Engineering Tables/Hilbert Transform Table

	Signal Name	Signal $s(t)\,$	Hilbert transform ${\mathcal {H}}\{s\}(t)$
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	$\chi _{[a,b]}(x)\,$	${\frac {1}{\pi }}\log \left\vert {\frac {x-a}{x-b}}\right\vert \,$