Noise Is 3 Orders of Magnitude Greater Than A Wave Form

[John Larkin]

On Fri, 3 Jul 2009 15:25:42 -0700 (PDT), Bret Cahill
<BretCahill@aol.com> wrote:

The sensor receives the loud noise, say, 10sin(0.7x),  plus the small
signal, say, sin(x ).  The signal, however, can be transformed into sin
(x)sin^2(100x) so the sensor receives

(10sin(0.7x) + sin(x)sin^2(100x))       x from 2 to 3.4

What you are doing is changing the problem.

As I pointed out above, I forgot to mention in the OP that the
designer could change the signal to suit the problem.

You are now looking at a
sin(100x) modulated by sin(x).

Actually it's a sin^2(100x) which is always positive.

Which is equivalent to 100% amplitude modulating at 200x.

Square wave chopping would work, too. That's more common in
synchronous detection instruments.

John

 

[doug]

John Larkin wrote:

On Fri, 3 Jul 2009 15:25:42 -0700 (PDT), Bret Cahill
BretCahill@aol.com> wrote:


The sensor receives the loud noise, say, 10sin(0.7x), plus the small
signal, say, sin(x ). The signal, however, can be transformed into sin
(x)sin^2(100x) so the sensor receives

(10sin(0.7x) + sin(x)sin^2(100x)) x from 2 to 3.4

What you are doing is changing the problem.

As I pointed out above, I forgot to mention in the OP that the
designer could change the signal to suit the problem.


You are now looking at a
sin(100x) modulated by sin(x).

Actually it's a sin^2(100x) which is always positive.


Which is equivalent to 100% amplitude modulating at 200x.

Square wave chopping would work, too. That's more common in
synchronous detection instruments.

John

Bret apparently has decided he knows physics and signal
processing better than all of us. I have no idea why he
is posting since he claims we are all wrong. He seems
to think the laws of physics do not apply to him.

 

[John Fields]

On Fri, 03 Jul 2009 23:23:10 -0800, doug <xx@xx.com> wrote:

Bret apparently has decided he knows physics and signal
processing better than all of us. I have no idea why he
is posting since he claims we are all wrong. He seems
to think the laws of physics do not apply to him.

---
Cahill is nothing more than a troll who posts for attention.

JF

 

[Greg Ewing]

Bret Cahill wrote:

Convert the signal to a higher frequency wave form that still has
characteristics of the original signal.

Yes, certainly. *If* you have a suitable noise-free
frequency band available, this is quite easy to do.
No revolutionary techniques are required.

Your example assumes that you do indeed have such
a band available, at about 100x the original signal
frequency, and wide enough to accommodate the
bandwidth of your signal.

In that case, the problem is easy to solve. Just
modulate your signal onto a carrier somehow (you're
using AM, but you could just as well use FM or some
other technique), use a filter at the receiving end
to separate the carrier from the noise, and then
demodulate.

Although it might not seem that way, this *is* what
you are effectively doing. You're just using a
somewhat unconventional technique to do the filtering
and demodulation. There may be simpler ways, e.g.
instead of sampling the zero crossings to cancel the
noise, just sample the peaks and troughs of the
carrier to measure its amplitude.

You don't strictly need to know the exact frequency
and phase of the carrier, although if you do happen
to know it, you can take advantage of that to
simplify any sample-oriented processing you want to
do.

What others are talking about concerning averaging
is what you need to do if you *don't* have a noise-free
band available, and you've no choice but to deal with
signal and noise together in the same band. In that
case, the only way to reduce noise is to reduce the
receiver's bandwith *somehow*, and averaging is one way
to achieve that -- and knowing the frequency and phase
of your carrier is a big help, because it lets you
implement a synchronous detector.

But as I said, you're assuming that you *can* find a
noise-free band, so you don't need averaging (except
maybe over a few cycles of your carrier frequency,
which is much higher than your signal frequency).

--
Greg

 

[Bob Masta]

On Fri, 03 Jul 2009 09:58:42 -0800, doug
<xx@xx.com> wrote:

Bret Cahill wrote:

http://www.daqarta.com/tm01.htm


I'm not saying your approach won't work in my case but your Fig. 1
isn't exactly my situation.

