abling8
Newbie level 4
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 σw²= 0.36. Therefore, the autocorrelation function of d is
Rdd(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.
Suppose that we wish to estimate a signal d
from the noisy observationx
= d + vwhere v
is unit variance white noise that is uncorrelated with d. Thesignal d
is an AR(1) process that is generated by the difference equationd
= 0.8d(n - 1) + wwhere w
is white noise with variance σw²= 0.36. Therefore, the autocorrelation function of d isRdd(k) = (0.8 )^|k|
(a) Design a Wiener filter to estimate d
and evaluate the mean-squareerror.
(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 estimateand compare it to d
.