440 B
440 B
Discreet Fourier transform
\begin{bmatrix}
\hat{f_1} \\
\hat{f_2} \\
\hat{f_3} \\
... \\
\hat{f_n}
\end{bmatrix}
=
\begin{bmatrix}
1 & 1 & 1 & ... & 1\\
1 & w_n & w_n^2 & ... & w_n^{n-1}\\
1 & w^2_n & w_n^4 & ... & w_n^{2(n-1)}\\
... & ... & ... & ... & ...\\
1 & w_n^{n-1} & w_n^{2(n-1)} & ... & w_n^{(n-1)^2}
\end{bmatrix}
\begin{bmatrix}
f_1 \\
f_2 \\
f_3 \\
... \\
f_n
\end{bmatrix}
w_n = e^{-2j \pi / n}