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### Filtering Noise from a signal

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```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??
```
 0

```On Jun 2, 1:21=A0am, "bos1234" <suren130@n_o_s_p_a_m.gmail.com> wrote:
> In class we analysed a signal and filtered the noise out. However the noi=
se
> 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

illywhacker;
```
 0

```illywhacker wrote:
> On Jun 2, 1:21 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??
>
> Google 'denoising'. There is a vast literature on this. Of course, you
>
> 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
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
```
 0

```On Jun 4, 2:30=A0am, Fred Marshall <fmarshallx@remove_the_xacm.org>
wrote:
> illywhacker wrote:
> > On Jun 2, 1:21 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 a=
ny
> >> techniques to filter out the noise??
>
> > Google 'denoising'. There is a vast literature on this. Of course, you
>
> > 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. =A0This 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) =A0will 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. =A0So, 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. =A0Then, the adaptation goes the same way -
> to eliminate energy in the output (the sum of the unfiltered signal path
> and the adaptive block). =A0Since 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. =A0And 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. =A0If the analysis bandwidth is wider than the adaptive filter
> resolution then filtering out adjacent random noise is helpful. =A0If 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. =A0I 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;
```
 0

```On Jun 3, 7:30=A0pm, Fred Marshall <fmarshallx@remove_the_xacm.org>
wrote:
> illywhacker wrote:
> > On Jun 2, 1:21 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 a=
ny
> >> techniques to filter out the noise??
>
> > Google 'denoising'. There is a vast literature on this. Of course, you
>
> > 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. =A0This 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) =A0will 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. =A0So, 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. =A0Then, the adaptation goes the same way -
> to eliminate energy in the output (the sum of the unfiltered signal path
> and the adaptive block). =A0Since 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. =A0And 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. =A0If the analysis bandwidth is wider than the adaptive filter
> resolution then filtering out adjacent random noise is helpful. =A0If 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. =A0I 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
```
 0

```On Jun 4, 10:48=A0am, maury <maury...@core.com> wrote:
> On Jun 3, 7:30=A0pm, Fred Marshall <fmarshallx@remove_the_xacm.org>
> wrote:
>
>
>
>
>
> > illywhacker wrote:
> > > On Jun 2, 1:21 am, "bos1234" <suren130@n_o_s_p_a_m.gmail.com> wrote:
> > >> In class we analysed a signal and filtered the noise out. However th=
e noise
> > >> was in a different bandwidth to the original signal hence it was eas=
y 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, yo=
u
>
> > > 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. =A0This 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) =A0will 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. =A0So, 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. =A0Then, the adaptation goes the same way=
-
> > to eliminate energy in the output (the sum of the unfiltered signal pat=
h
> > and the adaptive block). =A0Since 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. =A0And 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. =A0If the analysis bandwidth is wider than the adaptive filter
> > resolution then filtering out adjacent random noise is helpful. =A0If t=
he
> > 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. =A0I 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
```
 0

```On Jun 4, 5:54=A0pm, maury <maury...@core.com> wrote:
> On Jun 4, 10:48=A0am, maury <maury...@core.com> wrote:
>
>
>
>
>
> > On Jun 3, 7:30=A0pm, Fred Marshall <fmarshallx@remove_the_xacm.org>
> > wrote:
>
> > > illywhacker wrote:
> > > > On Jun 2, 1:21 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 e=
asy to
> > > >> filter.
>
> > > >> If noise and the signal were to overlap in freq. spectrum, are the=
re any
> > > >> techniques to filter out the noise??
>
> > > > Google 'denoising'. There is a vast literature on this. Of course, =
you
>
> > > > illywhacker;
>
> > > Right.
>
> > > In the automatic line canceler the "something" is the "reference sign=
al"
> > > which might be taken from a machine accelerometer or some such source=
..
> > > Then, if the machine is an interferer, it can be subtracted out subje=
ct
> > > 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 signa=
l
> > > of interest, while being at exactly one of the eliminated line
> > > frequencies, will go right through. =A0This 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 referenc=
e
> > > signal because the gain won't change fast enough.
> > > But, an equal burst in both of them (presumably from the reference
> > > source) =A0will 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 workin=
g
> > > toward zero. =A0So, small perturbations (differences in the differenc=
e)
> > > 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. =A0Then, the adaptation goes the same w=
ay -
> > > to eliminate energy in the output (the sum of the unfiltered signal p=
ath
> > > and the adaptive block). =A0Since one can only reduce the sum of two
> > > uncorrelated noises by shutting one off completely, the adaptive bloc=
k
> > > acts to shut off random noise and passes sinusoids. =A0And 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 rand=
om
> > > noise, on top of all this is the analysis bandwidth that will be
> > > applied. =A0If the analysis bandwidth is wider than the adaptive filt=
er
> > > resolution then filtering out adjacent random noise is helpful. =A0If=
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. =A0I believe th=
at
> > > 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!! =A0:)
>
> 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;
```
 0

```maury wrote:
> On Jun 4, 10:48 am, maury <maury...@core.com> wrote:
>> On Jun 3, 7:30 pm, Fred Marshall <fmarshallx@remove_the_xacm.org>
>> wrote:
>>
>>
>>
>>
>>
>>> illywhacker wrote:
>>>> On Jun 2, 1:21 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??
>>>> Google 'denoising'. There is a vast literature on this. Of course, you
>>>> 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

Maurice,

Gee.  That's what I tried to say!!
with:
In this case, having no reference, it ends up looking like a modestly
dynamic "comb" of bandpasses and in-band noise is passed through.

But I'd say that the ALE is a form of bandpass filter - considering
where you take the output and that filter's frequency response.   Oh
well, pass sinusoids, notch noise, same filter different words.
I generally think of notches and bandpasses as narrow and I think of an
ALE as having wide notches and narrow bandpasses - purely perspective
there.

Fred
```
 0

```illywhacker wrote:
> On Jun 4, 5:54 pm, maury <maury...@core.com> wrote:
-
>
> You know, no one on here is going to buy your magic line enhancer. I
> suggest you try to sell it elsewhere.
>
> illywhacker;

????

I was just quoting some facts.
I responded to your post because you said:

In contrast with the ANC where we "know" the reference signal, the ALE
is one where we "don't know" anything about the elusive reference signal.

I guess it depends on what we mean by "know something".
Maurice made it clearer what that "known" thing is in the case of an ALE:
It passes signal components that are correlated.

So, if we "know" that this is what we want (which is more often the case
than not) then it does something useful by reducing random noise
overall.  But, it doesn't reduce random noise in the bands that are
passed.  And, it doesn't seem to me that this is much knowledge about
the signal really.  But you can argue that point.

I'm not selling anything.  Just discussing characteristics as best I can.

bit of selling going on:

Grooup 1 and Group 2 were competitors.
Group 1 was invested in their FFT boxes.
Group 2 was invested in their ALE boxes.
Group 1 declared that the ALE boxes provided no benefit in order to show
that they were smarter than Group 2 and that Group 2 didn't know what

It seemed that Group 1 was reasonably correct as long as the signal
It seemed that Group 2 was justified in debating this point because the
signal space wasn't always static.
Eventually a side-by-side test in some practical context was done that
showed the ALE did something useful.
Of course, a lot depends on the application and the post processing
that's done.....

Fred

```
 0

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