Variable + Random Variable + Random Process
- Random Variable: is a variable described by a probability density function (PDF)
- 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)
- Random Process: key features
Expectation value: E[x(t)]
Auto-correlation function: .
Cross-correlation function: .
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.