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