Use the MATLAB randn function to generate 1000 points for x. Generate the output of the unknown system with the ?lter function and b=[1232 1] and a=[1]. Normalise the ?lter output so that its variance is unity, i.e. y = y./sqrt((sum(b.*b)); call the randn function again to generate 1000 points for the measurement noise, scale the values by 0.1 and add them to [ ], and calculate the Signal-to-Noise Ratio (SNR) in dB for y[k] (The power of zero mean white noise is 2 ; when a noise signal is scaled its standard deviation, i.e , gets scaled by the same factor).
- Use the xcorr function to estimate the cross-correlation and autocor relation elements to form R_{xx} and P_{zx}.
- Solve for the optimum Wiener ?lter. Is it close to that of the unknown system?
- Repeat the experiment by varying the scaling applied to the additive noise to 1.0 and 10.0, re-calculate the SNR for each case. What is the effect upon the Wiener solution? What happens if w is assumed to be greater than 4?