About the Multiplicative Inverse of a Non-Zero-Mean Gaussian Process

Abstract

We study the spectral properties of a stochastic process obtained by multiplicative inversion of a non-zero-mean Gaussian process. We show that its autocorrelation and power spectrum exist for most regular processes, and we find a convergent series expansion of the autocorrelation function in powers of the ratio between mean and standard deviation of the underlying Gaussian process. We apply the results to two sample processes, and we validate the theoretical results with simulations based on standard signal processing techniques.