Re: Problem rephrased: how to simplify summation of millions of exponentials symbolicly

• To: mathgroup at smc.vnet.net
• Subject: [mg50200] Re: Problem rephrased: how to simplify summation of millions of exponentials symbolicly
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Fri, 20 Aug 2004 04:57:43 -0400 (EDT)
• Organization: Universitaet Leipzig
• References: <cg20h0\$ok0\$1@smc.vnet.net>
• Reply-to: kuska at informatik.uni-leipzig.de
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

you have the r[a,b] only as a lookup table and expect
that you kan find asymbolic expression -- funny.

What is with a 2d Fourier transformation to do the summation
and obtain the discrete grid of values for u and v ?

Regards
Jens

networm wrote:
>
> Hi all,
>
> I have a summation of exponentials:
>
> SUM= 1+r(a1, b1)*exp(-j*(a1*u+b1*v))+r(a2, b2)*exp(-j*(a2*u+b2*v))+r(a3,
> b3)*exp(-j*(a3*u+b3*v))
>            + ...
>            + r(a1000000, b1000000)*exp(-j*(a1000000*u+b1000000*v))
>
> where "j" is the imaginary sign.  a1, a2, ... a1000000, b1, b2, ... b1000000
> are known constants... (a's and b's) constitute some grids on the 2D plane,
> r(a, b) is the function defined on this 2D plane...
> r(a, b) is known as a look-up-table, but there is no closed-form expression
> for r(a, b)...
> u, v are frequency variable in 2D case.
>
> Do you think it is possible to compute the close-form of the above SUM
> symbolically/analytically?
>
> If not, is there any simple/efficient way to compute it ?
>
> I just need to compute this huge expression once, then if an simplified
> symbolic expression is found, it will save my subsequent numerical
> evaluations(that's going to tens of millions...)

```

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