
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Use of Repeaters
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Delay DistortionThe velocity of propagation of a signal
through a guided medium varies with frequency.
Different frequency components travel at different speeds therefore arrive at a destination at different times.
Particularly critical for digital data because bits may spill over causing Inter-Symbol Interference.
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Transmission Impairments Visually
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NoiseWhat is Noise?
Any unwanted signalTypes of Noise
Thermal Intermodulation Impulse Crosstalk
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Thermal NoiseThermal noise, white noise
Due to random motion of atoms N = kTW k = Boltzman Constant (1.381 X 10-23 J/K) T = Absolute Temperature (Kelvin) W = Bandwidth (Hz) Why is it called White Noise?
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Inter-modulation NoiseInter-modulation noise
when two signals at different frequencies are mixed in the same medium, sum or difference of original frequencies or multiples of those frequencies can be produced, which can interfere with the intended signal - occurs when there is some non-linearity in the system
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NoiseCrosstalk
when there is an unwanted coupling between signal paths. For example some times talking on the telephone you can hear another conversation.
Impulse noise Due to lightning or some other random
transient phenomenon
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Effect of Noise
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Transmission Impairments in Un-Guided MediaFree-Space loss
Signal disperses with distanceAtmospheric Absorption
Attenuation caused by water vapor and oxygen
Water vapor: High around 22 GHz, less around 15 GHz
Oxygen: High around 60 GHz, less below 30 GHz
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Transmission Impairments in Un-Guided MediaMultipath
Receive multiple signals reflected by many obstacles
Refraction Radio waves get bent by change in speed
with altitudeThermal Noise
White noise. Important factor for satellite communications
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Channel CapacityThe rate at which digital data can be
transmitted over a given communication channel
Two formulations Shannon’s Formulation Nyquist Formulation
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Shannon’s LawConsiders the noise (only white noise)Key parameter is signal-to-noise ratio
(S/N, or SNR), which is the ratio of the power in a signal to the power contained in the noise, typically measured at the receiver - often expressed in decibels
Maximum theoretical error-free capacity in bits per second
C = W log2 (1+S/N)
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Signal to Noise Ratio - S/NSignal to Noise ratio: power in signal to power
contained in noiseDoubling the bandwidth doubles the data rateAt a given noise level, higher the data rate, the
higher the error rateIncreasing signal strength increases intermodulation
noiseWider the bandwidth, the more noise is admitted.As W increases, S/N decreasesGoal: Get highest data rate with lowest error rate at
cheapest cost
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Example with S/N of 1000 for Telephone LIneExample for voice-grade telephone line:Using Shannon's formulation for channel
capacity: C = W * log2(1 + S/N) Where log2 represent logarithm base 2 30 dB S/N = 1000 S/N C = 3100 * log2(1 + 1000) C = 30,894 bps
Hence the channel capacity is 30,894 bits per second.
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Nyquist LimitNyquist limit (in a noise-free environment)C = 2 W log2MGiven a bandwidth of W, highest signal
rate that can be carried is 2W with binary signaling (M=2)
For multilevel signalingC = 2W log2M
where M is the number of discrete signals or voltage levels
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Example with M-ary Signaling with 3100 Hz Bandwidth C = 2 W log2M
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BPS vs. BaudBPS=bits per secondBaud= Number of signal changes per
secondEach signal change can represent
more than one bit, through variations on amplitude, frequency, and/or phase
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Why Study Analog?Telephone system is primarily analog
rather than digital (designed to carry voice signals)
Low-cost, ubiquitous transmission medium
If we can convert digital information (1s and 0s) to analog form (audible tone), it can be transmitted inexpensively
Media are inherently analog too, real world is analog
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Analog TransmissionAnalog signal transmitted without
regard to contentMay be analog or digital dataAttenuated over distance Use amplifiers to boost signalAlso amplifies noise
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Digital TransmissionConcerned with contentIntegrity endangered by noise,
attenuation etc.Repeaters are usedRepeater receives signalExtracts bit patternRetransmitsAttenuation is overcomeNoise is not amplified
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Use of Repeaters
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Which Signal/Data is Better Analog or Digital?Digital is betterEven Analog data can be converted into
digital data and transmitted as digital dataDigital data provide the following
advantages: Digital technology Data integrity through EDC and ECC Capacity utilization through TDM Security and privacy through encryption Integration of all forms of information