A study of the fractal character in electronic noise processes

The time dependence of Johnson electronic noise in resistors is explored from the perspective of fractional Brownian motion (fBm). The electronic noise source, manufactured to generate broad white noise Fourier power spectrum, is studied for long-range dependence by the estimation of the Hurst exponent within the rescaled range analysis (R/S). It is found that most of the time series studied possessed characteristics of an ordinary Wiener–Brownian motion (H=0.5). However, a weak (4%), yet statistically significant deviation from this picture (H=0.521±0.004, df=62) was identified within one of the time series of considerable total size (450,000 data units), exhibiting persistent fBm. The R/S technique was also applied on pseudo-random computer simulated data, obeying the statistical distribution of the electronic noise records, to reveal anti-persistent fBm instead (H<0.5). The current analysis indicates that the observed shift from an ordinary Brownian motion to a persistent fBm may underline a trait of chaotic behaviour in the electronic noise process.