Évènement

An important class of processes used to model nonstationary signals is a class of harmonizable processes. These processes can be seen as the superposition of sine and cosine waves with random amplitudes. Their analysis allows us to study how different signal frequencies are correlated with each other. Covariance between frequencies is mostly measured by the spectral density function, while correlation is measured by the spectral coherence function.

In this talk, we focus on harmonizable processes whose spectral measure is concentrated on a union of lines, potentially with non-unit slopes. This class of processes is a generalization of well-known, almost periodically correlated processes. The processes studied have practical applications in communication, such as the location of moving sources such as aircrafts, rockets, or hostile jamming emitters that transmit signals.

First, we address the spectral density estimation problem. We propose a periodogram frequency-smoothed along the support line as the estimator. We establish the mean-square consistency of its normalized version, considering scenarios where the support line is known or unknown. In addition, we derive the asymptotic distribution of this estimator when the support line is known. Consequently, we obtain the asymptotic distribution of the spectral coherence estimator based on a periodogram frequency-smoothed along the support line. Moreover, we introduce a consistent subsampling technique designed specifically for the spectral analysis of the considered class of processes. This technique enables the construction of subsampling-based confidence intervals for spectral characteristics. To validate the theoretical findings, we provide a numerical example applied to models commonly used in acoustics and communication systems.

[1] Dudek, A.E., Majewski, B. and Napolitano, A. (2024), Spectral Density Estimation for a Class of Spectrally Correlated Processes. J. Time Ser. Anal., 45: 884-909. doi: 10.1111/jtsa.12742

[2] Dudek A.E. and Majewski B. (2024), Asymptotic distribution and subsampling in spectral analysis for spectrally correlated processes. submitted on August 2024. preprint: https://hal.science/hal-04675084