| Author |
Message |
Martin
Guest
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 Posted:
Sat Dec 10, 2005 1:16 am Post subject:
Extracting a signal from noise? |
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Hi,
I'm wondering what mathematical tools (techniques) are available to extract
signals from noise (other than fourier transforms)?
For example, take the following into consideration:
r = rand(1,400);
s = normalize(tan(0:0.05:19.95), -1, 1); #normalized between -1 and 1
x = r + s;
How can one extract the signal 's' from 'x' ? I know that if it was a
sinusoidal signal, the FFT could extract it, but i'm trying to find some
mathematical techniques to extract all kinds of signals from noise.
Anyone read the new paper: "New Technique for Finding Needles in Haystacks:
Geometric Approach to Distinguishing between a New Source and Random
Fluctuations" ? Will that technique be able to extract the tangential signal
above?
Thank you |
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Tim Wescott
Guest
|
| Posted:
Sat Dec 10, 2005 1:16 am Post subject:
Re: Extracting a signal from noise? |
|
|
Martin wrote:
| Quote: | Hi,
I'm wondering what mathematical tools (techniques) are available to extract
signals from noise (other than fourier transforms)?
For example, take the following into consideration:
r = rand(1,400);
s = normalize(tan(0:0.05:19.95), -1, 1); #normalized between -1 and 1
x = r + s;
How can one extract the signal 's' from 'x' ? I know that if it was a
sinusoidal signal, the FFT could extract it, but i'm trying to find some
mathematical techniques to extract all kinds of signals from noise.
Anyone read the new paper: "New Technique for Finding Needles in Haystacks:
Geometric Approach to Distinguishing between a New Source and Random
Fluctuations" ? Will that technique be able to extract the tangential signal
above?
Thank you
Search on "detection and estimation theory". |
--
Tim Wescott
Wescott Design Services
http://www.wescottdesign.com |
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Glennaebad
Guest
|
| Posted:
Sun Dec 11, 2005 1:16 am Post subject:
Re: Extracting a signal from noise? |
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|
"Martin" <yodlep@gmail.com> wrote in message
news:jMSdnTuDjr1WiAfenZ2dnUVZ_sKdnZ2d@rogers.com...
| Quote: | Hi,
I'm wondering what mathematical tools (techniques) are available to
extract
signals from noise (other than fourier transforms)?
For example, take the following into consideration:
r = rand(1,400);
s = normalize(tan(0:0.05:19.95), -1, 1); #normalized between -1 and
1
x = r + s;
How can one extract the signal 's' from 'x' ? I know that if it was a
sinusoidal signal, the FFT could extract it, but i'm trying to find some
mathematical techniques to extract all kinds of signals from noise.
Anyone read the new paper: "New Technique for Finding Needles in
Haystacks:
Geometric Approach to Distinguishing between a New Source and Random
Fluctuations" ? Will that technique be able to extract the tangential
signal
above?
Thank you
|
With FFT we normally use spectral subraction but that has problems such as
musical noise. There are thousands of papers on this topic.
Glen |
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Donald
Guest
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Stan Pawlukiewicz
Guest
|
| Posted:
Mon Dec 12, 2005 5:16 pm Post subject:
Re: Extracting a signal from noise? |
|
|
Martin wrote:
| Quote: | Hi,
I'm wondering what mathematical tools (techniques) are available to extract
signals from noise (other than fourier transforms)?
For example, take the following into consideration:
r = rand(1,400);
s = normalize(tan(0:0.05:19.95), -1, 1); #normalized between -1 and 1
x = r + s;
How can one extract the signal 's' from 'x' ? I know that if it was a
sinusoidal signal, the FFT could extract it, but i'm trying to find some
mathematical techniques to extract all kinds of signals from noise.
Anyone read the new paper: "New Technique for Finding Needles in Haystacks:
Geometric Approach to Distinguishing between a New Source and Random
Fluctuations" ? Will that technique be able to extract the tangential signal
above?
|
Do you have a complete reference?
I'd like to look at it.
|
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Rune Allnor
Guest
|
| Posted:
Tue Dec 13, 2005 9:15 am Post subject:
Re: Extracting a signal from noise? |
|
|
Martin wrote:
| Quote: | Hi,
I'm wondering what mathematical tools (techniques) are available to extract
signals from noise (other than fourier transforms)?
For example, take the following into consideration:
r = rand(1,400);
s = normalize(tan(0:0.05:19.95), -1, 1); #normalized between -1 and 1
x = r + s;
How can one extract the signal 's' from 'x' ? I know that if it was a
sinusoidal signal, the FFT could extract it, but i'm trying to find some
mathematical techniques to extract all kinds of signals from noise.
Anyone read the new paper: "New Technique for Finding Needles in Haystacks:
Geometric Approach to Distinguishing between a New Source and Random
Fluctuations" ? Will that technique be able to extract the tangential signal
above?
|
This is basically the Holy Grail of DSP.
The Great Idea of one of my former bosses is that you should "try all
possible
mathematical models for the signal, each model with all possible
parametrizations"
and "what pops out of the analysis in the end is the One True
Representation
of this signal." This guy really meant "all possible" in the literal
sense in
both instances where he used the term above.
I don't have the faintest clue what this claim is based on, but this
guy have
made a prosperous business out of selling such projects for the last
decade
or so.
For the record: Him trying to get me involved with such... ehum...
"bold" projects
was the direct reason for me going into sick leave for a full year, as
well as quitting
two jobs.
Rune |
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Peter K.
Guest
|
| Posted:
Tue Dec 13, 2005 5:16 pm Post subject:
Re: Extracting a signal from noise? |
|
|
"Rune Allnor" <allnor@tele.ntnu.no> writes:
| Quote: | This is basically the Holy Grail of DSP.
The Great Idea of one of my former bosses is that you should "try
all possible mathematical models for the signal, each model with all
possible parametrizations" and "what pops out of the analysis in the
end is the One True Representation of this signal." This guy really
meant "all possible" in the literal sense in both instances where he
used the term above.
|
OK, so just parameterize your signal by N values p_n (n=0..N-1). Where
p_n = x_n for all n, and where x_n is your data. Perfect match!
| Quote: | I don't have the faintest clue what this claim is based on, but this
guy have made a prosperous business out of selling such projects for
the last decade or so.
|
Ambitiuous is OK, preposterous == disasterous.
| Quote: | For the record: Him trying to get me involved with such... ehum...
"bold" projects was the direct reason for me going into sick leave
for a full year, as well as quitting two jobs.
|
:-(
Ciao,
Peter K. |
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