Spectral Analysis for Harmonizable Processes

Spectral estimation of nonstationary but harmonizable processes is considered. Given a single realization of the process, periodogram-like and consistent estimators are proposed for spectral mass estimation when the spectral support of the process consists of lines. Such a process can arise in signa...

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Bibliographic Details
Published in:The Annals of statistics 2002-02, Vol.30 (1), p.258-297
Main Authors: Lii, Keh-Shin, Rosenblatt, Murray
Format: Article
Language:English
Subjects:
60G12
62F12
62G07
62M15
aliasing
Average linear density
bias
consistency
Covariance
cyclostationary
Doppler
estimation
Exact sciences and technology
Fall lines
harmonizable processes
Inference from stochastic processes
time series analysis
Integers
Line spectra
Mass spectroscopy
Mathematics
multipath
Nonparametric inference
Overtone series
Parametric inference
Probability and statistics
Sciences and techniques of general use
Spectral Analysis and Kriging
Spectral density function
Spectral energy distribution
Spectroscopy
Stationary processes
Statistics
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Summary:Spectral estimation of nonstationary but harmonizable processes is considered. Given a single realization of the process, periodogram-like and consistent estimators are proposed for spectral mass estimation when the spectral support of the process consists of lines. Such a process can arise in signals of a moving source from array data or multipath signals with Doppler stretch from a single receiver. Such processes also include periodically correlated (or cyclostationary) and almost periodically correlated processes as special cases. We give detailed analysis on aliasing, bias and covariances of various estimators. It is shown that dividing a single long realization of the process into nonoverlapping subsections and then averaging periodogram-like estimates formed from each subsection will not yield meaningful results if one is estimating spectral mass with support on lines with slope not equal to 1. If the slope of a spectral support line is irrational, then spectral masses do not fold on top of each other in estimation even if the data are equally spaced. Simulation examples are given to illustrate various theoretical results.
ISSN:0090-5364
2168-8966
DOI:10.1214/aos/1015362193