$X(\omega)=\displaystyle\int_{-\infty}^{\infty}x(t)e^{-i\omega t}dt$

X(\omega)=\int_{-\infty}^{\infty}x(t)e^{-i\omega t}dt

$t=n\Delta t$

t=n\Delta t

$x(t)=x(t\pm kT)$

x(t)=x(t\pm kT)

$x(t)=\displaystyle\frac{a_0}{2}+\sum_{k=1}^{\infty}(a_k\cos\omega_kt+b_k\sin\omega_k t)$

x(t)=\displaystyle\frac{a_0}{2}+\sum_{k=1}^{\infty}(a_k\cos\omega_kt+b_k\sin\omega_k t)

$\omega_k=\displaystyle\frac{2\pi k}{T}$

\omega_k=\displaystyle\frac{2\pi k}{T}

$ a_k =\displaystyle\frac{2}{ T }\int_0^ T x(t) \cos \omega_k t dt $

a_k = T *@INT( x *cos( omega_k * t ), t ,0, T )

$b_k=\displaystyle\frac{2}{T}\int_0^Tx(t)\sin\omega_kt dt$

b_k=\displaystyle\frac{2}{T}\int_0^Tx(t)\sin\omega_kt dt

$a_0=2\bar{x}$

a_0=2\bar{x}

$x(t)=\bar{x}+\displaystyle\sum_{k=1}^{\infty}X_k\cos(\omega_kt-\phi_k)$

x(t)=\bar{x}+\sum_{k=1}^{\infty}X_k\cos(\omega_kt-\phi_k)

$X_k=\sqrt{a_k^2+b_k^2}$

X_k=\sqrt{a_k^2+b_k^2}

$\phi_k=\arctan\displaystyle\frac{b_k}{a_k}$

\phi_k=\arctan\displaystyle\frac{b_k}{a_k}

$x(t)=\displaystyle\int_{-\infty}^{\infty}X(\omega)e^{+i\omega t}d\omega$

x(t)=\int_{-\infty}^{\infty}X(\omega)e^{+i\omega t}d\omega

$ \omega = 2 \pi \nu $

omega = 2* pi * nu