Introduction - If you have any usage issues, please Google them yourself
Computer Experiments:
1. Consider an AR process x(n) defined by the difference equation
where v(n) is an additive white noise of zero mean and variance .The AR parameters and are both real valued:
a) Calculate the noise variance such that the AR process x(n) has unit variance .Hence , generate different realization of the process x (n).
b) Given the input x (n), an LMS filter of length M = 2 is used to estimate the unknown AR parameters and . The step size is assigned the value 0.05. Compute and plot the ensemble average curve of and by averaging the value of parameters and over an ensemble of 100 different realization of the filter. Calculate the time constant according to the experiment results and compare with the corresponded theoretical value.
c) For one realization of the LMS filter, compute the prediction error
And the two tap-weight errors
and
Using power spectral plots of , show that