Please anyone could help me with this question? Thanks!
Suppose that we wish to estimate a signal d
from the noisy observation
x
= d
+ v
where v
is unit variance white noise that is uncorrelated with d
. The
signal d
is an AR(1) process that is generated by the difference equation
d
= 0.8d(n - 1) + w
where w
is white noise with variance σ
w²= 0.36. Therefore, the autocorrelation function of d
is
R
dd(k) = (0.8 )^|k|
(a) Design a Wiener filter to estimate d
and evaluate the mean-square
error.
(b) The Wiener filter that you have designed in (a) is noncausal and therefore
unrealizable. Discuss a method to make it realizable.
(c) Using MATLAB, generate 500 samples of the processes x
and d
.
Use your Wiener filter to estimate d
from x
. Plot your estimate
and compare it to d
.