Oscillatory Integration?

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#412

From: Jack W. Sharer
Date: Thu, 03 Sep 1992 13:18

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I'm having to evaluate this integral:

          /\ 0.5
         /           N
        /      f(x) D (2 pi x + phi) dx
       /
     \/ -0.5

                       N
for N ~ 500 and where D (x) is the N-point Dirichlet kernel:


               iNx
       N      e    - 1
      D (x) = --------,  i = sqrt(-1)   (highly oscilatory for large N)
                ix
               e  - 1

I'm successfully using a 2000-point Simpson integration, but I cannot
begin to evaluate all the needed cases (limited by computer resources).

Could you suggest a change of variable or another technique which
would dramatically improve the integration speed?

Thanks, Jack Sharer, Penn State, j0s@psuvm.psu.edu

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Path: arc1-ca.pugleaf.net!sparky!uunet!cis.ohio-state.edu!pacific.mps.ohio-state.edu!linac!uwm.edu!psuvax1!psuvm!j0s
Organization: Penn State University
Date: Thu, 3 Sep 1992 09:18:26 EDT
From: Jack W. Sharer <J0S@psuvm.psu.edu>
Message-ID: <92247.091826J0S@psuvm.psu.edu>
Newsgroups: sci.math.num-analysis
Subject: Oscillatory Integration?
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