Chapter 4 Signals

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Chapter 4Signals

• Analog and digital
• Aperiodic and periodic signals
• Analog signals

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Signals

• Major distinction analog versus digital.
• Analog information is continuous and has infinite
  number of values. (Sinusoidal voltage )
• Digital information is discrete and has limited
  number of values (digital display,
• 0 or 1 for binary)

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Analog signals

• Signal may be periodic (continuously repeated
  pattern - like sine wave) or aperiodic.
• Periodic signal characterized by
• Amplitude value at any instant of time 
• Frequency f number of cycles per unit time 
• Period T amount of time of one cycle (1/f ) 
• Phase position of waveform relative to time
  zero.

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Digital Signals

• Also characterized by Amplitude, Period and
  Phase.
• Represented by square waves.
• Binary 1 and 0 can be represented by positive
  and negative voltages

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Figure 4-1
Transformation of Information to Signals
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Figure 4-3
Analog and Digital Signals
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Periodic Signals
Figure 4-4
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Periodic and Aperiodic Signals

• Periodic signals consists of continuously pattern
• Sine wave is the simplest periodic signal
• Aperiodic signal has no repetitive pattern
• Any aperiodic signal can be decomposed into an
  infinite number of periodic signals (Fourier
  transform)

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Figure 4-5
Aperiodic Signals
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Figure 4-6
Sine Wave
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Phases
Figure 4-7
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Figure 4-8
Amplitude Change
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Figure 4-9
Frequency Change
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Figure 4-10
Phase Change
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Figure 4-11
Time and Frequency Domain
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Time and Frequency Domain

• Time domain graphs Time on X-AXIS, Amplitude on
  Y-AXIS
• Frequency domain graphs Frequency on X-AXIS,
  Amplitude on Y-AXIS
• Frequency expressed in harmonics
• Translate between these domains using Fourier
  analysis

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Examples
Figure 4-12
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Signal with DC Component
Figure 4-13
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Figure 4-14
Complex Waveform
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Complex Signal I

• Harmonics multiple of "fundamental frequency"
• Frequency domain shows harmonic components of
  complex analog signal
• Complex signal is composition of sine waves, each
  having different harmonic and amplitude
  (specified through Fourier Analysis).
• As number of harmonics increases, the
  approximation of original signal improves.

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Complex Signal II

• As number of harmonics decreases, it becomes more
  difficult to accurately represent and recognize
  the signal.
• Bandwidth the range of frequencies (spectrum)
  the signal occupies
• BW fhigh - flow
• Frequency spectrum the combination of all sine
  wave signals that make up that signal

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Figure 4-15
Bandwidth
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Figure 4-16
Digital Signal
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Digital Signals

• Level 1 may be encoded as positive voltage and
  0 as zero voltage
• Bit Interval Time required to send one single
  bit
• Bit rate number of bit intervals per second
• or the number of bits sent in one second
• Bit rate is the inverse of bit intervals

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Figure 4-17
Amplitude, Period, and Phase for a Digital Signal
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Figure 4-18
Bit Rate and Bit Interval
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Figure 4-19
Harmonics of a Digital Signal
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Decomposition of Digital signal

• A digital signal can be decomposed into infinite
  number of sine waves (harmonics)
• Harmonics have different amplitude, frequency and
  phase.
• To receive an exact replica of digital signal all
  frequencies must be faithfully transferred
  through the medium.
• In practice only the significant amplitudes are
  sufficient for reasonable accuracy

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Figure 4-20
Exact and Significant Spectrums
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Figure 4-21
Bit Rates and Significant Spectrums
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Figure 4-22
Corruption Due to Insufficient Bandwidth
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Figure 4-23
Bandwidth and Data Rate
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Figure 4-24
Example
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Channel Capacity

• Channel Capacity The theoretical maximum
  information (data) rate of a transmission
  channel.
• Nyquist Theorem
  
• The rate at which digital data can be transmitted
  over a given communication channel, in a
  noise-free environment, is
• C 2 W log2M
• Nyquist, 1920
• (log2M log10M/ log102 log M/ 0.301)

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Channel Capacity - Nyquist
2-Level coding C 2 W X 1
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Multilevel Coding
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Voice Channel BW 300 Hz to 3.4 kHz
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Channel Capacity-Shannon

• Shannons law (considers the noise)
• C maximum capacity (bit/sec) in a channel
• W Bandwidth (Hz)
• (S/N) ratio (absolute) of signal to noise power

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Channel Capacity-Shannon

• key parameter is signal-to-noise ratio (S/N)
  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
• (S/N)dB 10 log (S/N)

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Performance

• Throughput
• Number of bits that can pass through the medium
  in one second (ex. a modem sends 56 kbps to the
  line)
• Propagation speed
• Distance a signal can travel through a medium in
  one second (ex. Light in vacuum 3x108 m/s but
  light in optical fiber 2x108m/s)
• Propagation time
• Time required for a signal (or a bit) to travel
  between two points of the medium
• tp Distance / Speed

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Transmission Impairments

• Signal corruption during transmission
• Signal received may differ from signal
  transmitted
• Analog - degradation of signal quality
• Digital - bit errors
• Caused by
• Attenuation and attenuation distortion
• Delay distortion
• Noise

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Attenuation

• 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
  frequency

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Signal Strength- Gain-Loss (1)
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Signal Strength- Gain-Loss (2)
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dBm

• dBm represents the power level of a signal with
  reference to 1mW
• e.g. 10mW expressed in dBm
  10 log(10mW/1mmW) 10 log10 10dBm
• 1mW 0dBm
• 10 mW 10dBm
• 1W 30dBm
• 1?W -30dBm ( 10 log (0.001mW/1mW)10x(-3)
• 1nW -60dBm
• 2mW 10log(2/1) 3dBm
• 4mW 6dBm
• 0.5 mW -3dBm

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Delay distortion

• Only in guided media
• the velocity of propagation of a signal through a
  guided medium varies with frequency

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Noise (1)

• Additional signals inserted between transmitter
  and receiver
• Thermal Noise
• Due to thermal agitation of electrons
• Uniformly distributed
• White noise
• Inter-modulation
• 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

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Noise (2)

• Crosstalk
• A signal from one line is picked up by another
  ( an unwanted coupling between signal paths)
• Impulse
• Irregular pulses or spikes
• e.g. External electromagnetic interference
• Short duration
• High amplitude

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Figure 7-6
Effect of Noise on Parallel Lines
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Figure 7-7
Noise on Twisted-Pair Lines
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Impulse noise is the primary source of error for
digital data. A sharp spike of energy of 0.01
seconds duration would not destroy any voice
data, but would wash out many bits of digital
data.
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Transmission Impairments