Zero-crossing intervals of Gaussian processes

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Abstract
The correlation between successive zero‐crossing intervals and their probability densities is experimentally studied for Gaussian processes having power spectra of Butterworth type. The assumption that successive zero‐crossing intervals from a Markov chain in the wide sense is found valid only for a process having a narrow‐band spectrum. The correlation coefficients between the lengths of several successive zero‐crossing intervals of a Gaussian process having a broad‐band spectrum decay slowly and reveal a peculiar oscillatory behavior as the number of intervals is increased. These results are interpreted by introducing a model. Results for Gaussian processes having power spectra of type (f/f0)2m[1+ (f/f0)2]−n are also given. The correlation of intervals is also determined by means of a single interval counter making efficient use of the so‐called bias effect, and its results agree closely with those from ordinary measurements using two interval counters.

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