Prev: Filtering Noise from a signal
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From: Fred Marshall on 3 Jun 2010 20:30
illywhacker wrote:
> On Jun 2, 1:21 am, "bos1234" <suren130(a)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??
>
> Google 'denoising'. There is a vast literature on this. Of course, you
> need to know *something* about your signal and your noise.
>
> illywhacker;

Right.

In the automatic line canceler the "something" is the "reference signal"
which might be taken from a machine accelerometer or some such source.
Then, if the machine is an interferer, it can be subtracted out subject
to being adjusted magnitude and phase vs. frequency which is what the
adaptive part of the filter is doing.

So, in a line canceler (where the "noise" has relatively steady (i.e.
short term stable) spectral character, a burst of energy in the signal
of interest, while being at exactly one of the eliminated line
frequencies, will go right through. This is because a stable line is
being subtracted - which is not the same as a notch filter.
And, come to think of it, so will such a burst in [only] the reference
signal because the gain won't change fast enough.
But, an equal burst in both of them (presumably from the reference
source) will be canceled if the amplitudes match.

I suppose one could say that it has the same sort of limitation as a
differentiator - it adjusts the difference between two signals working
toward zero. So, small perturbations (differences in the difference)
likely look relatively big at the output.

In an automatic line enhancer, there is no such reference and a "big
enough" delay is used to generate something like a reference where
random noise is decorrelated. Then, the adaptation goes the same way -
to eliminate energy in the output (the sum of the unfiltered signal path
and the adaptive block). Since one can only reduce the sum of two
uncorrelated noises by shutting one off completely, the adaptive block
acts to shut off random noise and passes sinusoids. And then, the
useful output is taken from the adaptive filter block as it is a
bandpass filter on all stable sinusoids.
In this case, having no reference, it ends up looking like a modestly
dynamic "comb" of bandpasses and in-band noise is passed through.

In the context of the line enhancer, which is a filter to reduce random
noise, on top of all this is the analysis bandwidth that will be
applied. If the analysis bandwidth is wider than the adaptive filter
resolution then filtering out adjacent random noise is helpful. If the
analysis bandwidth is equal to or narrower than the adaptive filter
resolution, then random noise within the analysis bands isn't reduced.
So, it helps to know the processing that will follow. I believe that
usually the processing *is* this filter so the latter applies.

Fred
From: illywhacker on 4 Jun 2010 05:04
On Jun 4, 2:30 am, Fred Marshall <fmarshallx(a)remove_the_xacm.org>
wrote:
> illywhacker wrote:
> > On Jun 2, 1:21 am, "bos1234" <suren130(a)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??
>
> > Google 'denoising'. There is a vast literature on this. Of course, you
> > need to know *something* about your signal and your noise.
>
> > illywhacker;
>
> Right.
>
> In the automatic line canceler the "something" is the "reference signal"
> which might be taken from a machine accelerometer or some such source.
> Then, if the machine is an interferer, it can be subtracted out subject
> to being adjusted magnitude and phase vs. frequency which is what the
> adaptive part of the filter is doing.
>
> So, in a line canceler (where the "noise" has relatively steady (i.e.
> short term stable) spectral character, a burst of energy in the signal
> of interest, while being at exactly one of the eliminated line
> frequencies, will go right through.  This is because a stable line is
> being subtracted - which is not the same as a notch filter.
> And, come to think of it, so will such a burst in [only] the reference
> signal because the gain won't change fast enough.
> But, an equal burst in both of them (presumably from the reference
> source)  will be canceled if the amplitudes match.
>
> I suppose one could say that it has the same sort of limitation as a
> differentiator - it adjusts the difference between two signals working
> toward zero.  So, small perturbations (differences in the difference)
> likely look relatively big at the output.
>
> In an automatic line enhancer, there is no such reference and a "big
> enough" delay is used to generate something like a reference where
> random noise is decorrelated.  Then, the adaptation goes the same way -
> to eliminate energy in the output (the sum of the unfiltered signal path
> and the adaptive block).  Since one can only reduce the sum of two
> uncorrelated noises by shutting one off completely, the adaptive block
> acts to shut off random noise and passes sinusoids.  And then, the
> useful output is taken from the adaptive filter block as it is a
> bandpass filter on all stable sinusoids.
> In this case, having no reference, it ends up looking like a modestly
> dynamic "comb" of bandpasses and in-band noise is passed through.
>
> In the context of the line enhancer, which is a filter to reduce random
> noise, on top of all this is the analysis bandwidth that will be
> applied.  If the analysis bandwidth is wider than the adaptive filter
> resolution then filtering out adjacent random noise is helpful.  If the
> analysis bandwidth is equal to or narrower than the adaptive filter
> resolution, then random noise within the analysis bands isn't reduced.
> So, it helps to know the processing that will follow.  I believe that
> usually the processing *is* this filter so the latter applies.


