Extraction of Signals from Noise

Wainstein, L. A.; Zubakov, V. D.; Mullin, Albert A.

doi:10.1119/1.1969250

Cited by 165 publications

(141 citation statements)

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“…It is also known that optimal prediction error for stationary Gaussian processes is zero for the case of degenerate spectral density. The related results can be found in Wainstein and Zubakov (1962), Knab (1981), Papoulis (1985), Marvasti (1986), Vaidyanathan (1987), Lyman et al (2000Lyman et al ( , 2001, Dokuchaev (2008Dokuchaev ( ,2010). …”

Section: Introductionmentioning

confidence: 64%

On predictors for band-limited and high-frequency time series

Dokuchaev

2012

Signal Processing

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Pathwise predictability and predictors for discrete time processes are studied in deterministic setting. It is suggested to approximate convolution sums over future times by convolution sums over past time. It is shown that all band-limited processes are predictable in this sense, as well as highfrequency processes with zero energy at low frequencies. In addition, a process of mixed type still can be predicted if an ideal low-pass filter exists for this process.

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Section: Introductionmentioning

confidence: 64%

On predictors for band-limited and high-frequency time series

Dokuchaev

2012

Signal Processing

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“…Notation and treatment of this Section essentially follow Ref. [22,25,41] (see also [7,42,43,44] for further details). We restrict our discussion to measurements made by a single detector.…”

Section: A Brief Summary Of Parameter Estimation Theorymentioning

confidence: 99%

Erratum: Parameter estimation of inspiralling compact binaries using 3.5 post-Newtonian gravitational wave phasing: The nonspinning case [Phys. Rev. D71, 084008 (2005)]

Arun¹,

Iyer²,

et al. 2005

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We revisit the problem of parameter estimation of gravitational-wave chirp signals from inspiralling non-spinning compact binaries in the light of the recent extension of the post-Newtonian (PN) phasing formula to order (v/c) 7 beyond the leading Newtonian order. We study in detail the implications of higher post-Newtonian orders from 1PN up to 3.5PN in steps of 0.5PN (∼ v/c), and examine their convergence. In both initial and advanced detectors the estimation of the chirp mass (M) and symmetric mass ratio (η) improve at higher PN orders but oscillate with every half-a-PN order. In initial LIGO, for a 10M⊙-10M⊙ binary at a signal-to-noise ratio (SNR) of 10, the improvement in the estimation of M (η) at 3.5PN relative to 2PN is ∼ 19% (52%). We compare parameter estimation in different detectors and assess their relative performance in two different ways: at a fixed SNR, with the aim of understanding how the bandwidth improves parameter estimation, and for a fixed source, to gauge the importance of sensitivity. Errors in parameter estimation at a fixed SNR are smaller for VIRGO than for both initial and advanced LIGO. This is because of the larger bandwidth over which it observes the signals. However, for sources at a fixed distance it is advanced LIGO that achieves the lowest errors owing to its greater sensitivity. Finally, we compute the amplitude corrections due to the 'frequency-sweep' in the Fourier domain representation of the waveform within the stationary phase approximation and discuss its implication on parameter estimation. We find that the amplitude corrections change the errors in M and η by less than 10% for initial LIGO at a signal-to-noise ratio of 10. Our analysis makes explicit the significance of higher PN order modelling of the inspiralling compact binary on parameter estimation.

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“…If the probability of a false-alarm (Type I error) is included as a parameter of a function relating the hit-rate to the signal energy, then the data may be mapped into a typical ROC space. Some writers prefer this method of presentation of a family of psychometric functions, particularly when the false-alarm rates vary over an enormous range, e.g., 10-0 to 10-1 • For example, see one of the most elegant and most complete presentations of signal detection theory (Wainstein & Zubakow, 1962).…”

Section: Therefore the Magnitude Of The Mld = (Lo/k)log(mi!mr) Whermentioning

confidence: 99%

Masking-level differences and the form of the psychometric function

Egan

Lindner

McFadden

1969

Perception & Psychophysics

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The detectability of an auditory signal that is presented in noise may be increased markedly by an appropriate change in the interaural relations of the signal or of the noise. The effects are so large that the enhanced detectability , or "release from masking," is typically measured, not as an increase in the detectability of the signal, but rather, as the change in the signal energy that is necessary in order to maintain the listener's performance at a constant level. This change in signal energy, expressed in decibels, is called a "masking-level difference," or MLD. The investigations of Licklider (1948), Hirsh (1948), and Hirsh and Webster (1949), mark the beginnings of this line of auditory research, and since the publication of these early studies, there has been a steady increase in our knowledge of binaural masking phenomena. In particular, Jeffress and his coworkers (e.g., Jeffress et al, 1952Jeffress et al, , 1956Blodgett et al, 1958;Robinson & Jeffress, 1963; Langford & Jeffress, 1964) have made many significant contributions to this area of audition. Recently, Durlach (1963), Green (I 966a), and others have developed theoretical approaches to these phenomena different from that developed by Jeffress, and these various models of binaural masking have contributed to an increased interest in MLDs.As an example of a masking-level difference, suppose that the "masked absolute threshold" is determined for a sinusoidal signal when it and a continuous masking noise are presented to the right ear only, a condition called Nm-Sm. Next, the noise waveform that is presented to the right ear is presented simultaneously to the left ear, so that the instantaneous sound pressure of the noise in the left ear is the same as that in the right ear. With this perfectly correlated "binaural noise," the masked threshold for the monaural signal in the right ear is redetermined. It is typically found under this condition, termed NO-Sm, that the intensity of the sinusoid must be decreased by about 9 dB (at 300 cps) in order to reestablish the masked threshold. This difference in signal intensity of 9 dB is the masking-level difference, or MLD, of NO-Sm relative to Nm-Srn. Although the magnitude of the MLD is a function of the frequency of the signal, the effect is easily measured over the range from 200 to 1000 cps.It might be conjectured that the MLD obtained for NO-Sm is due simply to a facilitative, or synergistic, effect from the noise in the nonsignal ear. That this is not the case is evidenced by the fact that if the two noises are uncorrelated (NU-Sm), the detectability of the signal is the same as with the monotic condition.The symbols used in the current literature on masking-level differences are sometimes confusing and it may help the reader to understand this nomenclature if the symbols employed in this paper to describe the various interaural conditions are all defined at this time. The symbols used are: N for the masking noise, S for the sinusoidal signal, 0 for an interaural phase shift of zero degrees, tt for...

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Extraction of Signals from Noise

Cited by 165 publications

References 0 publications

On predictors for band-limited and high-frequency time series

On predictors for band-limited and high-frequency time series

Erratum: Parameter estimation of inspiralling compact binaries using 3.5 post-Newtonian gravitational wave phasing: The nonspinning case [Phys. Rev. D71, 084008 (2005)]

Masking-level differences and the form of the psychometric function

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