  We express Witten's deformation of Morse functions using deformation to the
normal cone and $C^*$-modules. This allows us to obtain asymptotics of the
`large eigenvalues'. Our methods extend to Morse functions along a foliation.
We construct the Witten deformation using any generic function on an arbitrary
foliation on a compact manifold and establish the compactness of its resolvent.
When the foliation has a holonomy invariant transverse measure we show that our
result implies Morse inequalities obtained by Connes and Fack in a slightly
more general situation.
