Engineering Tables/Hilbert Transform Table

Current revision (unreviewed)

	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	$\chi_{[a,b]}(x) \,$	$\frac{1}{\pi}\log \left \vert \frac{x-a}{x-b}\right \vert \,$