Fourier Transform

1 min read Updated Fri Apr 24 2026 03:19:45 GMT+0000 (Coordinated Universal Time)

F(\omega) = \frac{1}{2\pi} \int_{-\infty}^{\infty} f(t) e^{-j\omega t}\,\text{d}t

$F$ is a continuous function of $\omega$ , and is called the spectrum of $f(t)$ .

Always done using numerical methods. Used for non-repetitive signals. Used in telecommunications, and in transient analysis, especially where the circuit parameters are frequency dependent.

Fourier inverse transform

F(t) = \int_{-\infty}^{\infty} F(\omega) e^{j\omega t}\,\text{d}\omega