It is the same situation just the spectrum of the noise is different.
In all of this, the game is the same because the physics is the
same. To get a signal to noise ratio or signal to interference ratio
larger than one, you need a bandwidth where the noise is smaller
than the signal. Averaging, which is applying a narrow bandpass
filter helps most for random noise.

Note that synchronous waveform averaging is *not*
a filter, and does not affect the bandwidth of the
recovered signal in the least. You still get
sharp transients, for example, if they were
present in the original.

Synchronous waveform averaging will reject any
signal that is not synchronous with the trigger,
not just random noise.

Best regards,


Bob Masta

DAQARTA v4.51
Data AcQuisition And Real-Time Analysis
www.daqarta.com
Scope, Spectrum, Spectrogram, Sound Level Meter
FREE Signal Generator
Science with your sound card!

 

[iman islam]

What are the ‘Five Pillars’ of Islam?
August 31st, 2008
I would be thankful if you give my article 5 minute of your value
time.

THANK YOU

What are the ‘Five Pillars’ of Islam?

They are the framework of the Muslim life: faith, prayer, concern for
the needy, self-purification, and the pilgrimage to Makkah for those
who are able.

First Pillar: Faith

There is no god worthy of worship except God and Muhammad is His
messenger. This declaration of faith is called the Shahada, a simple
formula which all the faithful pronounce. In Arabic, the first part is
la ilaha illa’Llah - ‘there is no god except God’; ilaha (god) can
refer to anything which we may be tempted to put in place of God–
wealth, power, and the like. Then comes illa’Llah: ‘except God’, the
source of all Creation. The second part of the Shahada is Muhammadun
rasulu’Llah: ‘Muhammad is the messenger of God.’ A message of guidance
has come through a man like ourselves.

Second Pillar: Prayer

Salat is the name for the obligatory prayers which are performed five
times a day, and are a direct link between the worshiper and God.
There is no hierarchical authority in Islam, and no priests, so the
prayers are led by a learned person who knows the Quran, chosen by the
congregation. These five prayers contain verses from the Quran, and
are said in Arabic, the language of the Revelation, but personal
supplication can be offered in one’s own language.

Prayers are said at dawn, noon, mid-afternoon, sunset and nightfall,
and thus determine the rhythm of the entire day. Although it is
preferable to worship together in a mosque, a Muslim may pray almost
anywhere, such as in fields, offices, factories and universities.
Visitors to the Muslim world are struck by the centrality of prayers
in daily life.

A translation of the Call to Prayer is:

‘God is most great. God is most great. God is most great. God is most
great. I testify that there is no god except God. I testify that there
is no god except God. I testify that Muhammad is the messenger of God.
I testify that Muhammad is the messenger of God. Come to prayer! Come
to prayer! Come to success (in this life and the Hereafter)! Come to
success! God is most great. God is most great. There is no god except
God.’

Once Muslims prayed towards Jerusalem, but during the Prophet’s
lifetime it was changed to Makkah. From the minbar, the pulpit, the
Imam who leads the prayer gives the sermon at the Friday noon
community prayers.

Third Pillar: Zakat

One of the most important principles of Islam is that all things
belong to God, and that wealth is therefore held by human beings in
trust. The word zakat means both ‘purification’ and ‘growth’. Our
possessions are purified by setting aside a proportion for those in
need, and, like the pruning of plants, this cutting back balances and
encourages new growth.

Each Muslim calculates his or her own zakat individually. For most
purposes this involves the payment each year of two and a half percent
of one’s capital. A pious person may also give as much as he or she
pleases as sadaqa, and does so preferably in secret. Although this
word can be translated as ‘voluntary charity’ it has a wider meaning.
The Prophet (SAW) said: ‘Even meeting your brother with a cheerful
face is charity.’

The Prophet (SAW) said: ‘Charity is a necessity for every Muslim.’ He
was asked: ‘What if a person has nothing?’ The Prophet (SAW) replied:
‘He should work with his own hands for his benefit and then give
something out of such earnings in charity.’ The Companions asked:
‘What if he is not able to work?’ The Prophet (SAW) said: ‘He should
help poor and needy persons.’ The Companions further asked ‘What if he
cannot do even that?’ The Prophet (SAW) said ‘He should urge others to
do good.’ The Companions said ‘What if he lacks that also?’ The
Prophet (SAW) said ‘He should check himself from doing evil. That is
also charity.’

