Abstract
In this paper, the complete statistical characterization of the amplitude spectrum at the output of a multiple-input ADC-based measurement system is derived under the assumption of input channels with different noise levels. In practical applications the input channels correspond to the spatial components of a vector field (e.g., magnetic/electric field). Each output spectral line represents the amplitude of the vector field at a specific frequency. Such amplitude is a random variable depending on the noise levels (internal and external noise) of the input channels. Closed form analytical solution for the probability density function of the vector field amplitude is not available in the mathematical literature under the hypothesis of different noise levels. Therefore, an analytical expression for the probability density function is derived on the basis of a Laguerre series expansion. The impact of the kind of time window, the sampling frequency, and the number of samples is clearly derived and put into evidence. Approximate analytical expressions for the mean value and the variance of the vector field amplitude are also provided. Analytical results are validated by means of numerical simulations.