Adaptive filters

Hi

I've read a book about adaptive noise reduction methods. I don't
understand why the original signal (without noise) is needed in Wiener
filtering, RLS filtering, LMS filtering... I mean, in most of the cases,
you don't have any reference of the original signal when you want to
reduce noise in a noisy signal! (otherwise, if you already know how the
original signal is, why do you have to handle the noisy signal??)

Maybe there is something that I don't understand about adaptive filtering
philosophy... Could you help me?

Thanks a lot

Thom

"thom" <soniceric@hotmail.com> wrote in message 
news:S4OdnSvnH_a-U8XZnZ2dnUVZ_sadnZ2d@giganews.com...
> Hi
>
> I've read a book about adaptive noise reduction methods. I don't
> understand why the original signal (without noise) is needed in Wiener
> filtering, RLS filtering, LMS filtering... I mean, in most of the cases,
> you don't have any reference of the original signal when you want to
> reduce noise in a noisy signal! (otherwise, if you already know how the
> original signal is, why do you have to handle the noisy signal??)
>
> Maybe there is something that I don't understand about adaptive filtering
> philosophy... Could you help me?
>
> Thanks a lot

The reference is used in the adaptation.  Don't think of the reference as 
"fixed".  It can vary -  and that's one of the good things about adaptive 
filters.

Indeed, if you knew everything about the reference, and it was stable, then 
maybe you could design a filter once and for all to do what you need.

Similar comments can be made for adaptive line cancellers.  The lines being 
cancelled can come and go and move around.  Otherwise you might apply some 
notch filters.

Fred 

thom wrote:
> Hi
> 
> I've read a book about adaptive noise reduction methods. I don't
> understand why the original signal (without noise) is needed in Wiener
> filtering, RLS filtering, LMS filtering... I mean, in most of the cases,
> you don't have any reference of the original signal when you want to
> reduce noise in a noisy signal! (otherwise, if you already know how the
> original signal is, why do you have to handle the noisy signal??)
> 
> Maybe there is something that I don't understand about adaptive filtering
> philosophy... Could you help me?
> 
> Thanks a lot
> 
> Thom

The reference signal could also be the noise itself. Furthermore, it is not
necessary that the noise is the exact noise which has "ruined" the original
signal. I believe it is sufficient that the reference noise has the same
characteristics (e.g. autocorrelation) as the noise in the measured signal.
Thus sometimes it is possible to record the noise with a second microphone
and use that as a reference signal.


-- 
Jani Huhtanen
Tampere University of Technology, Pori

Sorry I don't understand... Do I need a reference of the original signal
when I have only the noisy version of the signal, to implement adaptive
filtering? If the answer is "yes", can I build this reference from the
noisy signal??

Thom

"thom" <soniceric@hotmail.com> wrote in message 
news:W_CdnfCqXtjxSMXZRVn-gg@giganews.com...
> Sorry I don't understand... Do I need a reference of the original signal
> when I have only the noisy version of the signal, to implement adaptive
> filtering? If the answer is "yes", can I build this reference from the
> noisy signal??
>


Thom,

It sounds like you don't fully understand what a system looks like when it 
has an adaptive filter in it.  Here are some examples where "LMS" is the 
filter that adapts / changes:

  input--------->------------------------------->(+)----+----> e[n]
   ^                                                    |
   .                                              ^     |
   .                                              |     |
   .                                              |     | error
 noise ->----------------------->[LMS]------------+     | feedback
                                   ^                    | to
                                   |                    | control filter
                                   +--------------------+ changes
    Adaptive line-cancelling filter

    LMS adaptive filter adjusts to minimize e[n] which cancels noise
    in the signal by subtracting filtered version of noise.

    The LMS filter adjusts the amplitude and phase of its
    periodic input components to cancel the periodic noise
    component in the signal.

