Re: Writing our own low level m-file

You apparently want the poster to do the Fourier integral by finding
all the poles in the complex plane (or at least in half of it) by your
favorite method (Ivansson's) and using the residue theorem. This is a
reasonable approach if the function is analytic everywhere except for
certain known types of singularities), but since the OP was talking
about "discretizing the integral" as his first step, it seemed to
imply that his function is compactly supported or (equivalently) his
integral is over a finite domain, in which case integration via the
residue theorem is not really an option.

(Later on, the poster started talking about integrating from -infty to
+infty, so maybe you are right and he has an analytic integral over
the whole real line, in which case it is truly bizarre that he would
be talking about FFTs or discretizing the integral in the first
place.)

Sorry I reacted badly to your post, but I saw red when you seemed to
be suggesting that, as soon as an integrand has poles anywhere, you
have to start worrying about contour integrations and branch cuts, or
that you would have to use adaptive winding-number schemes to find all
of the roots (/ poles). Ordinary numerical quadrature deals with
poles (off the real axis) just fine, with exponential accuracy if you
use a good quadrature scheme, and indeed you can't effectively use
contour-integration methods (except for asymptotic approximations) for
integrals over finite domains on the real axis (which is what I
thought the context here was).

Steven
.

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