Fourier Series Coefficients

#Math

$\displaystyle c_{k}=\frac{1}{T_{0}}\int_{\tau}^{\tau+T_{0}} f(t)e^{-jk{\omega}_{0}t} , \mathrm{d}t$

• Fourier series coefficients

Properties (assuming

$\displaystyle \mathfrak{R}(c_{k})=\mathfrak{R}(c_{-k})$

$\displaystyle \mathfrak{I}(c_{k})=-\mathfrak{I}(c_{-k})$

$\displaystyle c^{*}{k}=c{-k}$

$\displaystyle \lvert c_{k}\rvert=\lvert c_{-k}\rvert$

$\displaystyle \angle c_{k}=-\angle c_{k}^{*}$