# Engineering Tables/Hilbert Transform Table

$s(t)\,$
$\mathcal{H}\{s\}(t)$
1 Sine $\sin(t)\,$ $-\cos(t)\,$
2 Cosine $\cos(t)\,$ $\sin(t)\,$
3   $1 \over t^2 + 1$ $t \over t^2 + 1$
4 Sinc function $\sin(t) \over t$ $1 - \cos(t) \over t$
5 Rectangular function $\sqcap(t)$ ${1 \over \pi} \ln \left | {t+{1 \over 2} \over t-{1 \over 2}} \right |$
6 Dirac delta function $\delta(t)\,$ ${1 \over \pi t}$
7 Indicator function $\chi_{[a,b]}(x) \,$ $\frac{1}{\pi}\log \left \vert \frac{x-a}{x-b}\right \vert \,$