This paper deals with continuous-parameter dyadic stationary processes. A necessary and sufficient condition for such a process to assume its spectral representation in terms of the generalized Walsh functions is given. The representation plays an important role in the analysis of such a process: we discuss laws of large numbers, sampling theorem, and the relationship between the dyadic stationary processes with spectral densities and linear dyadic processes.
The existence of a spectral representation shows the possibility of an analysis of dyadic stationary processes similar to that of ordinary stationary processes.
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