Martin Eisenberg <martin.eisenberg@udo.edu> writes:
> Hi John,
>
> maybe you can use Matching Pursuit. MP basically works by identifying
> a member of a dictionary (containing pulses of various widths and
> heights in your case) that best fits some part of the data,
> subtracting it out, and iterating on the residual. If you think that
> doesn't sound as cheap as you hoped for you're probably right. Still,
> i guess it can't hurt to look into the topic.
Hi Martin,
Thanks, looks interesting. It is useful to know of the existance of
things like this, (even if they may indeed be too expensive to
use). Simply the *names* of relevant algorithms is a big help when one
is unfamiliar with the field! And I have already found out things that
will be very useful in another project.
--
John Devereux
Reply by Martin Eisenberg●July 18, 20062006-07-18
Hi John,
maybe you can use Matching Pursuit. MP basically works by identifying
a member of a dictionary (containing pulses of various widths and
heights in your case) that best fits some part of the data,
subtracting it out, and iterating on the residual. If you think that
doesn't sound as cheap as you hoped for you're probably right. Still,
i guess it can't hurt to look into the topic.
Martin
--
Quidquid latine scriptum sit, altum viditur.
Reply by John Devereux●July 18, 20062006-07-18
"Ron N." <rhnlogic@yahoo.com> writes:
> John Devereux wrote:
>>
>> OK... But say I had some pulses 1 unit wide. I would need to be able
>> to distinguish 10 pulses 1 unit high, from 1 pulse 10 units high. It
>> seems to me that anything equivalent to a FT would not do this.
>>
>> I need to end up with the frequency distribution of pulse heights
>> (i.e. the number of pulses of each height that were detected).
>
> The signal would still need some analog of being bandlimited
> to below some Nyquist frequency or else there will be aliasing.
> 1 unit wide pulses would seem to violate that bandlimiting.
Sorry, by "1 unit" I just meant "some time period", nothing to do with
the sample interval.
> The process generating the rectangular pulses needs to be
> orthogonal or independant in some manner, otherwise I'm
> not sure how one could differentiate a bunch of pairs of
> identical and successive 5-wides from 10-wides.
I think the process will be "orthogonal or independent", if I am
interpreting those terms correctly.
--
John Devereux
Reply by John Devereux●July 18, 20062006-07-18
jim <"sjedgingN0sp"@m@mwt.net> writes:
> John Devereux wrote:
>>
>>
>> Hi jim,
>>
>> Imagine objects going past a detector. They have a range of sizes and
>> speeds. The width of a pulse will give the speed, and the height will
>> give the particle size. The average pulses/second will give me the
>> number density. But the arrival time will be random, and occasionally
>> overlapping.
>>
>
> Bear with me - my imagination is weak. Do you mean like bags on an
> airport baggage conveyor or do you mean the jumble of rocks and gravel
> that comes out of gravel pit before processing.
The jumble of rocks is a close analogy - although there will usually
be some space between them, so mostly can be counted
individually. Also they are in a fluid stream rather than on a
conveyor, so that different regions of the stream go at somewhat
different speeds. If it helps we can ignore the possibility of two
coming through together, for now, although in reality this can happen
occasionally.
> It also might help if you explained what the end goal is. I know you
> have said you want to extract some sort of statistics of the process.
> But what are you really looking for? For instance, in the end you might
> be trying to measure the overall volume of material conveyed.
The end goal is in fact the size distribution of the objects, i.e. the
number of each size that have gone past. The total volume is not
needed (although of course this could be calculated from the
distribution).
--
John Devereux
Reply by Jerry Avins●July 18, 20062006-07-18
John Devereux wrote:
> "BlagooBlanaa" <BlagooBlanaa@hotmail.com> writes:
>
>> walsh hadamard xform?
>
> Yes, I did look at "walsh functions", but could not quite see how to
> apply them to the problem.
Is it time for heuristics? Bandpass filter the signal so that the widest
and narrowest pulses of interest will be passed relatively intact. With
no signal present, there should be no long-term departure from zero
mean. If the short-term integral departs significantly (you decide what
is significant) from a random walk, a pulse is (or has recently been)
present. If that much seems to work, start refining.
