Minimum-variance time-frequency distribution kernels

Hearon, S.B.; Amin, Moeness G.

doi:10.1109/78.382412

Cited by 46 publications

(17 citation statements)

References 9 publications

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“…Previous work done by Stankovic and Ivanovic 28 and Hearon and Amin 29,30 dealt with complex noise and found that given an input complex white Gaussian noise with variance in 2 , the noise variance 2 produced by the input noise in time-frequency power spectrum can be successfully estimated. In this paper however, we deal with real white Gaussian noise only whose noise variance is given by 28,29 where W(,tϪu) is the weighting function of the kernel function ⌽͑,͒ and ''*'' indicates complex conjugate operation. From Eq.…”

Section: Noise Variance Calculationmentioning

confidence: 97%

Hyperbolic kernel for time-frequency power spectrum

Lê¹,

Dabke²,

Egan³

2003

Opt. Eng.

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We propose a new family of hyperbolic kernels ⌽ hyperbolic (,)ϭ͓sech(␤)͔ n , where nϭ1,3,5,..., for a joint timefrequency distribution. The first-order hyperbolic kernel sech(␤) is mainly considered. Theoretical aspects of the new hyperbolic kernel are examined in detail. The effectiveness of a kernel is determined by three factors: cross-term suppression, auto-term resolution, and noise robustness. The effectiveness of the new kernel is compared with other kernels including Choi-Williams, Wigner-Ville, and multiform tiltable exponential using two different signals: complex-exponential and chirp.

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Section: Noise Variance Calculationmentioning

confidence: 97%

Hyperbolic kernel for time-frequency power spectrum

Lê¹,

Dabke²,

Egan³

2003

Opt. Eng.

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“…This is also the way the kernel was used in this study. The Born-Jordan transform provides an esti mate of the time-frequency spectrum that minimizes the average variance for white noise processes [14]. Its kernel is defined as g(fJ, T) = sin(-rrfJT)/(-rrBT).…”

Section: Cohen-class Time-frequency Analysismentioning

confidence: 99%

Time-frequency parameters of the surface myoelectric signal for assessing muscle fatigue during cyclic dynamic contractions

Bonato

Roy

Knaflitz

et al. 2001

IEEE Trans. Biomed. Eng.

245

160

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Abstract-The time-dependent shift in the spectral content of the surface myoelectricsignal to lowerfrequencieshas proven to be a useful tool for assessinglocalized muscle fatigue. Unfortunately, the technique has been restricted to constant-force, isometric con tractions because of limitations in the processingmethods used to obtain spectral estimates. A novel approach is proposed for cal culating spectral parameters from the surface myoelectric signal during cyclicdynamic contractions. The procedure was developed using Cohen class time-frequency transfonns to define the instan taneous median and mean frequency during cyclic dynamic con tractions. Changes in muscle length, force, and electrode position contribute to the nonstationarity of the surface myoelectricsignal.These factors, unrelated to localized fatigue, can be constrained and isolated for cyclic dynamic contractions, where they are as sumed to be constant for identical phases of each cycle. Estima tion errors for the instantaneous median and mean frequency are calculated from synthesized signals. It is shown that the instan taneous median frequency is affected by an error slightly lower than that related to the instantaneous mean frequency. In addi tion, we present a sample application to surface myoelectricsignals recorded from the first dorsal interosseous muscle during repeti tive abduction/adduction of the indexfinger against resistance. Re sults indicate that the variability of the instantaneous median fre quency is related to the repeatability of the biomechanics of the exercise.

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“…This means that for white noise, D(t, f ; g) = 0, and the CKR is an unbiased estimator (Oh & Marks 1992). However, Hearon & Amin (1995) show that of all the Cohen TFRs the CKR has the highest variance, and hence the least desirable performance in the presence of noise. In addition, confidence contours cannot easily be constructed for the CKR since the stochastic distribution of the CKR is not calculable from the power spectrum as is the case for the other TFRs.…”

Section: Statistical Properties Of Tfrsmentioning

confidence: 97%

Wavelets With Ridges: A High-Resolution Representation of Cataclysmic Variable Time Series

Blackman

2010

ApJS

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Quasi-periodic oscillations and dwarf nova oscillations occur in dwarf novae and nova-like variables during outburst and occasionally during quiescence, and have analogues in high-mass X-ray binaries and black-hole candidates. The frequent low coherence of quasi-period oscillations and dwarf nova oscillations can make detection with standard time-series tools such as periodograms problematic. This paper develops tools to analyse quasi-periodic brightness oscillations. We review the use of time-frequency representations in the astronomical literature, and show that representations such as the Choi-Williams Distribution and Zhao-Atlas-Marks Representation, which are best suited to high signal-to-noise data, cannot be assumed a priori to be the best techniques for our data, which have a much higher noise level and lower coherence. This leads us to a detailed analysis of the time-frequency resolution and statistical properties of six time-frequency representations. We conclude that the wavelet scalogram, with the addition of wavelet ridges and maxima points, is the most effective time-frequency representation for analysing quasi-periodicities in low signal-to-noise data, as it has high time-frequency resolution, and is a minimum variance estimator.We use the wavelet ridges method to re-analyse archival data from VW Hyi, and find 62 new QPOs and 7 new long-period DNOs. Relative to previous analyses, our method substantially improves the detection rate for QPOs.

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Minimum-variance time-frequency distribution kernels

Cited by 46 publications

References 9 publications

Hyperbolic kernel for time-frequency power spectrum

Hyperbolic kernel for time-frequency power spectrum

Time-frequency parameters of the surface myoelectric signal for assessing muscle fatigue during cyclic dynamic contractions

Wavelets With Ridges: A High-Resolution Representation of Cataclysmic Variable Time Series

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