Fourier Transform Visualizer

Enter a time function, apply the Fourier properties, and watch the spectrum respond. Correspondence table

$$ X(\mathrm{j}\omega)=\mathcal{F}\{x(t)\}=\int_{-\infty}^{\infty} x(t)\,\mathrm{e}^{-\mathrm{j}\omega t}\,\mathrm{d}t $$

Fourier properties

Leave the other sliders neutral to study one property on its own.

0.0 \(x(t-t_0)\ \leftrightarrow\ X(\mathrm{j}\omega)\,\mathrm{e}^{-\mathrm{j}\omega t_0}\)
1.00 \(x(a\,t)\ \leftrightarrow\ \tfrac{1}{|a|}\,X\!\left(\mathrm{j}\tfrac{\omega}{a}\right)\)
0.00 π \(x(t)\,\mathrm{e}^{\mathrm{j}\omega_0 t}\ \leftrightarrow\ X(\mathrm{j}(\omega-\omega_0))\)
0° \(x(t)\,\mathrm{e}^{\mathrm{j}\varphi}\ \leftrightarrow\ X(\mathrm{j}\omega)\,\mathrm{e}^{\mathrm{j}\varphi}\)