Fourth Pillar: The Fast

Every year in the month of Ramadan, all Muslims fast from first light
until sundown, abstaining from food, drink, and sexual relations.
Those who are sick, elderly, or on a journey, and women who are
pregnant or nursing are permitted to break the fast and make up an
equal number of days later in the year. If they are physically unable
to do this, they must feed a needy person for every day missed.
Children begin to fast (and to observe the prayer) from puberty,
although many start earlier.

Although the fast is most beneficial to the health, it is regarded
principally as a method of self purification. By cutting oneself off
from worldly comforts, even for a short time, a fasting person gains
true sympathy with those who go hungry as well as growth in one’s
spiritual life.

Fifth Pillar: The Pilgrimage (Hajj)

The annual pilgrimage to Makkah, the Hajj, is an obligation only for
those who are physically and financially able to perform it.
Nevertheless, about two million people go to Makkah each year from
every comer of the globe providing a unique opportunity for those of
different nations to meet one another. Although Makkah is always
filled with visitors, the annual Hajj begins in the twelfth month of
the Islamic year (which is lunar, not solar, so that Hajj and Ramadan
fall sometimes in summer, sometimes in winter). Pilgrims wear special
clothes: simple garments which strip away distinctions of class and
culture, so that all stand equal before God.

The rites of the Hajj, which are of Abrahamic origin, include circling
the Ka’ba seven times, and going seven times between the mountains of
Safa and Marwa as did Hagar during her search for water. Then the
pilgrims stand together on the wide plain of Arafa and join in prayers
for God’s forgiveness, in what is often thought of as a preview of the
Last Judgment.

In previous centuries the Hajj was an arduous undertaking. Today,
however, Saudi Arabia provides millions of people with water, modem
transport, and the most up-to-date health facilities.

The close of the Hajj is marked by a festival, the Eid al-Adha, which
is celebrated with prayers and the exchange of gifts in Muslim
communities everywhere. This, and the Eid al-Fitr, a feast-day
commemorating the end of Ramadan, are the main festivals of the Muslim
calendar.


—————————————-

For more information about Islam

http://english.islamway.com/

http://www.islamhouse.com/

http://www.discoverislam.com/

http://www.islambasics.com/index.php

http://english.islamway.com/

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http://www.islamweb.net/ver2/MainPage/indexe.php

http://www.sultan.org/

Contact Us At

Imanway.group@gmail.com

 

[John Fields]

On Sat, 4 Jul 2009 03:13:50 -0700 (PDT), iman islam
<imanway2010@gmail.com> wrote:

What are the ‘Five Pillars’ of Islam?
August 31st, 2008
I would be thankful if you give my article 5 minute of your value
time.

---
OK, I read your article and now I have a question for you:

If Allah is all-powerful and knows the future, then he knows what is
going to happen from moment to moment, and how we live our lives is
unimportant since he will know in advance what we will do with them.

On the other hand, if we can exercise free will, then Allah can't
predict the future and isn't, as you claim, omniscient.

I've posed this question, many times, to you people, but have not yet
received a response of any kind.

I don't suppose this time will be any different.

JF

 

[John Larkin]

On Fri, 03 Jul 2009 23:23:10 -0800, doug <xx@xx.com> wrote:

John Larkin wrote:

On Fri, 3 Jul 2009 15:25:42 -0700 (PDT), Bret Cahill
BretCahill@aol.com> wrote:


The sensor receives the loud noise, say, 10sin(0.7x), plus the small
signal, say, sin(x ). The signal, however, can be transformed into sin
(x)sin^2(100x) so the sensor receives

(10sin(0.7x) + sin(x)sin^2(100x)) x from 2 to 3.4

What you are doing is changing the problem.

As I pointed out above, I forgot to mention in the OP that the
designer could change the signal to suit the problem.


You are now looking at a
sin(100x) modulated by sin(x).

Actually it's a sin^2(100x) which is always positive.


Which is equivalent to 100% amplitude modulating at 200x.

Square wave chopping would work, too. That's more common in
synchronous detection instruments.

John

Bret apparently has decided he knows physics and signal
processing better than all of us. I have no idea why he
is posting since he claims we are all wrong. He seems
to think the laws of physics do not apply to him.

He seems to have some idea for a gedget that needs synchronous
detection to do some measurement. But of course he'll never reveal
what he's actually trying to do. And he won't do any research on how
everybody else has been doing it for 60 years or so.

