Autocorrelation function of the sum of normal noise and two harmonic oscillations for a limited process and after Van Vleck transformation

• Published in: Radiophysics and quantum electronics 1998-09, Vol.41 (9), p.771-782
• Main Author: SODIN, L. G
• Format: Article
• Language: English
• Subjects: Astronomy; Autocorrelation functions; Correlation analysis; Earth, ocean, space; Estimates; Exact sciences and technology; Fundamental astronomy and astrophysics. Instrumentation, techniques, and astronomical observations; Gaussian; Harmonic oscillation; Mathematical procedures and computer techniques; Nonlinearity; Observation and data reduction techniques. Computer modeling and simulation; Quantum electronics; Random processes; Transformations (mathematics); Transforms
• ISSN: 0033-8443; 1573-9120
• DOI: 10.1007/BF02677632

This paper presents a rigorous analysis of statistical characteristics for the sum of a Gaussian random process and two harmonic oscillations transmitted through an inertialess limiter, a typical unit in radio astronomical spectrometers. The analysis was done for the two most interesting cases, that in which the dominant intensity belongs to the continuous-spectrum component, and that in which, conversely, the dominant intensity belongs to the discrete-spectrum component. The resulting expressions for the autocorrelation functions make it possible to estimate the power spectrum of a completely limited process and the spectrum of its Van Vleck transform. In both cases, the transformation improved the estimates of the autocorrelation function and the spectrum and reduced the nonlinear products, including the components with combination frequencies.[PUBLICATION ABSTRACT]