PE1-3.1 Discrete-Time Random Processes
You can define discrete-time random processes and model them as autoregressive, moving average or ARMA processes.
AR, MA and ARMA are the three standard ways to build a correlated random sequence out of white noise, and almost all of statistical signal processing assumes one of them. The AR model dominates in practice because its parameters fall out of a linear system — the Yule-Walker equations — while MA estimation is genuinely harder. If you have already met stochastic processes, this unit is the discrete-time, parametric-model version of the same material.
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Introduction and definitions for discrete-time random processes
The vocabulary for signals that are random and sampled, which the whole subject is written in. If stochastic processes are already familiar this is revision in discrete time.
Autoregressive (AR) processes
The first and most used model, where the present depends on its own past. Its parameters fall out of a linear system, which is why it dominates in practice.
Moving average (MA) processes
The second model, where the present depends on past inputs instead. Estimating it is genuinely harder, which is worth knowing before you choose a model.
Autoregressive moving average (ARMA) processes
The two combined, which fits more shapes with fewer parameters. The cost is that estimation now has the difficulty of the moving average half.
Choosing a model order
How many parameters to use, which is a real decision with a real penalty on either side. Too few misses structure and too many fits noise.
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