John

 

[John Larkin]

On Fri, 3 Jul 2009 11:30:19 -0700 (PDT), Bret Cahill
<BretCahill@aol.com> wrote:

http://www.daqarta.com/tm01.htm

I'm not saying your approach won't work in my case but your Fig. 1
isn't exactly my situation.

It is the same situation just the spectrum of the noise is different.

Which is everything when you want to reduce noise.

Not everything.

In all of this, the game is the same because the physics is the
same.

The math is entirely different. A smooth low frequency noise curve
can be sampled fewer times over longer intervals and the result can be
very accurate, especially with regression.

To get a signal to noise ratio or signal to interference ratio
larger than one, you need a bandwidth where the noise is smaller
than the signal.  

Convert the signal to a higher frequency wave form that still has
characteristics of the original signal.

Great as long as you don't do that to the noise, too.

John

 

In sci.physics Bret Cahill <BretCahill@aol.com> wrote:

Convert the signal to a higher frequency wave form that still has
characteristics of the original signal.

Great as long as you don't do that to the noise, too.

I'm still expecting some scholar to say this was done in the early
1880s.


Bret Cahill

Actually in 1918 by Edwin Armstrong.


--
Jim Pennino

Remove .spam.sux to reply.

 

[Bret Cahill]

I'm not saying your approach won't work in my case but your Fig. 1
isn't exactly my situation.

It is the same situation just the spectrum of the noise is different.
In all of this, the game is the same because the physics is the
same. To get a signal to noise ratio or signal to interference ratio
larger than one, you need a bandwidth where the noise is smaller
than the signal.  Averaging, which is applying a narrow bandpass
filter helps most for random noise.

Note that synchronous waveform averaging is *not*
a filter, and does not affect the bandwidth of the
recovered signal in the least.  

That's also true for the squared higher frequency sin wave method of
subtracting noise. A conventional filter doesn't determine the
amplitude of the noise and then subtract it. A conventional filter
just attenuates noise above or below a certain bandwith.

If the noise is about the same frequency as the signal, then a
conventional filter will not work.

You still get
sharp transients, for example, if they were
present in the original.

Filters can toss information as well as noise.

Synchronous waveform averaging will reject any
signal that is not synchronous with the trigger,
not just random noise.

The higher frequency sin^2 method doesn't require an average. In one
application all it takes is one period of ["sampling" by] the high
frequency wave to determine the noise as well as the signal.

Using regression and integrating over even part of the period of a
smooth low frequency noise wave would yield very high precision, even
if the "sampling" rate was fairly low.

              DAQARTA  v4.51
   Data AcQuisition And Real-Time Analysis
             www.daqarta.com

Can you reduce smooth well behaved low frequency noise by 99.995%?


Bret Cahill

 

[Bret Cahill]

Convert the signal to a higher frequency wave form that still has
characteristics of the original signal.

Yes, certainly. *If* you have a suitable noise-free
frequency band available, this is quite easy to do.
No revolutionary techniques are required.

The situation is so common and the applications so widespread and the
solution such a short distance "off trail" I was assuming they already
had 10,000 dirt cheap off-the-shelf versions of it as they generally
do in electronics.

That was the reason for the OP. Someone was supposed to answer, "TI
sells exactly what you want in their 87WA3 series. Anyone can wire
'em up in 5 minutes. I used them for blah blah blah . . ."

I was expecting / hoping for more responses like the www.DAQARTA.com
guy's.

It was only later that I came up with the sin^2 method and that was
presented mostly to clarify the OP, not to answer it.

Your example assumes that you do indeed have such
a band available, at about 100x the original signal
frequency, and wide enough to accommodate the
bandwidth of your signal.

Or the squared modulated signal.

In that case, the problem is easy to solve. Just
modulate your signal onto a carrier somehow (you're
using AM, but you could just as well use FM or some
other technique),

For lack of better terms I used/abused the AM/FM analogy on the two
basic solutions that led me here in the first place. The one I was
calling "FM" circumvents the noise issue altogether and has an easy to
enter niche market but the "AM" one has a noise issue but is much
cheaper and has a much larger market.

So I had the FM/AM mindset too but true/conventional AM doesn't square
the high frequency wave.

