Thread Subject: How to count number of spikes in a signal (related to noise)

I have a signal which, if no noise is present, looks roughly
like a parabola y = -X.^2. (i.e., x squared)

The ideal signal should be smooth like a parabola. However,
with noise, there can be many jagged spikes in the signal.

I would like to count the number of these spikes. This is
part of my effort to quantify noise in the signal.

Can anyone suggest a good option for counting the spikes in
a signal (in a given range)?

The jagged spikes (noise) can occur along the up and down
slopes or near the top and they can sometimes be very large
- even more than 50% of the amplitude of the parabola.
Individual spikes are usually very narrow as well.

Fit the data to your parabola model.

use diff on the error channel to find values over a
threshold spec.

count the diffs over your acceptance level.

"G.A.M. " <x0zero@gmail.com> wrote in message <fdtm0l$hp2
$1@fred.mathworks.com>...
> I have a signal which, if no noise is present, looks
roughly
> like a parabola y = -X.^2. (i.e., x squared)
>
> The ideal signal should be smooth like a parabola.
However,
> with noise, there can be many jagged spikes in the signal.
>
> I would like to count the number of these spikes. This is
> part of my effort to quantify noise in the signal.
>
> Can anyone suggest a good option for counting the spikes
in
> a signal (in a given range)?
>
> The jagged spikes (noise) can occur along the up and down
> slopes or near the top and they can sometimes be very
large
> - even more than 50% of the amplitude of the parabola.
> Individual spikes are usually very narrow as well.

Just a thought, if your noise spikes are very sharp, as you
suggest, it sounds like a task ideally tackled using
Wavelets. That is to say the noise is mainly present in the
fast detail, whereas your signal in mainly in the slow
detail.

Off the top of my head, I guess you could do something like
a wavelet smooth, to remove the fast transient information,
then subtract the smoothed parabola from the full waveform,
to end up with just the noise, which you could then
characterize much more easily.

There is probably a lot mor sophisticated Wavelet
techniques that you could use - perhaps one of the guru's
will respond.

Regards

Dave Robinson

On 2 Okt, 16:53, "G.A.M. " <x0z...@gmail.com> wrote:
> I have a signal which, if no noise is present, looks roughly
> like a parabola y = -X.^2. (i.e., x squared)
>
> The ideal signal should be smooth like a parabola. However,
> with noise, there can be many jagged spikes in the signal.
>
> I would like to count the number of these spikes. This is
> part of my effort to quantify noise in the signal.
>
> Can anyone suggest a good option for counting the spikes in
> a signal (in a given range)?
>
> The jagged spikes (noise) can occur along the up and down
> slopes or near the top and they can sometimes be very large
> - even more than 50% of the amplitude of the parabola.
> Individual spikes are usually very narrow as well.

Without having seen any of your data, this is what I
would try first:

1) Differentiate the data twice. The result ought to
   be constant for a perfect parabola.
2) Search the double-diff'ed data for large
   deviations from this constant value.

Rune

On Oct 3, 8:37 am, "Aslak Grinsted" <r...@phunck.cmo> wrote:
> > L=extr(x);
> > Nmax=sum(L(1));
> > Nmin=sum(L(2));
>
> > Total number of spikes is
> > N=Nmax+Nmin;
>
> > Hope it helps.
> > Mira
>
> yes you could use extr from the file exchange but you
> probably still need to remove the parabola shape from the
> signal. I think that wavelets is a bit overkill my self.
> Perhaps you can subtract a windowed mean:
>
> L=extr(x-smooth(x,10));
>
> or something similar ... or if it truly is like a parabola
> then perhaps you could robustfit to find a good set of
> model parameters and subtract that before counting local
> extrema.
>
> Also take a look at the stats output from robustfit. It
> might be exactly the kind of things you need
> for "quantifying the noise".

Thank you for your reply. Your two suggestions both sound very
intriguing. I will try both. I am currently smoothing with a median
filter and it works very well.

Using extr on the differences between the raw signal and the median
filtered signal is something I will try.

I also like the idea of using the stats from robustfit and I will try
this to see how well it works.

Your replies have been very helpful.

On Oct 3, 9:37 am, "Dave Robinson" <dave.robin...@somewhere.biz>
wrote:
> "Aslak Grinsted" <r...@phunck.cmo> wrote in message
>
> <fe02ea$md...@fred.mathworks.com>...
>
>
>
> > > L=extr(x);
> > > Nmax=sum(L(1));
> > > Nmin=sum(L(2));
>
> > > Total number of spikes is
> > > N=Nmax+Nmin;
>
> > > Hope it helps.
> > > Mira
>
> > yes you could use extr from the file exchange but you
> > probably still need to remove the parabola shape from the
> > signal. I think that wavelets is a bit overkill my self.
> > Perhaps you can subtract a windowed mean:
>
> > L=extr(x-smooth(x,10));
>
> > or something similar ... or if it truly is like a
> parabola
> > then perhaps you could robustfit to find a good set of
> > model parameters and subtract that before counting local
> > extrema.
>
> > Also take a look at the stats output from robustfit. It
> > might be exactly the kind of things you need
> > for "quantifying the noise".
>
> The reason that I originally suggested using Wavelets, is
> that I thought it might be more robust than conventional
> smoothing, as the original question never stated that noise
> came from a zero mean distribution.


You are correct. I need to do a lot of work in regard to the error
distribution. So far I am just using my domain knowledge. I believe
the errors tend to be more negative than positive and I do not believe
the mean is zero.


>This could have
> ramifications to the shape of the recovered 'base'
> distribution if the noise had a bias.
>


In practice, the median filter seems to work well. But that's just an
untested assumption at this point. I have not tried wavelets because I
don't know how to use a wavelet smooth yet (and I haven't found the
help I need in the ML documentation yet).