Re: how to simplify a summation of exponentials symbolicly/analytically?
From: networm (networm8848_at_yahoo.com)
Date: 08/17/04
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Date: Tue, 17 Aug 2004 09:07:54 -0700
"networm" <networm8848@yahoo.com> wrote in message
news:cfsced$rv4$1@news.Stanford.EDU...
> Hi all,
>
> I have a summation of exponentials:
>
> SUM= 1+exp(-j*(a1*u+b1*v))+exp(-j*(a2*u+b2*v))+exp(-j*(a3*u+b3*v))
> + ...
> + exp(-j*(a1000000*u+b1000000*v))
>
> where "j" is the imaginary sign. a1, a2, ... a1000000, b1, b2, ...
b1000000
> are known constants... 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 ? In Matlab and
> Maple...
>
>
How does supposing a's, b's are scattered on the 2D plane regularly.
Case 1) they are equal-distance real numbers;
Case 2) they are almost equal-distance, but in diamond shape, so like points
intersected by parallel lines...
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