آنالیز فوریه

${\displaystyle X(f)={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}x(t)\cdot e^{-i2\pi ft}dt}$

${\displaystyle x(t)={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}X(f)\cdot e^{i2\pi ft}df}$

${\displaystyle S[k]=\frac{1}{P}{\int }_P{s}_P(t)\cdot e^{-i2\pi \frac{k}{P}t}dt}$

${\displaystyle s_P(t)=\sum _{k=-\mathrm{\infty }}^{\mathrm{\infty }}S[k]\cdot e^{i2\pi \frac{k}{P}t}\stackrel{\mathcal{F}}{⟺}\sum _{k=-\mathrm{\infty }}^{+\mathrm{\infty }}S[k]\delta \left(f-\frac{k}{P}\right)}$