Mean square and almost sure Whittaker-type derivative sampling theorems are obtained for the class $L^\alpha( \Omega , {\mathfrak F}, {\mathsf P});\, 0 \leq \alpha \leq 2$ of stochastic processes having spectral representation, with the aid of the Weierstra{\ss} $\sigma$. Functions of this class are represented by interpolatory series.  The interpolation formul{\ae} are interpreted in the $\alpha$--mean and also in the almost sure ${\mathsf P}$ sense when the initial signal function and its derivatives (up to some fixed order) are sampled at the points of the integer lattice ${\mathbb Z}^2$. Finally, sampling sum convergence rate discussion is provided.