Lecture 14 Random Signals and Noise (I)

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Lecture 14Random Signals and Noise (I)

• Fall 2008
• NCTU EE
• Tzu-Hsien Sang

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Outline

• Terminology of Random Processes
• Correlation and Power Spectral Density
• Linear Systems and Random Processes
• Narrowband Noise

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Random Processes

• Informal Definition The outcomes ( events ) of a
  chance experiment are mapped into functions of
  time ( waveforms ).
• Cf. Random variables outcomes are mapped into
  numbers.
• Note Each waveform is called a sample function,
  or a realization. The totality of all sample
  functions is called an ensemble.
• Q Lets try to build an axiomatic theory. What
  will you do?

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• Wide-sense stationary (WSS)
• It is extremely difficult to verify whether a
  random process is stationary or not. For
  practical purposes, often WSS is good enough.
• A random process X(t) is wide-sense stationary
  if
• EX(t) constant, and
• EX(t)X(t?) RX(?) function of ? only.
• Remarks (i) strict-sense stationary ?
  wide-sense stationary
• (ii) For Gaussian random processes, WSS
  strict-sense stationary
• ( A Gaussian process has only two parameters
  mean and covariance )

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