Exact Discrete Gaussian Window
It can be shown [44] that
(4.58) |
where is the time index, and is the frequency index for a length (even) normalized DFT (DFT divided by ). In other words, the Normalized DFT (NDFT) of this particular sampled Gaussian pulse is exactly the complex-conjugate of the same Gaussian pulse. (The proof is nontrivial.)
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Gaussian Window and Transform