Noise Is 3 Orders of Magnitude Greater Than A Wave Form

[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. =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.  

It's surprising that a quick way of explaining why it won't work
hasn't appeared as is generally the case in electronics.

Certainly some scholarly type somewhere has a comprehensive list of
signal processing theories and equipment.

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.  

That's not an issue if a smooth noise has a period several times
longer than the higher frequency wave. The higher frequency wave and
the signal that modulates it would clearly appear w/o any
synchronization.

Put 5sin(1.2x) + sinxsin^2(5x) into www.wolframalpha.com

The original signal sinx can be easily retrieved without knowing the
phase or even the exact frequency of the modulated wave.

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.

The obvious problem with the subtracting approach is the sensor must
be much more precise to get a good measurement from the difference of
two large numbers. If you wanted to be +/- 1% accurate and the noise
was 100 times larger than the signal, then the sensor would need 4 sig
fig accuracy.

The period of the noise is so long, however, the sensor could rezero
itself just before and just after each signal measurement.

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Can you eliminate 99.9975% of noise?


Bret Cahill

 

[John Larkin]

On Fri, 3 Jul 2009 08:41:49 -0700 (PDT), Bret Cahill
<BretCahill@aol.com> wrote:

The system will attenuate the low frequency wave more than a high
frequency wave that isn't part of the low frequency wave.

Determining the amount of attenuation of the low frequency wave was,
in fact, the goal.

The high frequency component, however, should attenuate much like the
low frequency wave if it is tracing out the low frequency wave.

If the medium has different attenuation at different frequencies,
emphatically no. The measured attenuation will be the attenuation at
the modulating carrier frequency (complicated by sidebands) and not
the attenuation of the baseline signal. Your proposed modulation
(multiplying by a sin^2 waveform) is even more complex than regular
AM, because it includes a baseband component too. Radio stations
filter that bit out.

(Actually, to get the full solution, you'd have to compute the entire
spectrum of the complex modulated signal, and run each spectral line
through the transfer function of the process, then recombine. Could
get messy.)

If the attenuation is flat over frequency, why bother to modulate?
Just measure at a high frequency, above the range of the bandlimited
noise.

You can't fool Mother Nature with simple tricks.

John

 

[Bret Cahill]

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.

The noise frequency is limited to about +/- 50% - 75% of the signal
frequency.

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

So all you need is a highpass filter.

You'ld lose the signal with a simple filter.

But the math algorithm you
describe is about equivalent.

The signal is transformed to something that has a lot of the
characteristics of the original signal. For example, the integral is
1/2 the integral of the original curve.

The advantage is the transformed curve plots out the difference
between the noise and the transformed signal. Then the noise is
subtracted.

That is not a conventional filter.


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

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

 

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

On Jul 5, 9:00 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.comtosee 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.

Feel free to take your meds.

Just admit to yourself what is obvious to everyone else. You never
had any interest in this subject in the first place.

The dunces are like a bunch of chickens or school of mackerel. They
are attracted to anything shiny.

Then they reveal that they are dunces.


Bret Cahill

Yet more babble.


--
Jim Pennino

Remove .spam.sux to reply.

 

[Bret Cahill]

The system will attenuate the low frequency wave more than a high
frequency wave that isn't part of the low frequency wave.

Determining the amount of attenuation of the low frequency wave was,
in fact, the goal.

The high frequency component, however, should attenuate much like the
low frequency wave if it is tracing out the low frequency wave.

If the medium has different attenuation at different frequencies,
emphatically no. The measured attenuation will be the attenuation at
the modulating carrier frequency (complicated by sidebands) and not
the attenuation of the baseline signal.

How would that change the overall strategy? Even the original low
frequency signal without noise is attenuated somewhat by the medium.

The real problem is getting a really precise 4 - 5 sig fig reading
from the receiver to be able to have something meaningful left over
after the noise is subtracted out.

.. . .

If the attenuation is flat over frequency, why bother to modulate?

In this case it isn't flat. High frequency waves are attenuated more
than low frequency.

.. . .

You can't fool Mother Nature with simple tricks.

At least two famous physicists including Hawkings say that it's
impossible to destroy even the smallest part of a signal no matter how
hard you try.

I could be walking down the street minding my own business and get
_ambushed_ by this 2 nano volt signal.


Bret Cahill

 

[Bret Cahill]

On Jul 5, 9:00 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.comtosee 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.

Feel free to take your meds.

Just admit to yourself what is obvious to everyone else. You never
had any interest in this subject in the first place.

The dunces are like a bunch of chickens or school of mackerel. They
are attracted to anything shiny.

Then they reveal that they are dunces.


Bret Cahill


"When a true genius appears in the world, you may know him by this
sign, that the dunces are all in confederacy against him."

