Noise effects in time-domain systems involving three-axial field probes for the measurement of nonstationary radiated emissions

This paper deals with three-axial systems for timedomain measurement of radiated emissions. A statistical analysis is developed in order to assess the influence of noise on the system measurement uncertainty in the case of nonstationary emissions, for which averaging techniques cannot be exploited. For a vector field with spatial components consisting of multiple sinusoids in additive white or colored noise, the modifications in the statistics of the measured signals due to application of the discrete Fourier transform to the digitized time series are investigated. The analysis is carried out in the frequency domain, and is used for probabilistic detection and maximum likelihood estimation of the amplitude of spectral lines close to the noise floor (i.e., in the typical conditions imposed by short-time measurement windows due to signal nonstationarity). Results are extended to sum, sum of squares, and logarithm of the amplitude of the spectral lines. As an application example, statistical estimates are derived for the safety factor used to assess compliance with the International Commission on Non-Ionizing Radiation Protection (ICNIRP) guidelines, in case of nonionizing radiation exposure to multiple frequency magnetic fields. The theoretical work is validated both versus test signals with known statistical properties and against measurement data obtained with a time-domain system for magnetic field measurement in the bandwidth 100 kHz–1.5 GHz.