If X(t) is a continuous wide sense stationary (WSS) process, we know that 
E(X(t)) is independent of time
R_xx (t1,t2) depends on t1-t2 only.


Now if we have a function f(z) where z is any real number, inverse of f(z) exists and f(z) is monotonic and bounded (particularly, f(z)=tanh(z) )
can we say that X(t) and f(X(t)) are jointly WSS?

Particularly, if X(t) is a gaussian process or of the form X(t)=A(sin(wt+\theta)) with \thata ~ uniform(0,2\pi)