-- Jonathan Swift

 

[John Larkin]

On Sun, 5 Jul 2009 12:43:00 -0700 (PDT), Bret Cahill
<BretCahill@peoplepc.com> wrote:

The system will attenuate the low frequency wave more than a high
frequency wave that isn't part of the low frequency wave.

Determining the amount of attenuation of the low frequency wave was,
in fact, the goal.

The high frequency component, however, should attenuate much like the
low frequency wave if it is tracing out the low frequency wave.

If the medium has different attenuation at different frequencies,
emphatically no. The measured attenuation will be the attenuation at
the modulating carrier frequency (complicated by sidebands) and not
the attenuation of the baseline signal.

How would that change the overall strategy? Even the original low
frequency signal without noise is attenuated somewhat by the medium.

But the modulated signal doesn't have the same spectral components of
the original (baseband) signal. If the attenuation is different at
higher frequencies, the modulated signal isn't a surrogate for the low
frequency attenuation. If the attenuation measurement at high
frequencies is still useful, just use a high frequency signal,
bandpass filter, and dump the modulation concept.

The real problem is getting a really precise 4 - 5 sig fig reading
from the receiver to be able to have something meaningful left over
after the noise is subtracted out.

. . .


If the attenuation is flat over frequency, why bother to modulate?

In this case it isn't flat. High frequency waves are attenuated more
than low frequency.

Then the modulated signal is not representative of the low frequency
attenuation.

. . .

You can't fool Mother Nature with simple tricks.

At least two famous physicists including Hawkings say that it's
impossible to destroy even the smallest part of a signal no matter how
hard you try.

I could be walking down the street minding my own business and get
_ambushed_ by this 2 nano volt signal.

I'm working on a wideband preamp (audio to 20 MHz) looking for a
roughly 1 nv signal. About the best wideband amps you can build have a
nv of noise per root Hertz of measurement bandwidth, if, IF you do
everything right.

You're bumping up against fundamental sampling and information theory
limits. It's like conservation of energy: all sorts of tricks look
feasible, but every one is blocked by nature, in simple or sometimes
very sneaky ways.

John

 

[Bret Cahill]

"When a true genius appears in the world, you may know him by this
sign, that the dunces are all in confederacy against him."


-- Jonathan Swift

 

[Bret Cahill]

The system will attenuate the low frequency wave more than a high
frequency wave that isn't part of the low frequency wave.

Determining the amount of attenuation of the low frequency wave was,
in fact, the goal.

The high frequency component, however, should attenuate much like the
low frequency wave if it is tracing out the low frequency wave.

If the medium has different attenuation at different frequencies,
emphatically no. The measured attenuation will be the attenuation at
the modulating carrier frequency (complicated by sidebands) and not
the attenuation of the baseline signal.

How would that change the overall strategy?  Even the original low
frequency signal without noise is attenuated somewhat by the medium.

But the modulated signal doesn't have the same spectral components of
the original (baseband) signal. If the attenuation is different at
higher frequencies, the modulated signal isn't a surrogate for the low
frequency attenuation.

It doesn't need to be identical in every respect.

If the attenuation measurement at high
frequencies is still useful, just use a high frequency signal,
bandpass filter, and dump the modulation concept.

That would depend on how much it is attenuated.

The real problem is getting a really precise 4 - 5 sig fig reading
from the receiver to be able to have something meaningful left over
after the noise is subtracted out.

. . .

If the attenuation is flat over frequency, why bother to modulate?

In this case it isn't flat.  High frequency waves are attenuated more
than low frequency.

Then the modulated signal is not representative of the low frequency
attenuation.

Even if it wasn't it could still yield a useful number.

You can't fool Mother Nature with simple tricks.

At least two famous physicists including Hawkings say that it's
impossible to destroy even the smallest part of a signal no matter how
hard you try.

I could be walking down the street minding my own business and get
_ambushed_ by this 2 nano volt signal.

I'm working on a wideband preamp (audio to 20 MHz) looking for a
roughly 1 nv signal. About the best wideband amps you can build have a
nv of noise per root Hertz of measurement bandwidth, if, IF you do
everything right.

You're bumping up against fundamental sampling and information theory
limits. It's like conservation of energy: all sorts of tricks look
feasible, but every one is blocked by nature, in simple or sometimes
very sneaky ways.

There no mystery to this. A simple error analysis will show a
0.00001% error here will result in a 500% error there.

If they ever quantified the measurements/determinations made at the
Wimbledon men's finals, i.e. the d theta/dt of the racket, the sig
figs might be higher than the $ figs.


Bret Cahill

 

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

"When a true genius appears in the world, you may know him by this
sign, that the dunces are all in confederacy against him."


-- Jonathan Swift

But the fact that some geniuses were laughed at does not imply that all
who are laughed at are geniuses. They laughed at Columbus, they laughed
at Fulton, they laughed at the Wright Brothers. But they also laughed at
Bozo the Clown.


Carl Sagan


--
Jim Pennino

Remove .spam.sux to reply.

