I'm having trouble locating a satisfactory reference on discrete Fourier transform (DFT). I would like to get a clear understanding for 1. DFT over $\mathbb{C}$ and 2. DFT over a finite field $\mathbb{F}_q$. My goal is to understand why these transforms are both called 'DFT.' I'm assuming because they satisfy very similar properties. Any suggestions for references would be greatly appreciated!

  • $\begingroup$ They both only need the existence of primitive roots of unity of the prescribed order $N$. In $\Bbb{C}$ we have those for all $N$. In $\Bbb{F}_q$ we need $N$ to be a factor of $q-1$. Both are about sequences with period $N$. They are called discrete, because it it about sequences rather than functions with a continuous domain. $\endgroup$ – Jyrki Lahtonen Feb 12 '16 at 7:11

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