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From: dzk@cs.brown.edu (Danny Keren)
Subject: Average Distance Between Zero-Crossings
Message-ID: <1994Dec4.142644.559@cs.brown.edu>
Sender: news@cs.brown.edu
Organization: Brown University Department of Computer Science
Date: Sun, 4 Dec 1994 14:26:44 GMT
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Xref: glinda.oz.cs.cmu.edu sci.image.processing:11260 sci.math.num-analysis:17390

I read that the average distance between zero-crossings of a
response of a function g to Gaussian noise is the square root
of the integral of g squared divided by the integral of the
derivative of g squared, that is

     ------------------------------------
     |   
     |     Int(g^2(x)dx)
     |   _________________
\    |
 \   |   Int( (g'(x))^2 dx)
  \  |
    \|

where the integrals are between -infinity and infinity. My 
understanding is that "response of g to noise" means "convolution
of g with noise". 

Does anyone know why this is true? I'll be very grateful for a
formal proof, and also for an informal proof or some intuitive
explanation.

Thanks,


-Danny Keren.


