Signals
Signals are electric or electromagnetic
encoding of data
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Information, Data and Signals
Data - 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
Communcation
Computers 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 Time
The 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/Analo
g 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 Data
Analog 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 Signals
Some 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 Properties
Three 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 Bandwidth
Spectrum of a signal - the range of
frequencies it contains
Absolute bandwidth - the width of the
spectrum
Effective 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 Rate
Width of the spectrum of frequencies that
can be transmitted
if spectrum=300 to 3400Hz,
bandwidth=3100Hz
Greater bandwidth leads to greater costs
Limited bandwidth leads to distortion
Analog measured in Hertz, digital
measured in baud
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General Observations about
Signals
For a signal with multiple frequencies, energy
is in the first few frequency components
Increasing the bandwidth increases data rate
The transmission medium limits the
bandwidth
Greater the bandwidth, the greater the cost
For a given data rate, limiting the bandwidth,
increases distortion, and hence the error rate
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Transmission Impairments
Attenuation
Delay
Noise
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Attenuation
Loss of signal strength over distance
Use 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 Distortion
Analog signal is made up of several
frequencies
Attenuation is different for different
frequencies; Different losses at different
frequencies
More of a problem for analog signals than
digital
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Attenuation
Attenuation
– the strength of a signal falls off with
distance
Attenuation Distortion
– attenuation varies as a function of
frequency
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Attenuation is measured in
deciBels - dB
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dB Calculation
Example
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 Distortion
The 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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Noise
What is Noise?
Any unwanted signal
Types of Noise
Thermal
Intermodulation
Impulse
Crosstalk
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Thermal Noise
Thermal 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 Noise
Inter-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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Noise
Crosstalk
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 Media
Free-Space loss
Signal disperses with distance
Atmospheric 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 Media
Multipath
Receive multiple signals reflected by many
obstacles
Refraction
Radio waves get bent by change in speed with
altitude
Thermal Noise
White noise. Important factor for satellite
communications
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Channel Capacity
The 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 Law
Considers 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/N
Signal to Noise ratio: power in signal to power
contained in noise
Doubling the bandwidth doubles the data rate
At a given noise level, higher the data rate, the
higher the error rate
Increasing signal strength increases
intermodulation noise
Wider the bandwidth, the more noise is admitted.
As W increases, S/N decreases
Goal: Get highest data rate with lowest error rate
at cheapest cost
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Example with S/N of 1000 for
Telephone LIne
Example 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 Limit
Nyquist limit (in a noise-free environment)
C = 2 W log2M
Given a bandwidth of W, highest signal rate
that can be carried is 2W with binary
signaling (M=2)
For multilevel signaling
C = 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. Baud
BPS=bits per second
Baud= Number of signal changes per
second
Each 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 Transmission
Analog signal transmitted without regard to
content
May be analog or digital data
Attenuated over distance
Use amplifiers to boost signal
Also amplifies noise
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Digital Transmission
Concerned with content
Integrity endangered by noise, attenuation
etc.
Repeaters are used
Repeater receives signal
Extracts bit pattern
Retransmits
Attenuation is overcome
Noise is not amplified
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Use of Repeaters
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Which Signal/Data is Better
Analog or Digital?
Digital is better
Even Analog data can be converted into
digital data and transmitted as digital data
Digital 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
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