[R] FOURIER INTEGRALS IN R

[andrew]

Isn't it possible to write this as the real part of a fourier
transform?  You could then use the fft to calculate it for all the
values of x, all at once.  The Madan and Carr paper offers some
pointers on how to do this: http://www.imub.ub.es/events/sssf/vgfrier7.pdf

On May 6, 1:06 am, "Ravi Varadhan" <RVarad... at jhmi.edu> wrote:
> Your integrand is smooth.
>
> What are the limits of integration: 0 to 1 or 0 to infinity?  Main challenge
> is that it is increasingly oscillatory as x and/or t increase.  You can find
> the zeros of thecosinefunction and add up the integrals between successive
> zeros.  In what context does this inttegral arise?  It must have been
> studied well using asymptotic approximation and such.  
>
> Ravi.
>
> ----------------------------------------------------------------------------
> -------
>
> Ravi Varadhan, Ph.D.
>
> Assistant Professor, The Center on Aging and Health
>
> Division of Geriatric Medicine and Gerontology
>
> Johns Hopkins University
>
> Ph: (410) 502-2619
>
> Fax: (410) 614-9625
>
> Email: rvarad... at jhmi.edu
>
> Webpage:  http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
>
> ----------------------------------------------------------------------------
> --------
>
> -----Original Message-----
> From: r-help-boun... at r-project.org [mailto:r-help-boun... at r-project.org] On
>
> Behalf Of A Achilleos
> Sent: Tuesday, May 05, 2009 10:18 AM
> To: r-h... at r-project.org
> Subject: Re: [R] FOURIER INTEGRALS IN R
>
> Ok thanks..
>
> No, my function is not smooth.
>
> Actually, I am dealing with an integral having the following form, for
> example:
>
> \int cos(tx) (1-t^2)^3 \exp(0.5*t^2) dt
>
> I want to estimate this FourierCosineintegral for a given value of x.
>
> Thanks for the help.
>
> AA
>
> On Tue, May 5, 2009 2:34 am, andrew wrote:
> > integrate offers some one-dimensional algorithms, but you need to
> > start with a smooth function to get it to converge properly.  With a
> >cosineintegral, there may be certain routines that offer better value
> > for money: the Clenshaw-Curtis integration, or perhaps the FFT.  You
> > would have to recast your problem by doing some sort of substitution.
>
> > Perhaps post some latex code to show the exact type of integral you
> > are wanting to calculate.
>
> > Regards,
>
> > On May 5, 6:32 am, "Achilleas Achilleos" <ma... at bristol.ac.uk> wrote:
> >> Hi,
>
> >> I am wondering whether there exist any function in R (any package)
> >> that calculates Fourier Integrals.
>
> >> Particularly, I am interested for estimation of aCosineFourier
> >> integral...
>
> >> I would be much obliged if you could help me on this..
>
> >> Thanks.
>
> >> Andreas
>
> >> --
>
> >> ______________________________________________
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> > ______________________________________________
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>
> ----------------------
> A Achilleos
> ma... at bristol.ac.uk
>
> ______________________________________________
> R-h... at r-project.org mailing listhttps://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guidehttp://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
> ______________________________________________
> R-h... at r-project.org mailing listhttps://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guidehttp://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
>