This is a critical difference.

use a filter at the receiving end
to separate the carrier from the noise, and then
demodulate.

Although it might not seem that way, this *is* what
you are effectively doing. You're just using a
somewhat unconventional technique to do the filtering
and demodulation.

So I have until July 2, 2010 to file a PPA.

There may be simpler ways, e.g.
instead of sampling the zero crossings to cancel the
noise, just sample the peaks and troughs of the
carrier to measure its amplitude.

Actually that would _not_ work.

My background isn't signal processing but now I'm starting to wonder
if the hold up behind the larger solution might be traceable to a hold
up in electronics.

You don't strictly need to know the exact frequency
and phase of the carrier, although if you do happen
to know it, you can take advantage of that to
simplify any sample-oriented processing you want to
do.

What others are talking about concerning averaging
is what you need to do if you *don't* have a noise-free
band available, and you've no choice but to deal with
signal and noise together in the same band. In that
case, the only way to reduce noise is to reduce the
receiver's bandwith *somehow*, and averaging is one way
to achieve that -- and knowing the frequency and phase
of your carrier is a big help, because it lets you
implement a synchronous detector.

But as I said, you're assuming that you *can* find a
noise-free band, so you don't need averaging (except
maybe over a few cycles of your carrier frequency,
which is much higher than your signal frequency).

Some California physicist suggested it was impossible to destroy
information and recently S. Hawkings agreed. Shred and burn your
notes then put the ashes on a rocket headed toward a black hole and
10^68 years from now they'll know what you were trying to hide. The
same holds for DNA and your life experiences so everyone is in effect
immortal.

That's one very good reason to believe efforts at reducing noise /
getting information will be fruitful. I don't want to wait 10^67
years for it but then again, I'm not trying to destroy it either.


Bret Cahill

 

[Bret Cahill]

Convert the signal to a higher frequency wave form that still has
characteristics of the original signal.

Great as long as you don't do that to the noise, too.

I'm still expecting some scholar to say this was done in the early
1880s.


Bret Cahill

 

[John Larkin]

On Sat, 4 Jul 2009 12:24:15 -0700 (PDT), Bret Cahill
<BretCahill@aol.com> wrote:

Everything is known about the transmitted wave, i.e., the shape &
phase angle, except the amplitude.

All that is necessary is to recover is the amplitude of the wave.  Can
this be done when the noise is several orders of magnitude greater
than the signal?

Bret Cahill

Narrowing the final detection bandwidth is the only hope.
If the noise spectrum is white, narrow bandwidth through
averaging works. If you cannot average, there is trouble.
The old lockin amplifiers used a modulation or chopping signal
and a long time constant in the final filter.  I had signals
at times that required an hour of integration to detect. It
was slow but it worked.

I forgot to mention that the signal wave form can be anything that can
be generated.

For example, if something similar to an AM radio signal, say, f(t) =
(sint)(sin10t)(sin10t) was possible and the frequency of the noise was
about the same as the sin(t) factor, then f(t) will plot the noise
every time f(t) = 0.

In this case that would be ten times as often as the sin(t) factor.

The noise can then be subtracted to recover the wave form.

Bret Cahill

I think what's happening is that you have

1. Defined the noise to be bandlimited to radian frequencies below
about 1

The noise and the signal are both low and have about the same
frequency, ~ x/2pi.  There is little that can be done to change this
situation.  There is no time to wait more than several cycles for the
result either.

and

2. Up-converted (modulated) the signal to have usable (recoverable)
components around 10 times that frequency.

To plot the noise.  Every time sin 10t = 0, f(t) = zero, and the only
thing left is the low frequency noise.

You are assuming the ability to high-frequency modulate the signal
before the noise is added to it. So you already know what the
noiseless signal looks like.

As I said in the OP, "Everything is known about the transmitted wave,
i.e., the shape & phase angle, except the amplitude."

This works for the same reason reading a newspaper in a foreign
language is easy.  You already know what they are going to say.

Bret Cahill

Are you familiar with the way a lockin amplifier works?

Many thanks for the tip but phase lag is just a more sophisticated
form of filtering which is valuable in many situations where the noise
is all over the spectrum.

A lockin doesn't work by phase lag; it works by correlation.

This is not filtering noise; it's measuring it then subtracting it.

Basically the signal is brought to zero to identify the noise. Then
the noise is subtracted from whatever the receiver is putting out.

