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.

# Summation problem

Started by ●December 27, 2006

Reply by ●December 27, 20062006-12-27

Jerry Wolf wrote:> 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 ●December 27, 20062006-12-27

I appealed for help a little too soon. Further creative googling and link-following led me to: Weisstein, Eric W. "Exponential Sum Formulas." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/ExponentialSumFormulas.html and also http://mathworld.wolfram.com/Cosine.html http://mathworld.wolfram.com/Sine.html where the needed formulas were found. cheers, jerry

Reply by ●December 27, 20062006-12-27

"Jerry Wolf" <jjwolf22@verizon.net> writes:> 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