ZERO-CROSSING STATISTICS OF 1/F NOISE

Probability density distributions of the interval spacings between zero-crossings of band-limited Nyquist and 1/f noise signals are examined using an interval-to-pulseheight converter and a multichannel pulse-height analyzer. The Nyquist noise distributions follow a simple exponential law, as expected. In the case of 1/f noise, the distributions are approximately proportional to the inverse square of the spacing interval. The probability density is statistically stationary, that is, independent of sample length and independent of the sample selected. For signals in a 1 Hz to 5 kHz band the most probable spacing interval is 1.2×10-4 sec, which occurs with a maximum probability density of 2.2×103 sec-1. The most probable value is inversely proportional to the highest signal frequency present and the peak probability density is proportional to this frequency. © 1969 The American Institute of Physics.