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by Ron N.●July 18, 20062006-07-18
John Devereux wrote:
> "BlagooBlanaa" <BlagooBlanaa@hotmail.com> writes:
>
> > how would you extract a signal from noise with the FFT?
> > xform time series into frequency domain and then take
> > only the lower order frequency components - lo pass filter?
> >
> > what is an ft - an approximation of some time series via a
> > finite sum of orthogonal trig functions?
> >
> > what is a walsh-hadamard xform - an approximation of
> > a signal by a finite sum of orthogonal 'sequencies'...
> >
> > http://www.ciphersbyritter.com/RES/WALHAD.HTM
> >
> > and, moreover I can prove that the WHT is a special
> > case of the FT, in other words I can use an FFT algorithm
> > to attain a WHT of data.
> >
> > better, if you work hard with an fft algorithm, by unwinding
> > and hand calculating the butterflies, you can reduce the FFT
> > to an extremely simple form ideal for computing the WHT.
> >
> > so, whiten your time series by hi-pass filtering, and de-noise
> > by lo pass filtering. Does it matter if you are approximating
> > via FFT or via WHT?
> > Then you can obtain pulse height and width, perhaps via
> > IWHT
> >
>
> OK... But say I had some pulses 1 unit wide. I would need to be able
> to distinguish 10 pulses 1 unit high, from 1 pulse 10 units high. It
> seems to me that anything equivalent to a FT would not do this.
>
> I need to end up with the frequency distribution of pulse heights
> (i.e. the number of pulses of each height that were detected).
The signal would still need some analog of being bandlimited
to below some Nyquist frequency or else there will be aliasing.
1 unit wide pulses would seem to violate that bandlimiting.
The process generating the rectangular pulses needs to be
orthogonal or independant in some manner, otherwise I'm
not sure how one could differentiate a bunch of pairs of
identical and successive 5-wides from 10-wides.
IMHO. YMMV.
--
rhn A.T nicholson d.0.t C-o-M
Reply by jim●July 18, 20062006-07-18
John Devereux wrote:
>
> jim <"sjedgingN0sp"@m@mwt.net> writes:
>
> > Are you saying there are no limits to these pulses. There is no range of
> > how high or low they might be? No range of how wide or narrow? No limit
> > to the time period between pulses? Are they even sequential or can they
> > overlap one another. If there are truly no limits and are truly random
> > then your problem seems to me to be impossible to solve.
>
> Hi jim,
>
> Imagine objects going past a detector. They have a range of sizes and
> speeds. The width of a pulse will give the speed, and the height will
> give the particle size. The average pulses/second will give me the
> number density. But the arrival time will be random, and occasionally
> overlapping.
>
Bear with me - my imagination is weak. Do you mean like bags on an
airport baggage conveyor or do you mean the jumble of rocks and gravel
that comes out of gravel pit before processing.
It also might help if you explained what the end goal is. I know you
have said you want to extract some sort of statistics of the process.
But what are you really looking for? For instance, in the end you might
be trying to measure the overall volume of material conveyed.
> I realise there will be limits to what can be detected, such as when
> the objects are too small to be seen above the noise, and errors when
> two objects coincide.
>
> I was hoping for some kind of magic dsp transform, that could extract
> the parameters of this "signal", like the FFT can extract the
> frequency and amplitude of sine waves. What I want to end up with is a
> frequency distribution of pulse heights, and another one of pulse
> widths.
>
There might be an easy solution if you narrow the problem down
sufficiently. For instance, if the pulses came in 3 different heights
and 3 different widths then the problem should be a lot easier. And if
there was some linear or logarithmic relation ship between those
different sizes it should get even easier.
> --
>
> John Devereux
----== Posted via Newsfeeds.Com - Unlimited-Unrestricted-Secure Usenet News==----
http://www.newsfeeds.com The #1 Newsgroup Service in the World! 120,000+ Newsgroups
----= East and West-Coast Server Farms - Total Privacy via Encryption =----
Reply by John Devereux●July 18, 20062006-07-18
"BlagooBlanaa" <BlagooBlanaa@hotmail.com> writes:
> how would you extract a signal from noise with the FFT?
