Tabel properti:

Properti \(\boldsymbol{f(t)}\) \(\boldsymbol{F(\omega)}\)
Linearity \(a_1f_1(t)+a_2f_2(t)\) \(a_1F_1(\omega)+a_2F_2(\omega)\)
Scaling \(f(at)\) \(\frac{1}{|a|}f\left(\frac{\omega}{a}\right)\)
Time shift \(f(t-a)\) \(e^{-j\omega a}F(\omega)\)
Frequency shift \(e^{j\omega_0 t}f(t)\) \(F(\omega-\omega_0)\)
Modulation \(\cos(\omega_0 t)f(t)\) \(\frac{1}{2}[F(\omega+\omega_0)+F(\omega-\omega_0)]\)
Time differentiation \(\frac{df}{dt}\)

\(\frac{d^n f}{dt^n}\)		 \(j\omega F(\omega)\)

\((j\omega)^n F(\omega)\)
Time integration \(\int_{-\infty}^{t}f(t)\,d(t)\) \(\frac{F(\omega)}{j\omega}+\pi F(0)\delta(\omega)\)
Frequency differentiation \(t^nf(t)\) \((j)^n\frac{d^n}{d\omega ^n}F(\omega)\)
Reversal \(f(-t)\) \(F(-\omega)\) or \(F^*(\omega)\)
Duality \(F(t)\) \(2\pi f(-\omega)\)
Convolution in \(t\) \(f_1(t)*f_2(t)\) \(F_1(\omega)F_2(\omega)\)
Convolution in \(\omega\) \(f_1(t)f_2(t)\) \(\frac{1}{2\pi}F_1(\omega)*F_2(\omega)\)

Tabel pasangan:

\(\boldsymbol{f(t)}\) \(\boldsymbol{F(\omega)}\)
\(\delta (t)\) \(1\)
\(1\) \(2\pi\delta(\omega)\)
\(u(t)\) \(\pi\delta(\omega)+\frac{1}{j\omega}\)
\(u(t+\tau)-u(t-\tau)\) \(2\frac{\sin \omega\tau}{\omega}\)
\(|t|\) \(\frac{-2}{\omega ^2}\)
\(\text{sgn}(t)\) \(\frac{2}{j\omega}\)
\(e^{-at}u(t)\) \(\frac{1}{a+j\omega}\)
\(e^{at}u(-t)\) \(\frac{1}{a-j\omega}\)
\(t^n e^{-at}u(t)\) \(\frac{n!}{(a+j\omega)^{n+1}}\)
\(e^{-a|t|}\) \(\frac{2a}{a^2+\omega ^2}\)
\(e^{j\omega_0 t}\) \(2\pi\delta (\omega-\omega_0)\)
\(\sin \omega_0 t\) \(j\pi [\delta(\omega+\omega_0)-\delta(\omega-\omega_0)]\)
\(\cos \omega_0 t\) \(\pi [\delta(\omega+\omega_0)+\delta(\omega-\omega_0)]\)
\(e^{-at}\sin \omega_0 t\,u(t)\) \(\frac{\omega_0}{(a+j\omega)^2 +\omega_0^2}\)
\(e^{-at}\cos \omega_0 t\,u(t)\) \(\frac{a+j\omega}{(a+j\omega)^2 +\omega_0^2}\)