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Variable + Random Variable + Random Process

  1. Variable:
  2. Random Variable: is a variable described by a probability density function (PDF)
  3. Random Process: is a function of time t. The function value is a random variable described by a PDF.

  • Random Variable: key features
    Expectation value: E(x)
    Variance: Var(x)
    Covariance: Var(x,y)
  • Random Process: key features
    Expectation value: E[x(t)]
    Variance: Var[x(t)]
    Auto-correlation function: \varphi_{xx}=E[x(t_1), x(t_2)].
    Cross-correlation function: \varphi_{xy}=E[x(t_1), y(t_2)].

The main difference between random variables and random processes is the auto-correlation function, which describes the change of the process over time. Another important feature is power spectral density (PSD) function. Power spectral density function is equivalent to auto-correlation function because they can be converted to each other using Fourier transformation.

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