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Tuesday, 8 January 2008

fourier analysis - A sum involving sines

Consider a scaled sine function, sin(2pix/2n), for some positive integer n. For this, I have the following linear combination.



sum2n2x=1cxsin(2pix/2n).
(The upper limit to the sum is 2n2.)



The question is whether there exist cxin0,pm1,pm2, not all 0, that make the above expression 0, for infinitely many n?



If it helps, the above came up in a computation concerning the discrete Fourier Transform.

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