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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