Estimation of the time-varying frequency of a signal: the Cramer-Rao bound and the application of Wigner distribution

Davidson, T.N.; Jin, Qu

doi:10.1109/29.106870

Cited by 33 publications

(24 citation statements)

References 8 publications

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“…If the IF is a nonlinear function of time, then its estimate, using the WD, is biased. In the case of noisy signals, this estimate is highly signal and noise dependent [8], [17], [21]. Using the asymptotic formulae for the estimation variance and bias, we can, theoretically, find the optimal window length in the WD and resolve the bias-variance tradeoff.…”

Section: Introductionmentioning

confidence: 98%

Instantaneous frequency estimation using the Wigner distribution with varying and data-driven window length

Katkovnik

Stanković

1998

IEEE Trans. Signal Process.

207

115

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Estimation of the instantaneous frequency (IF) of a harmonic complex-valued signal with an additive noise using the Wigner distribution is considered. If the IF is a nonlinear function of time, the bias of the estimate depends on the window length. The optimal choice of the window length, based on the asymptotic formulae for the variance and bias, can be used in order to resolve the bias-variance tradeoff. However, the practical value of this solution is not significant because the optimal window length depends on the unknown smoothness of the IF. The goal of this paper is to develop an adaptive IF estimator with a time-varying and data-driven window length, which is able to provide quality close to what could be achieved if the smoothness of the IF were known in advance. The algorithm uses the asymptotic formula for the variance of the estimator only. Its value may be easily obtained in the case of white noise and relatively high sampling rate. Simulation shows good accuracy for the proposed adaptive algorithm.

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Section: Introductionmentioning

confidence: 98%

Instantaneous frequency estimation using the Wigner distribution with varying and data-driven window length

Katkovnik

Stanković

1998

IEEE Trans. Signal Process.

207

115

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“…In this case we define the peak edges as the midpoint between the first and second points of inflection. Determining and , therefore, requires solving for the zeros of and , respectively, where [see (11) at the bottom of the page]. For a particular value of and , one may numerically solve for the zeros of the nonlinear (9) and (11) to determine and .…”

Section: A Region Of Attractionmentioning

confidence: 99%

“…The discrete-time WHT, formed from samples, , of a signal , is given by (1) where is assumed to be even. The WVD is known to be an unbiased estimator of the IF for linear FM signals [11]. However, as the IF becomes nonlinear in nature, the WHT becomes increasingly biased and in most cases, not useful.…”

Section: The Whtmentioning

confidence: 99%

Parameter Estimation for Locally Linear FM Signals Using a Time-Frequency Hough Transform

Cirillo

Zoubir

Amin

2008

IEEE Trans. Signal Process.

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An estimator for the phase parameters of mono-and multicomponent FM signals, with both good numerical properties and statistical performance is proposed. The proposed approach is based on the Hough transform of the pseudo-Wigner-Ville timefrequency distribution (PWVD). It is shown that the numerical properties of the estimator can be improved by varying the PWVD window length. The effect of the window time extent on the statistical performance of the estimator is delineated. Experimental data is used for validation of the statistical properties.

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“…This fact has prompted development of various techniques to "clean" the tachometer output and reduce the amount of phase noise. These methods often include averaging tachometer phase by using a phase locked loop [14][15][16] or implementation of Kalman filtering techniques [17,18] to optimally combine several sources of information and produce the best possible estimate of the rotation frequency under existing measurement noise and uncertain dynamics of the system [19].…”

Section: Introductionmentioning

confidence: 99%

Adding a lens Improves spinning speed characterization

Mihaliuk

Gullion

2015

Solid State Nuclear Magnetic Resonance

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Highly stable sample rotation is important in many solid-state NMR experiments. Whether the necessary stability is achieved is not always clear. Typically only an average frequency over some time interval (often relatively long and unknown) is available from the spinning speed controller readout, which is not representative of the short-term variations of instantaneous rotation frequency. The necessity of the relatively slow measurement of spinning speed is a consequence of phase noise in the tachometer, which prevents speed measurement to be both rapid and precise at the same time. We show that adding a lens to the tachometer, without any other changes in the probe, reduces phase noise by nearly an order of magnitude and allows improved measurement of the spinning speed.

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Estimation of the time-varying frequency of a signal: the Cramer-Rao bound and the application of Wigner distribution

Cited by 33 publications

References 8 publications

Instantaneous frequency estimation using the Wigner distribution with varying and data-driven window length

Instantaneous frequency estimation using the Wigner distribution with varying and data-driven window length

Parameter Estimation for Locally Linear FM Signals Using a Time-Frequency Hough Transform

Adding a lens Improves spinning speed characterization

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