EE 551451, Fall, 2006 Communication Systems

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EE 551/451, Fall, 2006Communication Systems

• Zhu Han
• Department of Electrical and Computer Engineering
• Class 3
• Aug. 29th, 2006

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Signal Distortion during Transmission

• Chapter 3.4
• Equations
• Examples
• Addition AWGN, receiver noise
• Scalar antenna, channel loss, satellite
  transponder (nonlinear)
• Scaling A/D D/A
• Time shift delay
• Frequency shift Doppler (movement)
• Time differentiation RL circuit
• Time integration RC circuit
• Phase

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Distortionless Transmission

• Definition y(t)kg(t-?), Y(w)kG(w)exp(-jw?)
• Graphs example for time and frequency
• Phase distortionless or amplitude distortionless
• Examples PSK and ASK with their decision regions
• Human ears only need amplitude distortionless
• Video transmission needs phase distortionless

x(t)
Kx(t-t)
h(t)Kd(t-t)
X(f)
Kej2pftX(f)
H(f)Kej2pft
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LTI channel

• Linear time invariant channel
• Linearity means that the relationship between the
  input and the output of the system satisfies the
  scaling and superposition properties.
• Time invariance means that whether we apply an
  input to the system now or T seconds from now,
  the output will be identical, except for a time
  delay of the T seconds. More specifically, an
  input affected by a time delay should effect a
  corresponding time delay in the output, hence
  time-invariant.
• Example 3.17

h(t)
d(t)
LTI System
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Nonlinear Distortion

• Cannot write convolution in time and multiply in
  frequency
• Most system is nonlinear
• Design issue is to transmit the signal in the
  linear range.
• Examples of 3.18

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Energy Spectrum Density

• Parsevals Theorem
• Energy Spectrum Density/Power Spectrum Density
• How much energy in any narrow band of the
  spectrum
• Definition G(w)2, matlab psd
• Essential bandwidth of the signal example 3.20
• Energy of modulated signals
• Examples page 120
• Base band energy divided by half to the modulated
  band.
• Time autocorrelation function
• Computation, definition
• Relation with ESD
• Relation of ESD between input, output and system

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Multipath and Fading

• Multipath causes frequency response fluctuation
• Matlab example (psd)
• Impulse function flat Multipath
• Math g(t-c) lt-gt G(w)exp(-jw?)
• Propagation loss G(D)-a, a2 to 6.
• Slow fading (shadowing)
• FM radio on the highway.
• Fast fading
• Definition fdvcos?/?
• Doppler shifting cause time variance, frequency
  and phase changes

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Filters

• Ideal filter definition
• Low pass, high pass, bandpass
• Non-causal, infinite length of responses in time
  domain
• Practical filters
• Butterworth filter - no gain ripple in pass band
  and stop band, slow cutoff
• Chebyshev filter(Type I) - no gain ripple in stop
  band, moderate cutoff
• Chebyshev filter(Type II) - no gain ripple in
  pass band, moderate cutoff
• Elliptic filter - gain ripple in pass and stop
  band, fast cutoff
• Digital filter structure linear 1a1z-1a2z-2,
  , feedback
• Equalizer con. Enhance noise

Equalizer
Channel
N(f)
H(f)
X(f)
X(f)N(f)/H(f)
1/H(f)

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Filters

• Examples
• Tradeoff ripples in passband and stopband,
  cutoff

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Usage of Matlab

• Signal Processing Toolbox
• fdatool
• Examples
• Homework
• Sampling fs22.05KHz (44.1KHz CD) by source
  recoder
• wavread to read it
• fdatool lowpass, butterworth, order 5, reduce
  Fc, generate M file
• filter
• psd, legend, change the color and format of the
  lines, title, x,ylabel
• sound
• wavwrite

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Homework

• Due Sep 11th.
• 3.5-3
• 3.6-1
• 3.6-2
• 3.8-2
• Matlab
• Use source recorder, My name is ., save
  first_family.wav
• Filter by 5000KHZ, 2000KHz, 1000Hz, and the
  minimal that you can understand.
• Plot power spectrum density of input signal,
  filter, and the output signals.
• Save the files with name first_family_Fs.wav and
  save filter files.
• Print the figures and send me the wav and filter
  files.

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Questions?