Matched Filtering DC Noise Out

On 9/20/2009 6:37 PM, Bret Cahill wrote:
>>>>> If the noise includes some DC it seems that a matched filter would
>>>>> treat it as a zero frequency "curve" and eliminate it in the
>>>>> convolution along with all the higher frequency noise.
>>>> What noise?
>>> The noise that got into the original signal has some AC and a DC
>>> offset.
>>> Matched filtering should eliminate the DC as well as the AC.
>>> Bret Cahill

>> How can a matched filter eliminate in-band noise?   DC or AC?
>
> That's someone else's issue.

The point is the assumption is flawed.

> The immediate issue here is if can you assume DC to be a zero
> frequency AC as far as matched filtering is concerned.

You can always assume it.  It may completely screw up your system 
depending on its sensitivity to DC, though.

> If convolution in the time domain amounts to multiplication in the
> frequency domain then, at first glance, DC or square wave noise should
> be filtered along with the AC noise..

Convolution in TD is, in fact, multiplication in FD.   That doesn't 
change the issue of eliminating noise or interference in the passband of 
a filter.

It sounds to me like you are ascribing properties to matched filters 
that they don't have, e.g., eliminating noise or DC from the passband.

-- 
Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.abineau.com

> >>>>> If the noise includes some DC it seems that a matched filter would
> >>>>> treat it as a zero frequency "curve" and eliminate it in the
> >>>>> convolution along with all the higher frequency noise.
> >>>> What noise?
> >>> The noise that got into the original signal has some AC and a DC
> >>> offset.
> >>> Matched filtering should eliminate the DC as well as the AC.
> >>> Bret Cahill
> >> How can a matched filter eliminate in-band noise? � DC or AC?
>
> > That's someone else's issue.
>
> The point is the assumption is flawed.
>
> > The immediate issue here is if can you assume DC to be a zero
> > frequency AC as far as matched filtering is concerned.
>
> You can always assume it. �It may completely screw up your system
> depending on its sensitivity to DC, though.
>
> > If convolution in the time domain amounts to multiplication in the
> > frequency domain then, at first glance, DC or square wave noise should
> > be filtered along with the AC noise..
>
> Convolution in TD is, in fact, multiplication in FD. � That doesn't
> change the issue of eliminating noise or interference in the passband of
> a filter.
>
> It sounds to me like you are ascribing properties to matched filters
> that they don't have, e.g., eliminating noise or DC from the passband.

A simple analog R-to-ground C filter can eliminate DC so maybe that's
not so much an issue.

A bigger problem would be optimum pulse shaping when the 1st
derivative of the signal needs to be, for other reasons, at a minimum
as much as possible.  This consideration may outweigh the noise
problems and I may be stuck with a simple sine wave.

Is a simple sine wave any good in a matched filter or does the pulse
shape need more "personality" something for FFT to munch on?


Bret Cahill

> > >>>>> If the noise includes some DC it seems that a matched filter would
> > >>>>> treat it as a zero frequency "curve" and eliminate it in the
> > >>>>> convolution along with all the higher frequency noise.
> > >>>> What noise?
> > >>> The noise that got into the original signal has some AC and a DC
> > >>> offset.
> > >>> Matched filtering should eliminate the DC as well as the AC.
> > >>> Bret Cahill
> > >> How can a matched filter eliminate in-band noise? � DC or AC?
>
> > > That's someone else's issue.
>
> > The point is the assumption is flawed.
>
> > > The immediate issue here is if can you assume DC to be a zero
> > > frequency AC as far as matched filtering is concerned.
>
> > You can always assume it. �It may completely screw up your system
> > depending on its sensitivity to DC, though.
>
> > > If convolution in the time domain amounts to multiplication in the
> > > frequency domain then, at first glance, DC or square wave noise should
> > > be filtered along with the AC noise..
>
> > Convolution in TD is, in fact, multiplication in FD. � That doesn't
> > change the issue of eliminating noise or interference in the passband of
> > a filter.
>
> > It sounds to me like you are ascribing properties to matched filters
> > that they don't have, e.g., eliminating noise or DC from the passband.
>
> A simple analog R-to-ground C filter can eliminate DC so maybe that's
> not so much an issue.
>
> A bigger problem would be optimum pulse shaping when the 1st
> derivative of the signal needs to be, for other reasons, at a minimum
> as much as possible. �This consideration may outweigh the noise
> problems and I may be stuck with a simple sine wave.
>
> Is a simple sine wave any good in a matched filter or does the pulse
> shape need more "personality" something for FFT to munch on?

Mozart didn't like the flute for the same reason -- nothing but a
sterile sine wave.


Bret Cahill