That only works if the zero+measure thing is done at or above the
noise's Nyquist frequency, and that is in turn only meaningful if the
noise is bandlimited.

And you are able somehow to turn the signal on and off at that rate.

So all you need is a highpass filter. But the math algorithm you
describe is about equivalent.

For an accurate signal measurement both the noise and the noise +
signal output from the receiver must be known to a higher accuracy.

Integrating should yield that higher accuracy but it isn't always
necessary as it can work over _one single higher frequency wave
cycle_.

That sounds
maybe like what you are doing. If you know everything about the signal
but its amplitude, then you have or can construct a normalized (unity
amplitude) version of it. That will positively correlate with the
unknown-amplitude version of the signal but have zero correlation to
random noise.

Things like IR absorption spectrometers commonly chop (square wave
modulate) the light source and recover the signal with a synchronous
rectifier. That washes out any noise picked up in the optical path or
the detector. Things like this commonly dig signals out from 1000x the
noise... but slowly.

If the noise is known to be bandlimited, it's a lot easier... almost
cheating.

I ran it by a lawyer and he said it was completely legal.

I thought you *were* a lawyer.

John

 

In sci.physics Bret Cahill <BretCahill@aol.com> wrote:

On Jul 4, 10:45 am, j...@specsol.spam.sux.com wrote:
In sci.physics Bret Cahill <BretCah...@aol.com> wrote:

Convert the signal to a higher frequency wave form that still has
characteristics of the original signal.

Great as long as you don't do that to the noise, too.

I'm still expecting some scholar to say this was done in the early
1880s.

Bret Cahill

Actually in 1918 by Edwin Armstrong.

Amplitude of the high(er) frequency wave is modulated by the signal
curve.

Put sinxsin^2(10x) into

www.wolframalpha.com to see the difference with the common AM radio
signal.


Bret Cahill

Who cares and it is irrelevant to what I posted.


--
Jim Pennino

Remove .spam.sux to reply.

 

[Bret Cahill]

Everything is known about the transmitted wave, i.e., the shape &
phase angle, except the amplitude.

All that is necessary is to recover is the amplitude of the wave.  Can
this be done when the noise is several orders of magnitude greater
than the signal?

Bret Cahill

Narrowing the final detection bandwidth is the only hope.
If the noise spectrum is white, narrow bandwidth through
averaging works. If you cannot average, there is trouble.
The old lockin amplifiers used a modulation or chopping signal
and a long time constant in the final filter.  I had signals
at times that required an hour of integration to detect. It
was slow but it worked.

I forgot to mention that the signal wave form can be anything that can
be generated.

For example, if something similar to an AM radio signal, say, f(t) > >> >> >(sint)(sin10t)(sin10t) was possible and the frequency of the noise was
about the same as the sin(t) factor, then f(t) will plot the noise
every time f(t) = 0.

In this case that would be ten times as often as the sin(t) factor..

The noise can then be subtracted to recover the wave form.

Bret Cahill

I think what's happening is that you have

1. Defined the noise to be bandlimited to radian frequencies below
about 1

The noise and the signal are both low and have about the same
frequency, ~ x/2pi.  There is little that can be done to change this
situation.  There is no time to wait more than several cycles for the
result either.

and

2. Up-converted (modulated) the signal to have usable (recoverable)
components around 10 times that frequency.

To plot the noise.  Every time sin 10t = 0, f(t) = zero, and the only
thing left is the low frequency noise.

You are assuming the ability to high-frequency modulate the signal
before the noise is added to it. So you already know what the
noiseless signal looks like.

As I said in the OP, "Everything is known about the transmitted wave,
i.e., the shape & phase angle, except the amplitude."

This works for the same reason reading a newspaper in a foreign
language is easy.  You already know what they are going to say.

Bret Cahill

Are you familiar with the way a lockin amplifier works?

Many thanks for the tip but phase lag is just a more sophisticated
form of filtering which is valuable in many situations where the noise
is all over the spectrum.

This is not filtering noise; it's measuring it then subtracting it.

Basically the signal is brought to zero to identify the noise. Then
the noise is subtracted from whatever the receiver is putting out.

For an accurate signal measurement both the noise and the noise +
signal output from the receiver must be known to a higher accuracy.

