Filtering Noise from a signal

In class we analysed a signal and filtered the noise out. However the noise
was in a different bandwidth to the original signal hence it was easy to
filter.

If noise and the signal were to overlap in freq. spectrum, are there any
techniques to filter out the noise??

On Jun 1, 7:34&#4294967295;pm, "bos1234" <suren130@n_o_s_p_a_m.gmail.com> wrote:
> In class we analysed a signal and filtered the noise out. However the noise
> was in a different bandwidth to the original signal hence it was easy to
> filter.
>
> If noise and the signal were to overlap in freq. spectrum, are there any
> techniques to filter out the noise??

No, but there are techniques to reduce the noise provided that you
have a sample of it that does not include signal, like you might have
in speech. Search for "spectral subtraction".

John

On 06/01/2010 04:34 PM, bos1234 wrote:
> In class we analysed a signal and filtered the noise out. However the noise
> was in a different bandwidth to the original signal hence it was easy to
> filter.
>
> If noise and the signal were to overlap in freq. spectrum, are there any
> techniques to filter out the noise??

No.  The word "filter" is used as a close analogy to a filter that you 
might use to filter liquids in the kitchen, or in a chemistry class. 
When you use a coffee filter filter, for example, you use a filter that 
has pores that are smaller than the coffee grounds.  This lets the water 
and anything dissolved in it (like than nice coffee -- mmm!) through, 
but it blocks the coffee grounds because they won't fit.

A filter in signal processing terms is much the same, except instead of 
filtering by size, you're filtering by position in the spectrum.

Unless there is some characteristic of the signal that distinguishes it 
from the noise, you can't filter it out.

-- 
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com

Tim Wescott wrote:
> On 06/01/2010 04:34 PM, bos1234 wrote:
>> In class we analysed a signal and filtered the noise out. However the 
>> noise
>> was in a different bandwidth to the original signal hence it was easy to
>> filter.
>>
>> If noise and the signal were to overlap in freq. spectrum, are there any
>> techniques to filter out the noise??
> 
> No.  The word "filter" is used as a close analogy to a filter that you 
> might use to filter liquids in the kitchen, or in a chemistry class. 
> When you use a coffee filter filter, for example, you use a filter that 
> has pores that are smaller than the coffee grounds.  This lets the water 
> and anything dissolved in it (like than nice coffee -- mmm!) through, 
> but it blocks the coffee grounds because they won't fit.
> 
> A filter in signal processing terms is much the same, except instead of 
> filtering by size, you're filtering by position in the spectrum.
> 
> Unless there is some characteristic of the signal that distinguishes it 
> from the noise, you can't filter it out.
> 

Well .... what about a line canceller?  It uses a reference signal, 
which is suitably scaled and delayed, to be subtracted from a composite.
To the extent that the reference is stable and the desired signal isn't, 
then only the reference will be subtracted.  Any consituent of the 
composite that departs from the "reference model" will get through.
And, to your point, any constituent of the composite that is stable and 
matches the reference, will be attentuated.

[many words about dyamics, etc......]

We say "spectrum" which is defined over all time or over some temporal 
epoch.  But the actual signal may not even come close to having the 
stability implied by our model.  I think sometimes we forget that for 
convenience.

Fred

On 2 Jun, 04:47, Fred Marshall <fmarshallx@remove_the_xacm.org> wrote:

> We say "spectrum" which is defined over all time or over some temporal
> epoch. &#4294967295;But the actual signal may not even come close to having the
> stability implied by our model.

I think the spectrun is among the most stable representations
of a signal. Because it is determined by some property of the
source. In communications, channels bandwidths are determined
by strict political regulation.

In human speech, the anatomy of the vocal tract limits what
frequecy ranges can be emitted. The ears detect sounds over a
certain band.

Consider what information you, the human, can deduce from
even a short sample of speech from somebody who talks your
native language:

- The sex of the speaker
- The age of the speaker
- Whether the speaker is also a native of the language
- Some idea about the geographical origins of the speaker
- Some idea about the social standing of the speaker
- The speaker's state of mind

Of course, not all of these are relevant all the time,
and you will not get the right impression every time,
but given a speech sample you will be able to form some
sort of impression of the speaker.