I am not sure why you are replying to me, but as long as you have:
since we know nothing about the signal or the noise, it would seem
premature to offer a specific solution, don't you think?

illywhacker;
From: maury on 4 Jun 2010 11:48
On Jun 3, 7:30 pm, Fred Marshall <fmarshallx(a)remove_the_xacm.org>
wrote:
> illywhacker wrote:
> > On Jun 2, 1:21 am, "bos1234" <suren130(a)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??
>
> > Google 'denoising'. There is a vast literature on this. Of course, you
> > need to know *something* about your signal and your noise.
>
> > illywhacker;
>
> Right.
>
> In the automatic line canceler the "something" is the "reference signal"
> which might be taken from a machine accelerometer or some such source.
> Then, if the machine is an interferer, it can be subtracted out subject
> to being adjusted magnitude and phase vs. frequency which is what the
> adaptive part of the filter is doing.
>
> So, in a line canceler (where the "noise" has relatively steady (i.e.
> short term stable) spectral character, a burst of energy in the signal
> of interest, while being at exactly one of the eliminated line
> frequencies, will go right through.  This is because a stable line is
> being subtracted - which is not the same as a notch filter.
> And, come to think of it, so will such a burst in [only] the reference
> signal because the gain won't change fast enough.
> But, an equal burst in both of them (presumably from the reference
> source)  will be canceled if the amplitudes match.
>
> I suppose one could say that it has the same sort of limitation as a
> differentiator - it adjusts the difference between two signals working
> toward zero.  So, small perturbations (differences in the difference)
> likely look relatively big at the output.
>
> In an automatic line enhancer, there is no such reference and a "big
> enough" delay is used to generate something like a reference where
> random noise is decorrelated.  Then, the adaptation goes the same way -
> to eliminate energy in the output (the sum of the unfiltered signal path
> and the adaptive block).  Since one can only reduce the sum of two
> uncorrelated noises by shutting one off completely, the adaptive block
> acts to shut off random noise and passes sinusoids.  And then, the
> useful output is taken from the adaptive filter block as it is a
> bandpass filter on all stable sinusoids.
> In this case, having no reference, it ends up looking like a modestly
> dynamic "comb" of bandpasses and in-band noise is passed through.
>
> In the context of the line enhancer, which is a filter to reduce random
> noise, on top of all this is the analysis bandwidth that will be
> applied.  If the analysis bandwidth is wider than the adaptive filter
> resolution then filtering out adjacent random noise is helpful.  If the
> analysis bandwidth is equal to or narrower than the adaptive filter
> resolution, then random noise within the analysis bands isn't reduced.
> So, it helps to know the processing that will follow.  I believe that
> usually the processing *is* this filter so the latter applies.
>
> Fred

Fred,
The adaptive line enhancer (ALE) is a specific form of the LMS/NLMS
algorithm where the reference is constructed by delaying the input.
This means the input must be correlated with some delayed version of
itself for the ALE to work. Therefore, the ALE can not reduce random
noise. The ALE is indeed a form of notch filter.

Maurice Givens
From: maury on 4 Jun 2010 11:54
On Jun 4, 10:48 am, maury <maury...(a)core.com> wrote:
> On Jun 3, 7:30 pm, Fred Marshall <fmarshallx(a)remove_the_xacm.org>
> wrote:
>
>
>
>
>
> > illywhacker wrote:
> > > On Jun 2, 1:21 am, "bos1234" <suren130(a)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??
>
> > > Google 'denoising'. There is a vast literature on this. Of course, you
> > > need to know *something* about your signal and your noise.
>
> > > illywhacker;
>
> > Right.
>
> > In the automatic line canceler the "something" is the "reference signal"
> > which might be taken from a machine accelerometer or some such source.
> > Then, if the machine is an interferer, it can be subtracted out subject
> > to being adjusted magnitude and phase vs. frequency which is what the
> > adaptive part of the filter is doing.
>
> > So, in a line canceler (where the "noise" has relatively steady (i.e.
> > short term stable) spectral character, a burst of energy in the signal
> > of interest, while being at exactly one of the eliminated line
> > frequencies, will go right through.  This is because a stable line is
> > being subtracted - which is not the same as a notch filter.
> > And, come to think of it, so will such a burst in [only] the reference
> > signal because the gain won't change fast enough.
> > But, an equal burst in both of them (presumably from the reference
> > source)  will be canceled if the amplitudes match.
>
> > I suppose one could say that it has the same sort of limitation as a
> > differentiator - it adjusts the difference between two signals working
> > toward zero.  So, small perturbations (differences in the difference)
> > likely look relatively big at the output.
>
> > In an automatic line enhancer, there is no such reference and a "big
> > enough" delay is used to generate something like a reference where
> > random noise is decorrelated.  Then, the adaptation goes the same way -
> > to eliminate energy in the output (the sum of the unfiltered signal path
> > and the adaptive block).  Since one can only reduce the sum of two
> > uncorrelated noises by shutting one off completely, the adaptive block
> > acts to shut off random noise and passes sinusoids.  And then, the
> > useful output is taken from the adaptive filter block as it is a
> > bandpass filter on all stable sinusoids.
> > In this case, having no reference, it ends up looking like a modestly
> > dynamic "comb" of bandpasses and in-band noise is passed through.
>
> > In the context of the line enhancer, which is a filter to reduce random
> > noise, on top of all this is the analysis bandwidth that will be
> > applied.  If the analysis bandwidth is wider than the adaptive filter
> > resolution then filtering out adjacent random noise is helpful.  If the
> > analysis bandwidth is equal to or narrower than the adaptive filter
> > resolution, then random noise within the analysis bands isn't reduced.
> > So, it helps to know the processing that will follow.  I believe that
> > usually the processing *is* this filter so the latter applies.
>
> > Fred
>
> Fred,
> The adaptive line enhancer (ALE) is a specific form of the LMS/NLMS
> algorithm where the reference is constructed by delaying the input.
> This means the input must be correlated with some delayed version of
> itself for the ALE to work. Therefore, the ALE can not reduce random
> noise. The ALE is indeed a form of notch filter.
>
> Maurice Givens- Hide quoted text -
>
> - Show quoted text -