Integrating should yield that higher accuracy but it isn't always
necessary as it can work over _one single higher frequency wave
cycle_.

That sounds
maybe like what you are doing. If you know everything about the signal
but its amplitude, then you have or can construct a normalized (unity
amplitude) version of it. That will positively correlate with the
unknown-amplitude version of the signal but have zero correlation to
random noise.

Things like IR absorption spectrometers commonly chop (square wave
modulate) the light source and recover the signal with a synchronous
rectifier. That washes out any noise picked up in the optical path or
the detector. Things like this commonly dig signals out from 1000x the
noise... but slowly.

If the noise is known to be bandlimited, it's a lot easier... almost
cheating.

I ran it by a lawyer and he said it was completely legal.


Bret Cahill

 

[Bret Cahill]

On Jul 4, 10:45 am, j...@specsol.spam.sux.com wrote:

In sci.physics Bret Cahill <BretCah...@aol.com> wrote:

Convert the signal to a higher frequency wave form that still has
characteristics of the original signal.

Great as long as you don't do that to the noise, too.

I'm still expecting some scholar to say this was done in the early
1880s.

Bret Cahill

Actually in 1918 by Edwin Armstrong.

Amplitude of the high(er) frequency wave is modulated by the signal
curve.

Put sinxsin^2(10x) into

www.wolframalpha.com to see the difference with the common AM radio
signal.


Bret Cahill

 

[greg]

Bret Cahill wrote:

A conventional filter doesn't determine the
amplitude of the noise and then subtract it. A conventional filter
just attenuates noise above or below a certain bandwith.

But your method doesn't completely eliminate the noise
either. You're approximating it by interpolation, and
assuming that the result is "good enough".

There will always be some residual error -- and that
error is just the same as the residual amount of noise
that a conventional filter with equivalent passband
characteristics would let through.

Filters can toss information as well as noise.

So can your method, since you're assuming you can
interpolate between signal samples as well. To the
extent that's not exactly right, you've lost information.

--
Greg

 

[Bob Masta]

On Sat, 4 Jul 2009 10:10:54 -0700 (PDT), Bret
Cahill <BretCahill@aol.com> wrote:

I'm not saying your approach won't work in my case but your Fig. 1
isn't exactly my situation.

It is the same situation just the spectrum of the noise is different.
In all of this, the game is the same because the physics is the
same. To get a signal to noise ratio or signal to interference ratio
larger than one, you need a bandwidth where the noise is smaller
than the signal. =A0Averaging, which is applying a narrow bandpass
filter helps most for random noise.

Note that synchronous waveform averaging is *not*
a filter, and does not affect the bandwidth of the
recovered signal in the least. =A0

That's also true for the squared higher frequency sin wave method of
subtracting noise. A conventional filter doesn't determine the
amplitude of the noise and then subtract it. A conventional filter
just attenuates noise above or below a certain bandwith.

Just a word of caution about the general scheme of
subtracting noise: I suspect that variations on
this have been re-invented repeatedly, since it
sounds like such a great idea. The problem is
that when you actually go to implement it you find
the big "gotcha": It totally depends upon perfect
phase and amplitude matching. If you subtract a
version of the noise with a slight time or phase
or level shift, the performance goes downhill
drastically, and can even be worse than the raw
signal. In other words, it will be very hard to
make this work as a robust system.

Best regards,


Bob Masta

DAQARTA v4.51
Data AcQuisition And Real-Time Analysis
www.daqarta.com
Scope, Spectrum, Spectrogram, Sound Level Meter
FREE Signal Generator
Science with your sound card!

 

In sci.physics Bret Cahill <BretCahill@aol.com> wrote:

Convert the signal to a higher frequency wave form that still has
characteristics of the original signal.

Great as long as you don't do that to the noise, too.

I'm still expecting some scholar to say this was done in the early
1880s.

Bret Cahill

Actually in 1918 by Edwin Armstrong.

Amplitude of the high(er) frequency wave is modulated by the signal
curve.

Put sinxsin^2(10x) into

www.wolframalpha.comto see the difference with the common AM radio
signal.

Bret Cahill

Who cares

The people who click on threads on signal recovery.

and it is irrelevant to what I posted.

Feel free to start your own thread on whatever you are interested in.


Bret Cahill

Feel free to take your meds.



--
Jim Pennino

Remove .spam.sux to reply.