How do I find the Hilbert transform (qudrature) of a discrete signal by convolution with a Hilbert kernel?
The short answer: with a finite convolution you can't calculate the Hilbert transform exactly.

The long answer: You will have to make approximations and decide what types and amounts of error you can live with. This will depend heavily on the application, the signals itself and what you are trying to do with the results. This paper may give good guidance on math and potential trade offs http://www.andrewduncan.ws/air/index.html

Per se, the Hilbert Transform is not a smoothing operation. For example the HT of a cosine is a sine, which isn't any smoother.