The necessities in Random Processes

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Random Variables [edit | edit source]

Single Random Variables[edit | edit source]

  • Random Variables (A.pdf)
  • Distribution Function (A.pdf)
  • Density Function (A.pdf)
  • Gaussian Random Variables (A.pdf, B.pdf)
  • Other Distribution and Density Functions (A.pdf)
  • Conditional Distribution and Density Functions (A.pdf)


The Characteristics of a Single Random Variable[edit | edit source]

  • Expected Value (A.pdf)
  • Moments (A.pdf, B.pdf)
  • Moment Generating Functions (A.pdf)
  • Transformations of Random Variables (A.pdf)


Multiple Random Variables[edit | edit source]

  • Vector Random Variables (A.pdf)
  • Joint Distribution (A.pdf)
  • Joint Density (A.pdf)
  • Conditional Joint Distribution and Density (A.pdf)
  • Statistical Independence (A.pdf)
  • Sums of Random Variables (A.pdf)
  • Central Limit Theorem (A.pdf)


The Characteristics of Multiple Random Variables[edit | edit source]

  • Expected Values (A.pdf)
  • Joint Characteristic Functions (A.pdf)
  • Jointly Gaussian Random Variables (A.pdf)
  • Transformations of Multiple Random Variables (A.pdf)
  • Linear Transformation of Gaussian Random Variables (A.pdf)
  • Simulating Multiple Random Variables (A.pdf)
  • Sampling and Some Limit Theorem (A.pdf)
  • Complex Random Variables (A.pdf)


Random Processes [edit | edit source]

The Temporal Characteristics of Random Processes[edit | edit source]

  • Random Processes (A.pdf)
  • Joint Distribution, Independence, Processes (A.pdf)
  • Stationarity (A.pdf)
  • Example Random Processes (A.pdf)
  • Time Averages and Ergodicity (A.pdf)
  • Measurement of Correlation Functions (A.pdf)
  • Complex Random Processes (A.pdf)


The Spectral Characteristics of Random Processes[edit | edit source]

  • Power Density Spectrum - Continuous Time (A.pdf)
  • Auto Correlation Function (A.pdf)
  • Power Density Spectrum - Discrete Time (A.pdf)
  • Cross Power Density Spectrum (A.pdf)
  • Cross Correlation Function (A.pdf)
  • Noise Definitions (A.pdf)
  • Power Spectrum of Complex Random Processes (A.pdf)


Linear System with Random Inputs[edit | edit source]

  • Continuous Time LTI System (A.pdf)
  • Discrete Time LTI System (A.pdf)
  • System Response (A.pdf)
  • Spectral Characteristics (A.pdf)
  • Noise Modeling (A.pdf)


Optimum Linear System[edit | edit source]


Noise in Some Application Systems[edit | edit source]

  • AM Communication Systems (A.pdf)
  • FM Communication Systems (A.pdf)
  • Control Systems (A.pdf)
  • PLL Systems (A.pdf)
  • Random Waveforms (A.pdf)
  • Radar Systems (A.pdf)


Correlation and Power Spectra [edit | edit source]

  1. Correlation Functions of Random Signals (pdf)
  2. Spectra of Random Signals (pdf)


Ergodicity, Statistics, Estimation [edit | edit source]


Random Processes and Linear Systems [edit | edit source]



  1. Time Domain Techniques for Noisy Signals (A.pdf, B.pdf)
  2. Frequency Domain Techniques for Noisy Signals
  3. Correlation v.s. Convolution for Noisy Signals



  1. System Identification (pdf)
  2. Matched Filter [1]



go to [ Electrical_&_Computer_Engineering_Studies ]

  1. Understanding Digital Communications, See Baseband Mod/Demod Section