Engineering Tables/Hilbert Transform Table

	Signal Name	Signal $s(t)$	Hilbert transform $\mathscr{H}\{s\}(t)$
1	Sine	$\sin (t)$	$-\cos (t)$
2	Cosine	$\cos (t)$	$\sin (t)$
3		$\frac{1}{t^2+1}$	$\frac{t}{t^2+1}$
4	Sinc function	$\frac{\sin (t)}{t}$	$\frac{1-\cos (t)}{t}$
5	Rectangular function	$\sqcap (t)$	$\frac{1}{\pi }\ln \left|\frac{t+\frac{1}{2}}{t-\frac{1}{2}}\right|$
6	Dirac delta function	$\delta (t)$	$\frac{1}{\pi t}$
7	Indicator function	${\chi }_{[a,b]}(x)$	$\frac{1}{\pi }\log \left|\frac{x-a}{x-b}\right|$