A comparison between different discrete ambiguity domain definitions in stochastic time-frequency analysis

Authors:
Johan Sandberg;Maria Hansson-Sandsten
Affiliations:
Mathematical Statistics, Centre for Mathematical Sciences, Lund University, Lund, Sweden;Mathematical Statistics, Centre for Mathematical Sciences, Lund University, Lund, Sweden
Venue:
IEEE Transactions on Signal Processing
Year:
2009

Citing 10
Cited 2

Estimation of evolutionary spectrum based on short time Fourier transform and modified group delay

Signal Processing - Signal processing in communications
Kernels and Multiple Windows for Estimation of the Wigner-Ville Spectrum of Gaussian Locally Stationary Processes

IEEE Transactions on Signal Processing
Optimal kernels for nonstationary spectral estimation

IEEE Transactions on Signal Processing
Discrete-time, discrete-frequency, time-frequency analysis

IEEE Transactions on Signal Processing
An overview of aliasing errors in discrete-time formulations oftime-frequency representations

IEEE Transactions on Signal Processing
Shift covariant time-frequency distributions of discrete signals

IEEE Transactions on Signal Processing
A note on “An overview of aliasing errors in discrete-timeformulations of time-frequency representations”

IEEE Transactions on Signal Processing
Time-Frequency ARMA Models and Parameter Estimators for Underspread Nonstationary Random Processes

IEEE Transactions on Signal Processing
An adaptive optimal-kernel time-frequency representation

IEEE Transactions on Signal Processing
Nonstationary spectral analysis based on time-frequency operator symbols and underspread approximations

IEEE Transactions on Information Theory

Optimal stochastic discrete time-frequency analysis in the ambiguity and time-lag domain

Signal Processing
Optimal multitaper wigner spectrum estimation of a class of locally stationary processes using hermite functions

EURASIP Journal on Advances in Signal Processing - Special issue on recent advances in theory and methods for nonstationary signal analysis

Quantified Score

Hi-index	35.68

Visualization

Abstract

The ambiguity domain plays a central role in estimating the time-varying spectrum and in estimating the covariance function of nonstationary random processes in continuous time. For processes in discrete time, there exist different definitions of the ambiguity domain, but it is well known that neither of these definitions perfectly resembles the usefulness of the continuous ambiguity domain. In this paper, we present some of the most frequently used definitions of the ambiguity domain in discrete time: the Claasen-Mecklenbräuker, the Jeong-Williams, and the Nuttall definitions. For the first time, we prove their equivalence within some necessary conditions and we present theorems that justify their usage.