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「回路計算 - 離散フーリエ変換」の版間の差分
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| 28行目: | 28行目: | ||
<math> | <math> | ||
W = | W = | ||
\begin{ | \begin{pmatrix} | ||
W^{0} & W^{0} & W^{0} & \ldots & W^{0} \\ | W^{0} & W^{0} & W^{0} & \ldots & W^{0} \\ | ||
W^{0} & W^{1} & W^{2} & \ldots & W^{N - 1} \\ | W^{0} & W^{1} & W^{2} & \ldots & W^{N - 1} \\ | ||
| 34行目: | 34行目: | ||
\vdots & \vdots & \vdots & \ddots & \vdots \\ | \vdots & \vdots & \vdots & \ddots & \vdots \\ | ||
W^{0} & W^{N - 1} & W^{2(N - 1)} & \ldots & W^{(N - 1)^2} \\ | W^{0} & W^{N - 1} & W^{2(N - 1)} & \ldots & W^{(N - 1)^2} \\ | ||
\end{ | \end{pmatrix} | ||
</math><br> | </math><br> | ||
<br> | <br> | ||
* 離散フーリエ変換<br> | * 離散フーリエ変換<br> | ||
<math> | <math> | ||
\begin{ | \begin{pmatrix} | ||
X_{0} \\ X_{1} \\ X_{2} \\ \vdots \\ X_{N - 1} | X_{0} \\ X_{1} \\ X_{2} \\ \vdots \\ X_{N - 1} | ||
\end{ | \end{pmatrix} | ||
= | = | ||
\begin{ | \begin{pmatrix} | ||
W^{0} & W^{0} & W^{0} & \ldots & W^{0} \\ | W^{0} & W^{0} & W^{0} & \ldots & W^{0} \\ | ||
W^{0} & W^{1} & W^{2} & \ldots & W^{N - 1} \\ | W^{0} & W^{1} & W^{2} & \ldots & W^{N - 1} \\ | ||
| 49行目: | 49行目: | ||
\vdots & \vdots & \vdots & \ddots & \vdots \\ | \vdots & \vdots & \vdots & \ddots & \vdots \\ | ||
W^{0} & W^{N - 1} & W^{2(N - 1)} & \ldots & W^{(N - 1)^2} \\ | W^{0} & W^{N - 1} & W^{2(N - 1)} & \ldots & W^{(N - 1)^2} \\ | ||
\end{ | \end{pmatrix} | ||
\begin{pmatrix} | |||
\begin{ | |||
x_{0} \\ x_{1} \\ x_{2} \\ \vdots \\ x_{N - 1} | x_{0} \\ x_{1} \\ x_{2} \\ \vdots \\ x_{N - 1} | ||
\end{ | \end{pmatrix} | ||
</math><br> | </math><br> | ||
<br> | <br> | ||
* 逆離散フーリエ変換<br> | * 逆離散フーリエ変換<br> | ||
<math> | <math> | ||
\begin{ | \begin{pmatrix} | ||
x_{0} \\ x_{1} \\ x_{2} \\ \vdots \\ x_{N - 1} | x_{0} \\ x_{1} \\ x_{2} \\ \vdots \\ x_{N - 1} | ||
\end{ | \end{pmatrix} | ||
= | = | ||
\begin{ | \begin{pmatrix} | ||
W^{0} & W^{0} & W^{0} & \ldots & W^{0} \\ | W^{0} & W^{0} & W^{0} & \ldots & W^{0} \\ | ||
W^{0} & W^{-1} & W^{-2} & \ldots & W^{-(N - 1)} \\ | W^{0} & W^{-1} & W^{-2} & \ldots & W^{-(N - 1)} \\ | ||
| 68行目: | 67行目: | ||
\vdots & \vdots & \vdots & \ddots & \vdots \\ | \vdots & \vdots & \vdots & \ddots & \vdots \\ | ||
W^{0} & W^{-(N - 1)} & W^{-2(N - 1)} & \ldots & W^{-(N - 1)^2} \\ | W^{0} & W^{-(N - 1)} & W^{-2(N - 1)} & \ldots & W^{-(N - 1)^2} \\ | ||
\end{ | \end{pmatrix} | ||
\begin{pmatrix} | |||
\begin{ | |||
X_{0} \\ X_{1} \\ X_{2} \\ \vdots \\ X_{N - 1} | X_{0} \\ X_{1} \\ X_{2} \\ \vdots \\ X_{N - 1} | ||
\end{ | \end{pmatrix} | ||
</math><br> | </math><br> | ||
<br><br> | <br><br> | ||