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It can be shown [44] that
![$\displaystyle e^{-j\frac{\pi}{8}} \, e^{j\frac{2\pi}{N}\frac{1}{2}n^2} \;\longleftrightarrow\; e^{j\frac{\pi}{8}} \, e^{-j\frac{2\pi}{N}\frac{1}{2}k^2}$](img571.png) |
(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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