Thursday, 27 October 2011

Attenuation of Digital Signals

Signal strength falls off with distance
• Depends on medium
• Received signal strength:
— must be enough to be detected
— must be sufficiently higher than noise to be received
without error
• Attenuation is an increasing function of
Delay Distortion

• Only in guided media
• Propagation velocity varies with frequency

• Additional signals inserted between transmitter
and receiver
• Thermal
— Due to thermal agitation of electrons
— Uniformly distributed
— White noise
• Intermodulation
— Signals that are the sum and difference of original
frequencies sharing a medium

• Crosstalk
— A signal from one line is picked up by another
• Impulse
— Irregular pulses or spikes
— e.g. External electromagnetic interference
— Short duration
— High amplitude
Channel Capacity
Data rate

In bits per second, bps (not Bps)
— Rate at which data can be communicated

— In cycles per second of Hertz, Hz
— Constrained by transmitter and medium
• Convention: not all k’s are equal
— data rates are given as power of 10
• e.g., kHz is 1000Hz
— data is given in terms of power of 2
• e.g., KByte is 1024 Bytes

Nyquist Bandwidth

• If rate of signal transmission is 2B
then a signal with frequencies no
greater than B is sufficient to carry
the signal rate.
— Why? Assume we have a square wave
of repeating 101010. If a positive pulse
is a 1 and a negative pulse is 0, then
each pulse lasts 1/2 T1 (T1 = 1/f1) and
the data rate is 2f1 bits per second.

• If we limit the components to a maximum
frequency (restrict the bandwidth) we need to
make sure the signal is accurately represented.
• Based on the accuracy we require, the
bandwidth can carry a particular data rate. The
theoretical maximum communication limit is
given by the Nyquist formula:
C= 2B log2M
C = capacity or data transfer rate in bps
B = bandwidth (in hertz)
M = number of possible signaling levels
Signal Strength

— An important parameter in communication is the strength
of the signal transmitted. Even more important is the
strength being received.
— As signal propagates it will be attenuated (decreased)
— Amplifiers are inserted to increase signal strength
— Gains, losses and relative levels of signals are expressed in
• This is a logarithmic scale, but strength usually falls logarithmically
• Calculation of gains and losses involves simple addition and
Delay Distortion

— Different frequency components of a signal
• are attenuated differently, and
• travel at different speeds through guided
— This may lead to delay distortion
Shannon capacity

— A transmission line may experience interference
from a number of sources, called noise. Noise is
measured in terms of signal to noise power ratio,
expressed in decibels:

Cross Talk

— near-end crosstalk (NEXT), cross talk of strong
transmit (output) signal to weak receive (input)
— adaptive NEXT canceling using op-amp


• Impulse Noise
— impulse caused by switching, lightning etc.
• Thermal Noise
— present irrespective of any external effects
— caused by thermal agitation of electrons

• White Noise
random noise – entire spectrum
— listen:
• Pink Noise
— “realistic spectrum”
— the power spectral density is inversely proportional
to the frequency
— listen:


CS 420/520

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