 

[Greg Ewing]

Bret Cahill wrote:

The advantage is the transformed curve plots out the difference
between the noise and the transformed signal. Then the noise is
subtracted.

That is not a conventional filter.

It's an unconventional way of implementing a filter,
but it's still a filter, and the end result will be
equivalent to using some conventional filter to
separate the carrier from the noise.

I'm not saying your technique won't work. Quite
likely it could be made to work. But it won't work
any *better* than using conventional AM modulation
and filtering. It can't, for fundamental mathematical
reasons.

--
Greg

 

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

"When a true genius appears in the world, you may know him by this
sign, that the dunces are all in confederacy against him."

-- Jonathan Swift

But the fact that some geniuses were laughed at does not imply that all
who are laughed at are geniuses. They laughed at Columbus, they laughed
at Fulton, they laughed at the Wright Brothers. But they also laughed at
Bozo the Clown.


Carl Sagan


--
Jim Pennino

Remove .spam.sux to reply.

 

[Bret Cahill]

The advantage is the transformed curve plots out the difference
between the noise and the transformed signal.  Then the noise is
subtracted.

That is not a conventional filter.

It's an unconventional way of implementing a filter,
but it's still a filter,

It would be interesting if it's unconventional.

I came up with it a few minutes after the OP killing time because of a
delay.

and the end result will be
equivalent to using some conventional filter to
separate the carrier from the noise.

I'm not saying your technique won't work. Quite
likely it could be made to work. But it won't work
any *better* than using conventional AM modulation
and filtering.

The system will not respond in the same way as to a conventional AM
wave form.

For one thing, higher frequencies are attenuated more than lower
frequencies.

The higher frequency here only changes sign as often as the signal
wave so the media doesn't "see" a +/- high frequency AM wave but
something much like the original low frequency signal.

It can't, for fundamental mathematical
reasons.

Bret Cahill

 

[Bret Cahill]

"When a true genius appears in the world, you may know him by this
sign, that the dunces are all in confederacy against him."

-- Jonathan Swift

 

[Androcles]

"Benj" <bjacoby@iwaynet.net> wrote in message
news:45c19d6e-e684-43ab-ab64-eb80c3e07d7a@x5g2000yqk.googlegroups.com...
On Jul 5, 10:00 pm, j...@specsol.spam.sux.com wrote:

But the fact that some geniuses were laughed at does not imply that all
who are laughed at are geniuses. They laughed at Columbus, they laughed
at Fulton, they laughed at the Wright Brothers. But they also laughed at
Bozo the Clown.

Carl Sagan

Carl Sagan was the Bozo the Clown of science...
====================================
Took over from Einstein, did he?

 

[Benj]

On Jul 5, 10:00 pm, j...@specsol.spam.sux.com wrote:

But the fact that some geniuses were laughed at does not imply that all
who are laughed at are geniuses. They laughed at Columbus, they laughed
at Fulton, they laughed at the Wright Brothers. But they also laughed at
Bozo the Clown.

Carl Sagan

Carl Sagan was the Bozo the Clown of science...

 

[Bret Cahill]

On Jul 6, 8:00 am, j...@specsol.spam.sux.com wrote:

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

"When a true genius appears in the world, you may know him by this
sign, that the dunces are all in confederacy against him."

-- Jonathan Swift

But the fact that some geniuses were laughed at does not imply that all
who are laughed at are geniuses. They laughed at Columbus, they laughed
at Fulton, they laughed at the Wright Brothers. But they also laughed at
Bozo the Clown.

Carl Sagan

"So what if I'm a clown?"

-- Nietzsche

 

[Bret Cahill]

"When a true genius appears in the world, you may know him by this
sign, that the dunces are all in confederacy against him."

-- Jonathan Swift

But the fact that some geniuses were laughed at does not imply that all
who are laughed at are geniuses. They laughed at Columbus, they laughed
at Fulton, they laughed at the Wright Brothers. But they also laughed at
Bozo the Clown.

Carl Sagan

A good clown is much more likely to be a genius that the average
person.


Bret Cahill

 

[Androcles]

"Bret Cahill" <BretCahill@aol.com> wrote in message
news:77c2d98d-bb7a-4721-bebb-209f6b6a4e06@p36g2000prn.googlegroups.com...

But the fact that some geniuses were laughed at does not imply that all
who are laughed at are geniuses. They laughed at Columbus, they laughed
at Fulton, they laughed at the Wright Brothers. But they also laughed
at
Bozo the Clown.

Carl Sagan

Carl Sagan was the Bozo the Clown of science...
====================================
Took over from Einstein, did he?

Sagan was a Nobel laureate?

Even Bozo the Clown could be sensible when he wasn't performing

in front of an audience.
http://tinyurl.com/c53cqo
http://www.androcles01.pwp.blueyonder.co.uk/QUESTION.htm