Extracting pulse height and width from noise

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.

- pulse height, width and arrival time are "random"

- I do not actually need the height and width of a *particular* pulse,
  I am more interested in the distribution of heights and the
  distribution of widths.

I was wondering if there was some clever dsp way to achieve this,
(analogous to using an FFT to extract sinusoidal signals, perhaps).

-- 

John Devereux

Have you considered different correlation techniques?  There are lots
of IEE and IEEE papers to this effect, since this is a common problem
in Radar applications.

John Devereux 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.
>
> - pulse height, width and arrival time are "random"
>
> - I do not actually need the height and width of a *particular* pulse,
>   I am more interested in the distribution of heights and the
>   distribution of widths.
>
> I was wondering if there was some clever dsp way to achieve this,
> (analogous to using an FFT to extract sinusoidal signals, perhaps).
> 
> -- 
> 
> John Devereux

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.

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.
>
>- pulse height, width and arrival time are "random"
>
>- I do not actually need the height and width of a *particular* pulse,
>  I am more interested in the distribution of heights and the
>  distribution of widths.
>
>I was wondering if there was some clever dsp way to achieve this,
>(analogous to using an FFT to extract sinusoidal signals, perhaps).
>

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?

-- 

John Devereux

Minimize the square of the difference between a template of the signal based 
on the current estimate of the three parameters and the current measured 
signal.  This is a minimization problem.  Thiunking about the problem, 
Hooke-Jeeves may be the better choice since it doesn't require the Jacobian 
and uses only function values.  The function values in this case are the 
square of the difference between the template and the signal.

In article <87irlx35pu.fsf@cordelia.devereux.me.uk>, John Devereux 
<jdREMOVE@THISdevereux.me.uk> 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?
>

walsh hadamard xform?

"John Devereux" <jdREMOVE@THISdevereux.me.uk> wrote in message 
news:87ac7bvzsk.fsf@cordelia.devereux.me.uk...
>
> 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.
>
> - pulse height, width and arrival time are "random"
>
> - I do not actually need the height and width of a *particular* pulse,
>  I am more interested in the distribution of heights and the
>  distribution of widths.
>
> I was wondering if there was some clever dsp way to achieve this,
> (analogous to using an FFT to extract sinusoidal signals, perhaps).
>
> -- 
>
> John Devereux 

"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.

-- 

John Devereux

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

cheers

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

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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

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