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A little bit of background: I am interested in whitening in the least-square estimation.

In this sense, consider a univariate signal $y$. Assuming the covariance of $y$ is $\mathbf{A}\sigma^2$. If we knew matrix $\bf A$, then, whitenning of this signal could be done by: $\mathbf{A}^{-1/2}\bf y$. Since the $\mathbf{A}^{-1/2}\bf y$ has a covariance matrix of $\mathbf{A}^{-1/2} \bf A \mathbf{A}^{-1/2}\sigma^2 = I\sigma^2$. Thus, $\mathbf{A}^{-1/2}\bf y$ is whitened.

In practice, the $A$ is unknown but can be estimated using different methods such maximum likelihood or Yule-Walker. Here is what I am interested to figure out.

To be more specific, for this purpose one can use Yule-Walker equation in particular and assume an AR(p) model, say order $p=1$ and estimate the model parameter of this autoregressive.

This is indeed a filter, but my question is how to characterize this filter in frequency domain? How can I find the $H(z)$ of this filter? Is there a way to find its zeros and poles and further know the characteristics of this filter?

I would appreciate if you could help me.

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Hi: The material you are asking about is on page 7 of the document at the link below.

http://www.ee.ic.ac.uk/hp/staff/dmb/courses/DSPDF/DSPDF_2010.pdf

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