Tuesday, 8 January 2008

fourier analysis - A sum involving sines

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



sum2n2x=1cxsin(2pix/2n).sum2n2x=1cxsin(2pix/2n).
(The upper limit to the sum is 2n22n2.)



The question is whether there exist cxin0,pm1,pm2cxin0,pm1,pm2, not all 00, that make the above expression 00, for infinitely many nn?



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

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