Non-power-law behavior observed in zero-crossing intervals of 1/f~(alpha) noise

摘要

Previously we derived the probability density function (PDF) of the zero-crossing interval for 1/f~(alpha) noise and found that the PDF, L(t) follows the power law of the form 1/t~(c), where the exponent c relates to the exponent alpha as c velence 3 - alpha when 0 < alpha < 1 and c velence (5 - alpha)/2 when 1 < alpha < 2. (Proc. SPIE Vol. 5471, p. 29, 2004). This analytical result agreed with numerical experiments for relatively large values of alpha but not for small values, i.e., the experimental PDF deviates from the power law in the range 0 <= alpha approx.< 0.7. We present here a discrete version of the previous theory by noting that the experimental data is defined only on discrete time points. The result agrees well with the experiment for the whole range of a and explains the deviation from the power law of PDF in the range of small alpha.