Category:Discrete Fourier Transforms
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This category contains results about Discrete Fourier Transforms.
Definitions specific to this category can be found in Definitions/Discrete Fourier Transforms.
Let $\sequence {x_k}_{1 \mathop \le k \mathop \le n}$ be a finite sequence of complex numbers for some $n \in \N_{>0}$.
The discrete Fourier transform of $\sequence {x_k}_{1 \mathop \le k \mathop \le n}$ is the sequence $\sequence {\hat x_k}_{1 \mathop \le k \mathop \le n}$ where:
- $\hat x_k = \ds \sum_{r \mathop = 1}^n x_r \map \exp {\dfrac {-2 \pi i k r} n}$