On Walsh differentiable dyadically stationary random processes

Some basic properties of dyadically stationary (DS) processes are introduced, including continuity and spectral representation. A sampling theorem based on the Walsh functions is investigated for random signals that are not necessarily sequency-limited. By using the concept of a dyadic derivative, the resulting aliasing error is calculated together with the speed of convergence. An example gives a glimpse into the possibilities of applying the sampling theorem as well as the dyadic derivative.