    ************************************************************************
                                  error feedback to control filter changes
                                   +--------------------+
                                   |                    |
                                   |                    |
                                   |                    |
  input------+---------------------|------------>(+)----+----> e[n]
             |                     |              ^
             |                     |              |
             |   +-----------+     v              |
             +---| Delay     |-->[LMS]------------+----------> o[n]
                 +-----------+

    Adaptive enhancer

    LMS adaptive filter adjusts to minimize e[n] which cancels signal

    o[n] ideally contains only signal

*****************************************************************************
                                  error feedback to control filter changes
                                   +--------------------+
                                   |                    |
                                   |                    |
                                   |                    |
  input---+------------------------|------------>(+)----+----> e[n]
          |                        |              ^
          |                        |              |
          |  +-----------+         v              |
          +--|   Delay   |------>[LMS]------------+----------> o[n]
          |  +-----------+         |
          |                        |
          |                        |
          |                        v              |
          +--------------------->[LMS]------------+----------> p[n]

     Adaptive predictor

     LMS adaptive filter adjusts to minimize e[n] which uses

     a delayed version of the input as a reference signal.

     So, the filter adapts to "predict" the input to the delay.

     Then, input the real time signal into the same filter to

     view a prediction of the input.

**************************************************************************

So, only the line canceller needs a "reference" and, indeed, the reference 
can be different than the version of interference that's in the signal. 
Often it's possible for the reference to be a *better / higher SNR* version 
of the interference.  For example, an accelerometer on a machine that causes 
interference elsewhere - with the objective to remove the interference at 
that latter location / signal.

There is *no* notion really of an "original signal", just the signal and the 
interference that exist *now*.  The point of being adaptive is to adjust to 
accomodate changes in both of them.  Again, if the signal and interference 
were unchanging then adaptation would be uncessary unless it's just a handy 
way of designing a fixed filter.  It's usually not worth it - but may be in 
some circumstances.

Fred

In some cases you do know the signal exactly (or at least with a high
probability). For example, in QPSK there are only four possible signals that
were transmitted. If you assume the one that is closest to what you actually
received then you essentially do know the original signal.

In other cases all you really need to know is the statistics of the original
signal. For example, you know that a speech waveform is fairly predictable
at least over short intervals. Noise on the other hand is totally
unpredictable. So if I use an adaptive filter to predict a voice signal and
compare it against the noisy voicy signal I actually received I can assume
that everything that wasn't predictable was noise and subtract it out.

-Clark

"thom" <soniceric@hotmail.com> wrote in message
news:S4OdnSvnH_a-U8XZnZ2dnUVZ_sadnZ2d@giganews.com...
> Hi
>
> I've read a book about adaptive noise reduction methods. I don't
> understand why the original signal (without noise) is needed in Wiener
> filtering, RLS filtering, LMS filtering... I mean, in most of the cases,
> you don't have any reference of the original signal when you want to
> reduce noise in a noisy signal! (otherwise, if you already know how the
> original signal is, why do you have to handle the noisy signal??)
>
> Maybe there is something that I don't understand about adaptive filtering
> philosophy... Could you help me?
>
> Thanks a lot
>
> Thom

Normally you have two inputs - SIgnal + Noise and Nosie alone for the
ref.
You don't need the 'true' signal - as you say what's the point!

The biggest trouble is getting noise alone. In speech + noise we can
get this during pauses in the speech - harder than it sounds otherwise
we woudl have cracked all teh problems by now.

Tam

thom wrote:

> Hi
>
> I've read a book about adaptive noise reduction methods. I don't
> understand why the original signal (without noise) is needed in Wiener
> filtering, RLS filtering, LMS filtering... I mean, in most of the cases,
> you don't have any reference of the original signal when you want to
> reduce noise in a noisy signal! (otherwise, if you already know how the
> original signal is, why do you have to handle the noisy signal??)
>
> Maybe there is something that I don't understand about adaptive filtering
> philosophy... Could you help me?

Thom,

I already described to you how adaptive filtering (in predictor
configuration) with only signal + noise as input can be used for noise
reduction, here (the "Spectral Subtraction" thread):

http://groups.google.ch/group/comp.dsp/msg/162e07132ee98e70

Regards,
Andor