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Colored Noise in Noise cancellation

Started by pacman101 December 10, 2010
Hello,

I can't seem to find references on the performance of noise cancellation
algorithms namely LMS, RLS, NLMS, etc when it comes to suppressing colored
noise.  

I have read somewhere that these algorithms do not perform very well when
the noise spectrum isn't flat but I can't seem to find a reference to that
claim.  

Can somebody explain this behavior to me and why?  Is this even true?  Can
you point to a good reference?

The noise I am trying to cancel out is not flat and there are very large
differences in amplitudes across the frequency band.  I am doing this for
RF.

Thank you

JT
On 12/10/2010 12:33 PM, pacman101 wrote:
> Hello, > > I can't seem to find references on the performance of noise cancellation > algorithms namely LMS, RLS, NLMS, etc when it comes to suppressing colored > noise. > > I have read somewhere that these algorithms do not perform very well when > the noise spectrum isn't flat but I can't seem to find a reference to that > claim. > > Can somebody explain this behavior to me and why? Is this even true? Can > you point to a good reference? > > The noise I am trying to cancel out is not flat and there are very large > differences in amplitudes across the frequency band. I am doing this for > RF.
I don't know anything about this application specifically, but I would think that -- if you structured your algorithm right -- you could do better with colored noise than with white, as you'd have more predictability. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" was written for you. See details at http://www.wescottdesign.com/actfes/actfes.html

pacman101 wrote:
> Hello, > > I can't seem to find references on the performance of noise cancellation > algorithms namely LMS, RLS, NLMS, etc when it comes to suppressing colored > noise.
Those algoritms do not suppress noise. They minimize mean square error.
> I have read somewhere that these algorithms do not perform very well when > the noise spectrum isn't flat but I can't seem to find a reference to that > claim.
There is nothing special about colored interference spectrum; colored signal spectrum could be the problem though.
> Can somebody explain this behavior to me and why? Is this even true? Can > you point to a good reference? > > The noise I am trying to cancel out is not flat and there are very large > differences in amplitudes across the frequency band. I am doing this for > RF.
Are you sure there isn't a trivial bug somewhere? Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
> > >pacman101 wrote: >> Hello, >> >> I can't seem to find references on the performance of noise
cancellation
>> algorithms namely LMS, RLS, NLMS, etc when it comes to suppressing
colored
>> noise. > >Those algoritms do not suppress noise. They minimize mean square error. > >> I have read somewhere that these algorithms do not perform very well
when
>> the noise spectrum isn't flat but I can't seem to find a reference to
that
>> claim. > >There is nothing special about colored interference spectrum; colored >signal spectrum could be the problem though. > >> Can somebody explain this behavior to me and why? Is this even true?
Can
>> you point to a good reference? >> >> The noise I am trying to cancel out is not flat and there are very
large
>> differences in amplitudes across the frequency band. I am doing this
for
>> RF. > >Are you sure there isn't a trivial bug somewhere? > > >Vladimir Vassilevsky >DSP and Mixed Signal Design Consultant >http://www.abvolt.com >
From what I have read from some IEEE paper is that when the noise spectrum is not white, these algorithms converge slower, but I do not know if it gives the same amount of noise suppression. It makes sense when the noise isn't constantly on, in that case the noise is nonstationary. These algorithms do perform very well when the signals are highly non-stationary since they have to keep reconverging.
On Dec 10, 2:33=A0pm, "pacman101" <janpac01@n_o_s_p_a_m.yahoo.com>
wrote:
> Hello, > > I can't seem to find references on the performance of noise cancellation > algorithms namely LMS, RLS, NLMS, etc when it comes to suppressing colore=
d
> noise. =A0 > > I have read somewhere that these algorithms do not perform very well when > the noise spectrum isn't flat but I can't seem to find a reference to tha=
t
> claim. =A0 > > Can somebody explain this behavior to me and why? =A0Is this even true? =
=A0Can
> you point to a good reference? > > The noise I am trying to cancel out is not flat and there are very large > differences in amplitudes across the frequency band. =A0I am doing this f=
or
> RF. > > Thank you > > JT
These algorithms attempt to estimate the Wiener filter which relys on the input autocorrelation and the input/desired cross correlation. The only constraint on the signal is that the desired response and the interference be uncorrelated. The fastest convergence ususally will result when a single-frequency sinusoid is the desired. The slowest convergence usually will result when the desired is guassian and white. The worst overall convergence will occur when the desired is a single-frequency sinusoid. The best overall convergence will occur when the desired is gaussian and white. Vlad is correct when he says these algorithms can only minimize the mean-squared error. If your model is exact, and if the interference is not correlated with the desired, you should have no problem. Maurice Givens
On Dec 11, 9:33=A0am, "pacman101" <janpac01@n_o_s_p_a_m.yahoo.com>
wrote:
> Hello, > > I can't seem to find references on the performance of noise cancellation > algorithms namely LMS, RLS, NLMS, etc when it comes to suppressing colore=
d
> noise. =A0 > > I have read somewhere that these algorithms do not perform very well when > the noise spectrum isn't flat but I can't seem to find a reference to tha=
t
> claim. =A0 > > Can somebody explain this behavior to me and why? =A0Is this even true? =
=A0Can
> you point to a good reference? > > The noise I am trying to cancel out is not flat and there are very large > differences in amplitudes across the frequency band. =A0I am doing this f=
or
> RF. > > Thank you > > JT
You don't define your problem very well. First of all you miss-spell Colour - that's important. Are you are using LMS, RLS etc to identify an FIR unknown system or are you filtering random coloured signal from random coloured noise? How many sensors are available and where? If the eigenvalues of the correlation matrix is ill-conditioned then the convergence may be a bit slow. Hardy
On 12/10/2010 12:33 PM, pacman101 wrote:
> Hello, > > I can't seem to find references on the performance of noise cancellation > algorithms namely LMS, RLS, NLMS, etc when it comes to suppressing colored > noise. > > I have read somewhere that these algorithms do not perform very well when > the noise spectrum isn't flat but I can't seem to find a reference to that > claim. > > Can somebody explain this behavior to me and why? Is this even true? Can > you point to a good reference? > > The noise I am trying to cancel out is not flat and there are very large > differences in amplitudes across the frequency band. I am doing this for > RF. > > Thank you > > JT
I agree that the objectives could be clearer. The only "noise canceller" I know about attempts to remove correlated interference - the output of a repeating sweep generator for example. The adapted filter adjusts frequency magnitude and phase in order to deliver a signal that can optimally subtract from the signal channel. Where you get the input for that filter depends on the application and what's available for that purpose. In the end, the adapted filter has to "shut off" at frequencies where its input is random / uncorrelated. And, the filter ends up looking like a set of bandpasses that deliver the signal to be subtracted out. So, I'd say that it doesn't matter what the noise amplitudes are with frequency (the "color") because the filter is going to shut off (i.e. attenuate) anyway. The color may affect convergence and dynamic change rates but I'd think that would be a secondary effect. Sounds like there's pretty good consensus here. Fred