Ben Bolker (bolker@zoo.ufl.edu)
Thu, 18 Nov 1999 10:11:05 -0500 (EST)
On Thu, 18 Nov 1999, Bill Simpson wrote:
> 1. First example, from the classic Bracewell The Fourier transform and its
> applications, chap 3 (p.32 in 2nd edition):
> {2 2 3 3 4} * {1 1 2} = {2 4 9 10 13 10 8}
> where * denotes convolution (discrete in this case). See bottom of this
> email for his definition of convolution.
> In R I get:
> x<-c(2,2,3,3,4)
> h<-c(1,1,2)
> convolve(x,h,type="o")
> [1] 4 6 10 11 14 7 4
> I think "open" is the right type. I want to get length(x)+length(h)-1
> terms in the convolution output, which is what "open" gives. I definitely
> don't want "circular"
The difference between the definitions is a sign change in the index of
the filter: f[i-j] vs. f[j-i] (if the filter is symmetric then it wouldn't
matter). If you do
convolve(x,rev(h),type="o")
you'll get the answer from Bracewell. The definition in R makes more
sense to me, but that's personal I guess.
>
> h<-dnorm(x, mean=50, sd=10)
> # the filter is a Gaussian
>
> plot(convolve(y,h, type="open"))
> #weird
> points(pnorm(x,mean=50,sd=10))
> #what I expected, since convolution with a step is integration
Here the problem is that the filter is "running off the end".
If you extend the filter with ones
y <- c(y,rep(1,100))
and redo the analysis you'll see that it levels off at 1 for a while and
then drops back down.
Hope that helps ... (as usual, someone else has probably answered this
one already).
Ben
-- -------------------------------------------- Ben Bolker bolker@zoo.ufl.edu Zoology Department, University of Florida http://www.zoo.ufl.edu/bolker 318 Carr Hall/Box 118525 tel: (352) 392-5697 Gainesville, FL 32611-8525 fax: (352) 392-3704-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request@stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
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