A discrete signal x is generated by the recursive process $$ x_n = x_{n-1} - 0.2 x_{n-2} + w_n $$

where $w_n$ is white noise with zero mean and unit variance. What is the optimum order of a linear predictor for this signal? What are the values of the prediction coefficients? What is the average power of the residual?

I would really appreciate if someone could help me with this question.

It's a past paper question not homework.


  • $\begingroup$ By "power if the residual" do you mean: What is the variance of $x_n$? $\endgroup$
    – Peter K.
    Commented Dec 7, 2015 at 22:17

1 Answer 1


From the definition of the process you know that


Since $w_n$ is white you can't predict it, so the best linear predictor for the given process is the filter


which is a first order filter. It estimates the future sample $x_{n+1}$ by computing


The residual error is equal to $w_n$, which has an average power of $1$.


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