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Subject: Re: How to count number of spikes in a signal (related to noise)
Date: Tue, 2 Oct 2007 16:17:14 +0000 (UTC)
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"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