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Make N be the smallest power of 2 larger than 3*K+1

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Ian Jauslin
2022-05-26 20:54:30 -04:00
parent 480ce57afa
commit 77043e249c
4 changed files with 86 additions and 5 deletions
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docs/nstrophy_doc/nstrophy_doc.tex
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@ -108,9 +108,9 @@ in which $\mathcal F^*$ is defined like $\mathcal F$ but with the opposite phase
\end{equation}
provided
\begin{equation}
N_i>4K_i.
N_i>3K_i.
\end{equation}
Indeed, $\sum_{n_i=0}^{N_i}e^{-\frac{2i\pi}{N_i}n_im_i}$ vanishes unless $m_i=0\%N_i$ (in which $\%N_i$ means `modulo $N_i$'), and, if $p,q\in\mathcal K$, then $|p_i+q_i|\leqslant2K_i$.
Indeed, $\sum_{n_i=0}^{N_i}e^{-\frac{2i\pi}{N_i}n_im_i}$ vanishes unless $m_i=0\%N_i$ (in which $\%N_i$ means `modulo $N_i$'), and, if $p,q,k\in\mathcal K$, then $|p_i+q_i-k_i|\leqslant3K_i$, so, as long as $N_i>3K_i$, then $(p_i+q_i-k_i)=0\%N_i$ implies $p_i+q_i=k_i$.
Therefore,
\begin{equation}
T(\hat\varphi,k)