> xform time series into frequency domain and then take
> only the lower order frequency components - lo pass filter?
>
> what is an ft - an approximation of some time series via a
> finite sum of orthogonal trig functions?
>
> what is a walsh-hadamard xform - an approximation of
> a signal by a finite sum of orthogonal 'sequencies'...
>
> http://www.ciphersbyritter.com/RES/WALHAD.HTM
>
> and, moreover I can prove that the WHT is a special
> case of the FT, in other words I can use an FFT algorithm
> to attain a WHT of data.
>
> better, if you work hard with an fft algorithm, by unwinding
> and hand calculating the butterflies, you can reduce the FFT
> to an extremely simple form ideal for computing the WHT.
>
> so, whiten your time series by hi-pass filtering, and de-noise
> by lo pass filtering. Does it matter if you are approximating
> via FFT or via WHT?
> Then you can obtain pulse height and width, perhaps via
> IWHT
>
OK... But say I had some pulses 1 unit wide. I would need to be able
to distinguish 10 pulses 1 unit high, from 1 pulse 10 units high. It
seems to me that anything equivalent to a FT would not do this.
I need to end up with the frequency distribution of pulse heights
(i.e. the number of pulses of each height that were detected).
--
John Devereux
Reply by John Devereux●July 18, 20062006-07-18
jim <"sjedgingN0sp"@m@mwt.net> writes:
> Are you saying there are no limits to these pulses. There is no range of
> how high or low they might be? No range of how wide or narrow? No limit
> to the time period between pulses? Are they even sequential or can they
> overlap one another. If there are truly no limits and are truly random
> then your problem seems to me to be impossible to solve.
Hi jim,
Imagine objects going past a detector. They have a range of sizes and
speeds. The width of a pulse will give the speed, and the height will
give the particle size. The average pulses/second will give me the
number density. But the arrival time will be random, and occasionally
overlapping.
I realise there will be limits to what can be detected, such as when
the objects are too small to be seen above the noise, and errors when
two objects coincide.
I was hoping for some kind of magic dsp transform, that could extract
the parameters of this "signal", like the FFT can extract the
frequency and amplitude of sine waves. What I want to end up with is a
frequency distribution of pulse heights, and another one of pulse
widths.
--
John Devereux
Reply by jim●July 18, 20062006-07-18
John Devereux wrote:
>
> John_W_Herman@yahoo.com (John Herman) writes:
>
> > In article <87ac7bvzsk.fsf@cordelia.devereux.me.uk>, John Devereux
> > <jdREMOVE@THISdevereux.me.uk> wrote:
> >>
> >>Hi,
> >>
> >>I have an application with random, nominally rectangular pulses in
> >>the presence of (white) noise. I want to extract the pulse heights
> >>and widths.
>
> > It almost sounds like an intelligence problem. If you want that
> > information, you will probably need to do a least fit to the
> > waveform. The three parameters you will need for the fit, height,
> > width, and position, will need to be estimated. I suggest that you
> > use the Levenburg-Marquadt algorithm. I've used Hooke-Jeeves for
> > this too.
>
> OK, Thanks.
>
> I am not sure how this would work though. For a given region of the
> input data, I do not know in advance how many pulses are present, so I
> don't see how to parameterise the model. Although I suppose one could
> make the number of pulses itself another parameter?
Are you saying there are no limits to these pulses. There is no range of
how high or low they might be? No range of how wide or narrow? No limit
to the time period between pulses? Are they even sequential or can they
overlap one another. If there are truly no limits and are truly random
then your problem seems to me to be impossible to solve.
-jim
>
> --
>
> John Devereux
----== Posted via Newsfeeds.Com - Unlimited-Unrestricted-Secure Usenet News==----
http://www.newsfeeds.com The #1 Newsgroup Service in the World! 120,000+ Newsgroups
----= East and West-Coast Server Farms - Total Privacy via Encryption =----