Talk:A derivation of the discrete Fourier transform

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I suggest a merge with Fourier transform if it is that useful or a creation of a pages derivations of Fourier transform--Cronholm144 23:04, 12 May 2007 (UTC)

[edit] Alternate derivation without continuous time Fourier integrals

I find the nicer derivation to be the one that starts with length N discrete sequence, and shows that this can be expressed in terms of an N dimensional unit impulse basis set. Using standard theorems in linear algebra we know that we change the basis, and we select the sampled complex sinusoids and expand the original sequence in terms of them. We find the coefficients using inner products. The coefficients are the DFT and the expansion in terms of the sampled sinuisoids are the IDFT. No real need for knowledge of the continuous time stuff which is more difficult to justify mathematically. DivisionByZer0 02:32, 29 June 2007 (UTC)