# Noise estimation

Started by August 12, 2010
```On Aug 12, 3:32&#2013266080;pm, Tim Wescott <t...@seemywebsite.com> wrote:
> On 08/12/2010 12:13 PM, Doug wrote:
>
>
>
>
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> > On Aug 12, 11:27 am, Vladimir Vassilevsky<nos...@nowhere.com> &#2013266080;wrote:
> >> Doug wrote:
> >>> Hello,
>
> >>> Is there a method to estimate the statistical properties of additive
> >>> noise from a received signal observation. &#2013266080; Assume we have
>
> >>> y(k) = x(k) + n(k)
>
> >>> and we observe the received signal y(k). &#2013266080;I would like to know if
> >>> there is a way to determine the autocorrelation of the noise process
> >>> n(k), that is Rnn. &#2013266080;This is not a speech problem. &#2013266080;x(k) is a digital
> >>> PAM signal that is corrupted by ISI, it can be assumed
> >>> cyclostationary.
>
> >>> To simplify the problem, we can assume the noise is white Gaussian
> >>> noise, can we determine the noise variance, sigma^2, and hence Rnn for
> >>> this simplified case? &#2013266080;Ideally I don't want to assume anything about
> >>> the noise, but if assuming white gaussian noise make things tractable,
> >>> I take that solution over nothing
>
> >> Synchronize to the baud rate and compare the statistics at the end and
> >> at the 1/2 of the symbol interval.
>
> >> VLV- Hide quoted text -
>
> >> - Show quoted text -
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>
> > It is no problem to do symbol synchronization, but I don't understand
> > how comparing the statistics at mid-sym and end-sym will get you
> > anything. &#2013266080;Do you have more info or point me to a good reference?
>
> > Also, I just read that one way get sigma^2 is to find the minimum
> > eigenvalue of Ryy. &#2013266080;This makes some sense and given the fact that x(k)
> > has a zero in its power spectral density I think the noise in that
> > region should yield a good result. &#2013266080;Does anyone have more information
> > on this technique??
>
> If things are too messed up to get good symbol detection I don't think
> this will work.
>
> Just making a plain old filter around a zero in the signal spectrum and
> estimating energy content should, however, make for a fairly decent
> measure of noise.
>
> --
>
> Tim Wescott
> Wescott Design Serviceshttp://www.wescottdesign.com
>
> Do you need to implement control loops in software?
> "Applied Control Theory for Embedded Systems" was written for you.
> See details athttp://www.wescottdesign.com/actfes/actfes.html- Hide quoted text -
>
> - Show quoted text -

Thank you all for the advice.  I think measuring the noise in a null
may work for my puposes, thanks Tim.

-Doug
```