> In the course of understanding a cross-correlation problem (this is not
> homework!), I need to evaluate:
>
> sum (n = 0 to N) exp (j * n * theta)
>
> or equivalently:
>
> sum (n = 0 to N) cos(n* theta) + j * sum(n = 0 to N) sin(n *
> theta)
>
> where N is 150 or so and theta is something rather small, on the order
> of 0.001 * pi.
>
> I'd guess these summations are somewhat common and I could find them in
> some listing or other, but my lone math handbook lacks them, and so far
> I haven't found any such listing on the web. Can anyone give me a
> pointer to them? Many thanks.
Are you asking about the relationship
sum (n = 0 to N) z^n = (1 - z^(N+1)) / (1 - z)
???
--
% Randy Yates % "I met someone who looks alot like you,
%% Fuquay-Varina, NC % she does the things you do,
%%% 919-577-9882 % but she is an IBM."
%%%% <yates@ieee.org> % 'Yours Truly, 2095', *Time*, ELO
http://home.earthlink.net/~yatescr
> In the course of understanding a cross-correlation problem (this is not
> homework!), I need to evaluate:
>
> sum (n = 0 to N) exp (j * n * theta)
>
> or equivalently:
>
> sum (n = 0 to N) cos(n* theta) + j * sum(n = 0 to N) sin(n *
> theta)
>
> where N is 150 or so and theta is something rather small, on the order
> of 0.001 * pi.
>
> I'd guess these summations are somewhat common and I could find them in
> some listing or other, but my lone math handbook lacks them, and so far
> I haven't found any such listing on the web. Can anyone give me a
> pointer to them? Many thanks.
>
> cheers,
> jerry wolf
> spaceflight systems corp.
Maybe you could approximate the sum with a definite integral and get a
formula that way, since you'd be integrating sines and cosines which
are easy to solve.
John
Reply by Jerry Wolf●December 27, 20062006-12-27
In the course of understanding a cross-correlation problem (this is not
homework!), I need to evaluate:
sum (n = 0 to N) exp (j * n * theta)
or equivalently:
sum (n = 0 to N) cos(n* theta) + j * sum(n = 0 to N) sin(n *
theta)
where N is 150 or so and theta is something rather small, on the order
of 0.001 * pi.
I'd guess these summations are somewhat common and I could find them in
some listing or other, but my lone math handbook lacks them, and so far
I haven't found any such listing on the web. Can anyone give me a
pointer to them? Many thanks.
cheers,
jerry wolf
spaceflight systems corp.