Friday, December 1, 2017

power spectral density - Decorrelating Stationary Colored Gaussian Noise -- Effect On The Desired Signal


So given stationary colored gaussian noise $\mathbf{n}$, I know that I can decorrelate it by first finding it's autocorrelation $R_{nn}$ and performing $R^{-\frac{1}{2}}_{nn} \mathbf{n}$.


In practice of course, I need to estimate $R_{nn}$, which I can do via averaging $\mathbf{r}_{nn}$ or by fitting it to an AR model.


So, suppose I have a good estimate $\hat{R}_{nn}$, for a finite data record of length $N$. Such that the resulting spectrum of the noise frame is white enough, according to some metric.


Now, suppose I have a signal $\mathbf{x} = \mathbf{s} + \mathbf{n}$. I want to decorrelate the noise, such that after the decorrelation, I get a signal in white noise. From what I have read, the way to do this is to also apply $R^{-\frac{1}{2}}_{nn} \mathbf{x}$.


However, won't this distort the desired signal $\mathbf{s}$? Can anyone point me to some references regarding this?


Also: How else can I decorrelate colored noise in order to get my signal embedded in white noise?





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