Experimental Results on the Level Crossing Intervals of the Phase of Sine Wave Plus Noise

Experimental study was made on the level crossing intervals of a phase process of a sine wave plus narrow-band Gaussian noise. Since successive level crossings of phase do not necessarily occur alternately in the upward and downward direction due to the phase jump beyond 2π, the usual definitions of the probability densities of the level crossing intervals for continuous random processes are not applicable in the case of the phase process. Therefore, the probability densities of level crossing intervals of phase process are newly defined. Measurements of these densities were performed for noise having lowpass spectra of Gaussian and 7th order Butterworth types. Results are given for various values of the signal-to-noise power ratio and of the crossing level, and compared with corresponding approximation developed under the assumption of quasi-independence. The validity of the assumption depends on the spectrum shape of the noise.