The power classes-quadratic time-frequency representations with scale covariance and dispersive time-shift covariance

Hlawatsch, Franz; Papandreou-Suppappola, Antonia; Boudreaux-Bartels, G.F.

doi:10.1109/78.796440

Cited by 36 publications

(43 citation statements)

References 52 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If , the time-scale coherent state has been shifted by in time. If , the coherent state has been shifted in time at a different rate at any given scale, or subjected to a generalized time-shift, see [3, p. 2663], [21].…”

Section: A 1-d Localization Operatorsmentioning

confidence: 99%

Multiple Multidimensional Morse Wavelets

Metikas

Olhede

2007

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

Abstract-This paper defines a set of operators that localize a radial image in space and radial frequency simultaneously. The eigenfunctions of the operator are determined and a nonseparable orthogonal set of radial wavelet functions are found. The eigenfunctions are optimally concentrated over a given region of radial space and scale space, defined via a triplet of parameters. Analytic forms for the energy concentration of the functions over the region are given. The radial function localization operator can be generalised to an operator localizing any 2 ( 2 ) function. It is demonstrated that the latter operator, given an appropriate choice of localization region, approximately has the same radial eigenfunctions as the radial operator. Based on a given radial wavelet function a quaternionic wavelet is defined that can extract the local orientation of discontinuous signals as well as amplitude, orientation and phase structure of locally oscillatory signals. The full set of quaternionic wavelet functions are component by component orthogonal; their statistical properties are tractable, and forms for the variability of the estimators of the local phase and orientation are given, as well as the local energy of the image. By averaging estimators across wavelets, a substantial reduction in the variance is achieved.

show abstract

Section: A 1-d Localization Operatorsmentioning

confidence: 99%

Multiple Multidimensional Morse Wavelets

Metikas

Olhede

2007

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

show abstract

“…When it is assumed that, at the source, all the harmonics of the wave are localized at the same instant , the transfer function can be written as (2) where is the group delay of the wave at frequency as it is defined in the signal processing community, and is the group delay of the wave between the source and the sensor at frequency . This delay is directly related to the group velocity by…”

Section: A One-dimensional Analysismentioning

confidence: 99%

“…the Fourier transform (FT) of can be 2 In the name f-k spectrum, the f refers to temporal frequency and the k to the wave number linked to the spatial frequency.…”

Section: B Multisensor Analysismentioning

confidence: 99%

“…Within the signal processing community, these waves have been widely studied. Their description in the time-frequency plane is problematic because their dispersive characteristics make the standard quadratic time-frequency representations (TFRs) (such as the Wigner distribution) unsuitable [2], [3]. In this paper, we consider data recorded by a linear array of sensors.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dispersion estimation from linear array data in the time-frequency plane

Roueff

Mars

Chanussot

et al. 2005

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

“…Gaussian chirplets do not form an orthogonal basis and adaptive matching pursuit Gaussian chirplet decompositions have thus been advocated (Yin et al, 2002). Philosophically related is research by Hlawatsch et al (1999) and Papandreou-Suppappola et al (2001 who explore time and frequency warping.…”

Section: Introductionmentioning

confidence: 99%

A generalized demodulation approach to time-frequency projections for multicomponent signals

2005

View full text Add to dashboard Cite

We introduce a flexible approach for the time-frequency analysis of multicomponent signals involving the use of analytic vectors and demodulation. The demodulated analytic signal is projected onto the time-frequency plane so that, as closely as possible, each component contributes exclusively to a different 'tile' in a wavelet packet tiling of the time-frequency plane, and at each time instant the contribution to each tile definitely comes from no more than one component. A single reverse demodulation is then applied to all projected components. The resulting instantaneous frequency of each component in each tile is not constrained to a set polynomial form in time, and is readily calculated, as is the corresponding Hilbert energy spectrum. Two examples illustrate the method.In order to better understand the effect of additive noise, the approximate variance of the estimated instantaneous frequency in any tile has been formulated by starting with pure noise and studying its evolving covariance structure through each step of the algorithm. The validity and practical utility of the resulting expression for the variance of the estimated instantaneous frequency is demonstrated via a simulation experiment.

show abstract

The power classes-quadratic time-frequency representations with scale covariance and dispersive time-shift covariance

Cited by 36 publications

References 52 publications

Multiple Multidimensional Morse Wavelets

Multiple Multidimensional Morse Wavelets

Dispersion estimation from linear array data in the time-frequency plane

A generalized demodulation approach to time-frequency projections for multicomponent signals

Contact Info

Product

Resources

About