t=n\Delta t

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)

a_0=2\bar{x}

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

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

The relationship between the angular frequency ($\omega$) and the sound frequency ($\nu$) is expressed as:

kyon

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

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

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

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

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

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