Trigonometric Interpolation

Complex trigonometric interpolation

$x\_n\; =\; \backslash frac\{2\; \backslash pi\; n\}\{N\}\; \backslash mbox\{\; ,\; \}\; n\; =\; 0,\backslash ldots,N-1$

$f(x\_n)\; =\; y\_n$.

$T\_\{N-1\}(x)\; =\; \backslash sum\_\{n=0\}^\{N-1\}\; a\_n\; e^\{\backslash mathrm\{i\}nx\}$

$a\_n\; =\; \backslash frac\{1\}\{N\}\; \backslash sum\_\{m=0\}^\{N-1\}\; y\_n\; \backslash omega\_\{N\}^\{-mn\}\; \backslash mbox\{\; ,\; \}\; m\; =\; 0,\backslash ldots,N-1$

$\backslash omega\_N^\{i\}$

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