Once you find an acceptable step size, use it throughout all 6 test cases. Then decrease the step size to the original value and plot again. Use software available on the web to solve for the optimal FIR coefficients. This will be used for evaluation purposes. Compare to your experimental value.
Software is also available for the eigenanalysis.
Based on the SNRs, determine the likely order of the unknown system. Optimal Predictors - 10 points. The systems should estimate a value 2 time steps in the future. The second predictor should perform optimally for noise with a variance of 2.0. Find these predictors via hand calculations.