The mapping that may be used to map low pass analog filters into high pass digital filters and high pass analog filters into low pass digital filters are:
1
\(s = \frac{{1 - {z^{ - 1}}}}{{1 + {z^{ - 1}}}}\)
2
\(s = \frac{{1 + z}}{{1 - z}}\)
3
\(s = \frac{{1 - {z^{ - 1}}}}{2}\)
4
\(s = \frac{{1 + {z^{ - 1}}}}{{1 - {z^{ - 1}}}}\)