  We define exact functors from categories of Harish-Chandra modules for
certain real classical groups to finite-dimensional modules over an associated
graded affine Hecke algebra with parameters. We then study some of the basic
properties of these functors. In particular, we show that they map irreducible
spherical representations to irreducible spherical representations and,
moreover, that they preserve unitarity. In the case of split classical groups,
we thus obtain a functorial inclusion of the real spherical unitary dual (with
real infinitesimal character) into the corresponding p-adic spherical unitary
dual.