>&#4294967295;I think sometimes we forget that for convenience.

The sad athing is - I think most people never even considered
the signal to be the slightest instable or have any hint of
random properties.

Rune

On Jun 1, 6:34&#4294967295;pm, "bos1234" <suren130@n_o_s_p_a_m.gmail.com> wrote:
> In class we analysed a signal and filtered the noise out. However the noise
> was in a different bandwidth to the original signal hence it was easy to
> filter.
>
> If noise and the signal were to overlap in freq. spectrum, are there any
> techniques to filter out the noise??

Yes there are. Go to
http://www.danvillesignal.com/comp.dsp-conference/comp.dsp-conference-presentations.html
and look at the paper on noise reduction techniques. For example,
let's say the noise is 6 dB below the signal, then you can use
coefficient shirkage: take FFT, do coefficient shirkage, take IFFT.
Voila, no noise.

On 06/01/2010 05:40 PM, Tim Wescott wrote:
> On 06/01/2010 04:34 PM, bos1234 wrote:
>> In class we analysed a signal and filtered the noise out. However the
>> noise
>> was in a different bandwidth to the original signal hence it was easy to
>> filter.
>>
>> If noise and the signal were to overlap in freq. spectrum, are there any
>> techniques to filter out the noise??
>
> No. The word "filter" is used as a close analogy to a filter that you
> might use to filter liquids in the kitchen, or in a chemistry class.
> When you use a coffee filter filter, for example, you use a filter that
> has pores that are smaller than the coffee grounds. This lets the water
> and anything dissolved in it (like than nice coffee -- mmm!) through,
> but it blocks the coffee grounds because they won't fit.
>
> A filter in signal processing terms is much the same, except instead of
> filtering by size, you're filtering by position in the spectrum.
>
> Unless there is some characteristic of the signal that distinguishes it
> from the noise, you can't filter it out.
>
Actually, I shouldn't have given you a flat "no".  Look into Wiener 
filtering and Kalman filtering -- both of these are ways to find optimal 
filters when the noise and signal spectra overlap.  Both of them work 
better the more you know about the signal and the noise (and both of 
them can fail absurdly if your real signal and/or noise doesn't match 
your assumptions -- but there are ways around that).

You're still playing a game where you're using what you know about the 
signal and the noise to tease them out.

Note, also, that spread spectrum reception uses a time-domain "filter" 
that will pull a signal out of -- apparently -- nothing; that's because 
the underlying assumption of spectral analysis is that both signal and 
noise are stationary, while spread spectrum techniques use a signal that 
has considerable correlation over time, just in a way that doesn't show 
up in a Fourier transform.

-- 
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com

On Jun 2, 11:34&#4294967295;am, "bos1234" <suren130@n_o_s_p_a_m.gmail.com> wrote:
> In class we analysed a signal and filtered the noise out. However the noise
> was in a different bandwidth to the original signal hence it was easy to
> filter.
>
> If noise and the signal were to overlap in freq. spectrum, are there any
> techniques to filter out the noise??

With some sort of extra information - perhaps! Normally we need either
a second signal + noise of some sort related to the first or some
measure of the noise on its own.

Hardy

On Jun 2, 6:49&#4294967295;pm, Tim Wescott <t...@seemywebsite.now> wrote:
> You're still playing a game where you're using what you know about the
> signal and the noise to tease them out.
>

This is the only game in town! This is more or less all of singal
processing.

illywhacker;

Dnia 02-06-2010 o 04:47:19 Fred Marshall <fmarshallx@remove_the_xacm.org>  
napisa&#4294967295;(a):

(...)
> Well .... what about a line canceller?  It uses a reference signal,
(...)

You assume a line and you cancel it.
You assume a noise and you cancel it.

If your assumption is proper
than substraction also will be proper.

I would look for noise shaping and Kalman filtering.
If the nois is stationary than there would be no need
to use adaptive assumptions for it.

-- 
Mikolaj