Engineering Tables/Hilbert Transform Table

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  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 \,