[time-nuts] looking for algorithms to locate edge location in noisy data

[beale]

I'm just starting to play around with some timing signals. I'm just wondering 
if some of you experts can refer me to some reading on algorithms to find the 
location of an edge in noisy data. For example, this waveform:

https://picasaweb.google.com/lh/photo/aPZbcgu9neWRJAGd_VoGng?feat=directlink

Now, I know I've got every kind of analog signal problem here, very low 
bandwidth, random length wires instead of a proper scope probe, unterminated 
lines, vertical scale that doesn't use the scope's already limited 8-bit 
dynamic range etc.  I can improve the signal, but I'm just using that trace to 
illustrate several issues in general.  I wonder what a good algorithm or 
procedure might be to extract the best available edge timing resolution from a 
set of data describing a waveform of this approximate shape.  

In this case, by best I mean the most repeatable result in the face of a 
bandwidth-limited signal with given level of random noise and quantization 
error.  I imagine I would want to generate a prototype waveform and then slide 
it back and forth over each given waveform in turn, and look for the best match 
position (cross correlation) ?

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Re: [time-nuts] looking for algorithms to locate edge location in noisy data

[Chris Albertson]

On Mon, Mar 14, 2011 at 12:26 PM, beale be...@bealecorner.com wrote:
  I imagine I would want to generate a prototype waveform and then
slide it back and forth over each given waveform in turn, and look for
the best match position (cross correlation) ?

I think that is called an autocorrelation.
http://en.wikipedia.org/wiki/Autocorrelation
There is a quick way to calculate this using FFT.

But in this special case could your prototype be a perfect unit
height square wave.  Then I think the time domain calculation is
simpler, I think.

But this s a real special case. so I think what I'd do is fit a line
to the linear part of the slope (say from 20% to 80% of logic high)
using least squares then solve for the mid point voltage.   Any method
like that that uses a large number of samples should reduce noise


-- 
=
Chris Albertson
Redondo Beach, California

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