Exact Autocorrelation of the Multiplicative Inverse of a Non-Zero-Mean Complex Gaussian Process

2025/09/15 by Marco Lanucara, Lanucara, Marco
Computer Science · Decision Sciences · Environmental Science · Mathematics · #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.2509.11650

arxiv created 2026/08/03 · arxiv updated 2026/08/04

Abstract

We study the spectral properties of a stochastic process obtained by multiplicative inversion of a non-zero-mean complex Gaussian process. We show that its autocorrelation function and power spectrum exist for most regular processes, and we derive a first order differential equation for the autocorrelation function, which follows from a demonstrated recurrence relation between the coefficients of its series expansion. Finally, we obtain a closed-form expression of the autocorrelation function based on the first and second order statistics of the underlying Gaussian process.

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