Intrinsic Random Functions and the Paradox of $1/{\text{f}}$ Noise

Abstract

By means of a generalized Fejer theorem, certain stationary increment random functions and random fields are shown to possess nonintegrable time invariant spectra. The periodogram computed from a stationary increment process is shown to have the same sort of asymptotic statistical properties (e.g., central limit theorem) as the periodogram of a stationary process does. These results throw light on the paradoxical nature of Flicker noise and related phenomena that occur with random fields.