Let me make an addendum. The input signal is the reference in the
tradictional sense of the LMS algorithm. The input to the ALE is a
delayed version of the input (reference). Boy, that sure clears things
up!! :)

Maurice
From: illywhacker on 4 Jun 2010 13:14
On Jun 4, 5:54 pm, maury <maury...(a)core.com> wrote:
> On Jun 4, 10:48 am, maury <maury...(a)core.com> wrote:
>
>
>
>
>
> > On Jun 3, 7:30 pm, Fred Marshall <fmarshallx(a)remove_the_xacm.org>
> > wrote:
>
> > > illywhacker wrote:
> > > > On Jun 2, 1:21 am, "bos1234" <suren130(a)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??
>
> > > > Google 'denoising'. There is a vast literature on this. Of course, you
> > > > need to know *something* about your signal and your noise.
>
> > > > illywhacker;
>
> > > Right.
>
> > > In the automatic line canceler the "something" is the "reference signal"
> > > which might be taken from a machine accelerometer or some such source..
> > > Then, if the machine is an interferer, it can be subtracted out subject
> > > to being adjusted magnitude and phase vs. frequency which is what the
> > > adaptive part of the filter is doing.
>
> > > So, in a line canceler (where the "noise" has relatively steady (i.e.
> > > short term stable) spectral character, a burst of energy in the signal
> > > of interest, while being at exactly one of the eliminated line
> > > frequencies, will go right through.  This is because a stable line is
> > > being subtracted - which is not the same as a notch filter.
> > > And, come to think of it, so will such a burst in [only] the reference
> > > signal because the gain won't change fast enough.
> > > But, an equal burst in both of them (presumably from the reference
> > > source)  will be canceled if the amplitudes match.
>
> > > I suppose one could say that it has the same sort of limitation as a
> > > differentiator - it adjusts the difference between two signals working
> > > toward zero.  So, small perturbations (differences in the difference)
> > > likely look relatively big at the output.
>
> > > In an automatic line enhancer, there is no such reference and a "big
> > > enough" delay is used to generate something like a reference where
> > > random noise is decorrelated.  Then, the adaptation goes the same way -
> > > to eliminate energy in the output (the sum of the unfiltered signal path
> > > and the adaptive block).  Since one can only reduce the sum of two
> > > uncorrelated noises by shutting one off completely, the adaptive block
> > > acts to shut off random noise and passes sinusoids.  And then, the
> > > useful output is taken from the adaptive filter block as it is a
> > > bandpass filter on all stable sinusoids.
> > > In this case, having no reference, it ends up looking like a modestly
> > > dynamic "comb" of bandpasses and in-band noise is passed through.
>
> > > In the context of the line enhancer, which is a filter to reduce random
> > > noise, on top of all this is the analysis bandwidth that will be
> > > applied.  If the analysis bandwidth is wider than the adaptive filter
> > > resolution then filtering out adjacent random noise is helpful.  If the
> > > analysis bandwidth is equal to or narrower than the adaptive filter
> > > resolution, then random noise within the analysis bands isn't reduced..
> > > So, it helps to know the processing that will follow.  I believe that
> > > usually the processing *is* this filter so the latter applies.
>
> > > Fred
>
> > Fred,
> > The adaptive line enhancer (ALE) is a specific form of the LMS/NLMS
> > algorithm where the reference is constructed by delaying the input.
> > This means the input must be correlated with some delayed version of
> > itself for the ALE to work. Therefore, the ALE can not reduce random
> > noise. The ALE is indeed a form of notch filter.
>
> > Maurice Givens- Hide quoted text -
>
> > - Show quoted text -
>
> Let me make an addendum. The input signal is the reference in the
> tradictional sense of the LMS algorithm. The input to the ALE is a
> delayed version of the input (reference). Boy, that sure clears things
> up!!  :)
>
> Maurice- Hide quoted text -
>
> - Show quoted text -

You know, no one on here is going to buy your magic line enhancer. I
suggest you try to sell it elsewhere.

illywhacker;
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