I have a signal processing problem where I have the Additive Noise Model (assume Gaussian noise).
$$ y = x + w $$
where, $y$ is corrupted signal, $x$ is original signal & $w$ is a non-white noise vector. In other words the distribution of entries of $w$ are not i.i.d. and may be a function of $x$.
I have a filtering operation which can perform filtering on Additive white noise model, $\hat{x} = Hy$ where $H$ is a linear filter. I want to know if there is any method by which I can transform the above signal with the additive white noise model so that the new model is :
$$ y = x_1 + u \\ u \sim \mathcal{N} (0,\sigma^2 I) $$
Where, $u$ is i.i.d.
I have tried to do this with whitening transform, but to no avail. The problem is how to I get covariance matrix of $w$ to incorporate into my framework?