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Andthemapf:`2(znzn)!`2(znzn)givenbyf(i(n;m))0n;m=bi(n;m)0n;misthesocalleddiscretefouriertransform(dft).thismapisrealizedbytheformulabi(k;l)=hi;expk;li Kexpk;lk2=1 N2n�1xn=0n�1xm=0i(n;m)e�2i(k published presentations and documents on DocSlides.
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