peak finding

John,

There is a peak finding algorithm attributed to Prof. Ripley in the R-help
archive.  It has a span parameter which might give you something close to
what you seem to be looking for.

http://finzi.psych.upenn.edu/R/Rhelp02a/archive/33097.html

-Christos

Finding peaks and valleys has several issues:

1. Impact of noise.
2. Mathematical smoothness of the underlying signal.
3. Boundary conditions at the beginning and end of the data series.
4. Bias from smoothing.

If the noise is not too bad, I'd try fitting a smoothing spline, and 
then use the null derivative points to punctuate the extrema.

If the noise is severe, you probably will need some domain knowledge, 
and will end up with perhaps locally weighted regression, followed by 
extrema search.

For cases where the noise is trivial, the following short function 
might be useful in picking off peaks (and symmetrically modified, valleys):

#findpeaks()
#Copyright 2007 by Robert A LaBudde, all rights reserved
#find peaks in (x,y) curve
findpeaks<- function(x, y) {
   nx<- length(x)
   ny<- length(y)
   if (nx != ny) {
     print ('>> findpeaks01: x and y must be same length!')
     stop
     }
   ipeak<- NULL
   xpeak<- NULL
   ypeak<- NULL
   yprv<- y[1]
   for (i in 1:ny) {
     ynext<- ifelse(i==ny,y[ny],y[i+1])
     if(yprv < y[i] & y[i] > ynext) { #found local peak
       ipeak<- c(ipeak,i)
       xpeak<- c(xpeak,x[i])
       ypeak<- c(ypeak,y[i])
       }
     yprv<- y[i]
     }
   return(data.frame(ipeak,x=xpeak,y=ypeak))
   }

Trivial though it may be, it actually works quite well for its 
intended purpose.

================================================================
Robert A. LaBudde, PhD, PAS, Dpl. ACAFS  e-mail: ral at lcfltd.com
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