سری فوریه گسسته کاهنده

${\displaystyle x_n=\sum _{k=-q}^q{X}_k{e}^{\frac{-i2\pi k{t}_n}{T}}+{\epsilon }_n,t_n\text{ arbitrary },n=1,\dots ,N}$

${\displaystyle WX=x+\epsilon }$

${\displaystyle \hat{X}=(W^{H}W{)}^{-1}{W}^{H}x}$

${\displaystyle \hat{x}=Wx}$

${\displaystyle \frac{dx}{dt}(t_n)=\sum _{k=-q}^q\frac{-i2\pi k}{T}{X}_k{e}^{\frac{-i2\pi k{t}_n}{T}},n=1,\dots ,N}$