Some properties of the generalized time frequency representation with cone-shaped kernel

Oh, Sung‐Kwun; Marks, Robert J.

doi:10.1109/78.143445

Cited by 30 publications

(5 citation statements)

References 12 publications

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“…Cone-shaped kernels have a shape like a cone in the ambiguity plane [17,18]. They are suitable for unsteady rotational speed with constant angular accelerations within a given limitation e K :…”

Section: Application Of Cone-shaped and Adaptive Smoothing Kernelsmentioning

confidence: 99%

Fault Detection in Gear Drives With Non-Stationary Rotational Speed-Part I: The Time-Frequency Approach

Meltzer

Ivanov

2003

Mechanical Systems and Signal Processing

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Section: Application Of Cone-shaped and Adaptive Smoothing Kernelsmentioning

confidence: 99%

Fault Detection in Gear Drives With Non-Stationary Rotational Speed-Part I: The Time-Frequency Approach

Meltzer

Ivanov

2003

Mechanical Systems and Signal Processing

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“…and r(τ ) is the auto-covariance of the noise. 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.…”

Section: Statistical Properties Of Tfrsmentioning

confidence: 99%

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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“…The cone-kernel representation (CKR) [19,20] has been designed speci"cally to achieve good TFRs and IT attenuation for signals of multiple sinusoidal bursts with quasistationary instantaneous frequencies such that are encountered in voiced speech signals. For constant-frequency signals and chirp signals, the CKR will severely distort the signal compared to the WDF due to the signi"cant negative components that occur when it makes the integral over the entire time}frequency domain zero.…”

mentioning

confidence: 99%

Development of Enhanced Wigner–ville Distribution Function

Lee

Kim

2001

Mechanical Systems and Signal Processing

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Some properties of the generalized time frequency representation with cone-shaped kernel

Cited by 30 publications

References 12 publications

Fault Detection in Gear Drives With Non-Stationary Rotational Speed-Part I: The Time-Frequency Approach

Fault Detection in Gear Drives With Non-Stationary Rotational Speed-Part I: The Time-Frequency Approach

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

Development of Enhanced Wigner–ville Distribution Function

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