Spectral analysis for harmonizable processes
Keh-Shin Lii,Murray Rosenblatt +1 more
TLDR
In this article, periodogram-like and consistent estimators are proposed for spectral mass estimation when the spectral support of the process consists of lines, and detailed analysis on aliasing, bias and covariances of various estimators.Abstract:
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.read more
Citations
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Journal ArticleDOI
Cyclostationarity: half a century of research
TL;DR: A concise survey of the literature on cyclostationarity is presented and includes an extensive bibliography and applications of cyclostatedarity in communications, signal processing, and many other research areas are considered.
Journal ArticleDOI
Untangling cross-frequency coupling in neuroscience
Juhan Aru,Jaan Aru,Viola Priesemann,Michael Wibral,Luiz Lana,Gordon Pipa,Wolf Singer,Raul Vicente +7 more
TL;DR: This work organizes the available and potential novel statistical/modeling approaches according to their biophysical interpretability of cross-frequency coupling to provide a road map towards an improved mechanistic understanding of CFC.
Journal ArticleDOI
Bibliography on cyclostationarity
TL;DR: The present bibliography represents a comprehensive list of references on cyclostationarity and its applications by listing most of the existing references up to the year 2005 and by providing a detailed classification group.
Journal ArticleDOI
Cyclostationarity: Limits and generalizations
TL;DR: Limits to the applicability of the cyclostationary model in the presence of relative motion between transmitter and receiver are enlightened and two new classes of signals that extend the class of the almost-cyclostationARY signals and allow one to overcome these limits are reviewed.
Journal ArticleDOI
A test for second order stationarity of a multivariate time series
TL;DR: In this paper, it is shown that the test statistic under the null of stationarity asymptotically has a chi-squared distribution, whereas under the alternative of local stationarity, it has a noncentral chi-square distribution.
References
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Journal ArticleDOI
Exploitation of spectral redundancy in cyclostationary signals
TL;DR: It is shown that the cyclostationarity attribute, as it is reflected in the periodicities of (second-order) moments of the signal, can be interpreted in terms of the property that allows generation of spectral lines from the signal by putting it through a (quadratic) nonlinear transformation.
Journal ArticleDOI
Fitting time series models to nonstationary processes
TL;DR: In this paper, a general minimum distance estimation procedure for nonstationary time series models with an evolutionary spectral representation is presented and the asymptotic properties of the estimate are derived under the assumption of possible model misspecification.
Book
Cyclostationarity in Communications and Signal Processing
TL;DR: This book brings together the latest work in the field by the foremost experts and presents it in a tutorial fashion, instrumental in furthering progress in understanding and using cyclostationarity in all fields where it arises.
Book
Ocean Acoustic Tomography
TL;DR: In this paper, the authors present a comprehensive presentation of the underlying oceanography and mathematics necessary to understand and develop such a system, as well as numerous models for data interpretation, including forward and inverse tomography.