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...)