Numerical Spread: Quantifying Local Stationarity

Hedges, Robert A.; Suter, Bruce W.

doi:10.1006/dspr.2002.0428

Cited by 2 publications

(3 citation statements)

References 9 publications

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“…We found that periodic (circular) extension created unpalatable mixing effects of a fundamentally non-stationary object. Edge-effects are discussed more carefully in [11]. The best choice of edge treatment will depend on the statistical and deterministic properties of the chosen EMAF.…”

Section: B Initial Estimationmentioning

confidence: 99%

“…Using thresholding methods, we have produced an estimate of the AF in the entire ambiguity plane. We also propose an estimator of the spread of the estimated AF, see [2], [11]. Note that for processes that are not strictly underspread, our thresholding procedure will identify regions where the mean of the EMAF is sufficiently distinct in magnitude from the variance of the EMAF.…”

Section: A Estimated Spreadmentioning

confidence: 99%

“…The problem in this case is quite different to estimating the AF, as we cannot assume the raw wavelet/evolutionary spectra exhibit compression. Hedges and Suter [11] calculated the spread of the AF, based on exceedances of the magnitude of the EMAF over a (fixed and user tuned) threshold in a given direction in the local time-frequency plane. The stochastic properties of the EMAF were not treated by Hedges and Suter, and instead their investigation focused on some effects from different boundary treatments.…”

Section: Introductionmentioning

confidence: 99%

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Estimation of Ambiguity Functions With Limited Spread

Hindberg

Olhede

2010

IEEE Trans. Signal Process.

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This paper proposes a new estimation procedure for the ambiguity function of a non-stationary time series. The stochastic properties of the empirical ambiguity function calculated from a single sample in time are derived. Different thresholding procedures are introduced for the estimation of the ambiguity function. Such estimation methods are suitable if the ambiguity function is only non-negligible in a limited region of the ambiguity plane. The thresholds of the procedures are formally derived for each point in the plane, and methods for the estimation of nuisance parameters that the thresholds depend on are proposed. The estimation method is tested on several signals, and reductions in mean square error when estimating the ambiguity function by factors of over a hundred are obtained. An estimator of the spread of the ambiguity function is proposed.

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Section: B Initial Estimationmentioning

confidence: 99%

Section: A Estimated Spreadmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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