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A class of random processes whose covariance functions are invariant under the shift by the dyadic addition is considered. These processes are called to be dyadic stationary. It is shown in theorem 2 ...that a dyadic stationary process has always spectral representation in terms of the system of Walsh functions parallel to an ordinary stationary process in terms of the system of trigonometric functions. By making use of spectral representation in terms of the system of Walsh functions, necessary and sufficient conditions for a dyadic stationary process to be a dyadic linear process introduced in Morettin (1974) are shown in theorems 3 and 4.show more
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