Proceedings ArticleDOI
Affine smoothing of the Wigner-Ville distribution
Patrick Flandrin,Olivier Rioul +1 more
- pp 2455-2458
TLDR
It is shown, in particular, that Gaussian kernels provide a continuous transition between spectrograms and scalograms by means of the Wigner-Ville distribution, which makes it a versatile tool for the analysis of nonstationary signals.Abstract:
A formalism of signal energy representations depending on time and scale is presented. Precise links between time-frequency and time-scale energy distributions are provided. It is known that a full description of the former is given by Cohen's class, which can be described as a generalization of the spectrogram appropriately parameterized by a smoothing function acting on the Wigner-Ville distribution. A full description of the latter is given, resulting in a class of representations in which the smoothing of the Wigner-Ville distribution is scale-dependent. Through proper choice of the smoothing function, interesting properties may be imposed on the representation, which makes it a versatile tool for the analysis of nonstationary signals. Also, specific choices allow known definitions to be recovered (including the Bertrands' and the energetic version of the wavelet transform, referred to as the scalogram). Another very flexible choice uses separable smoothing functions. It is shown, in particular, that Gaussian kernels provide a continuous transition between spectrograms and scalograms by means of the Wigner-Ville distribution. >read more
Citations
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Journal ArticleDOI
Wavelet Transforms and their Applications to Turbulence
TL;DR: Wavelet transforms are recent mathematical techniques, based on group theory and square integrable representations, which allows one to unfold a signal, or a field, into both space and scale, and possibly directions.
Journal ArticleDOI
Linear and quadratic time-frequency signal representations
TL;DR: A tutorial review of both linear and quadratic representations is given, and examples of the application of these representations to typical problems encountered in time-varying signal processing are provided.
Journal ArticleDOI
Time-scale energy distributions: a general class extending wavelet transforms
Olivier Rioul,Patrick Flandrin +1 more
TL;DR: The theory of a new general class of signal energy representations depending on time and scale is developed, and specific choices allow recovery of known definitions, and provide a continuous transition from Wigner-Ville to either spectrograms or scalograms (squared modulus of the WT).
Journal ArticleDOI
A signal-dependent time-frequency representation: optimal kernel design
TL;DR: A new time-frequency distribution that adapts to each signal and so offers a good performance for a large class of signals is introduced that is formulated in Cohen's class as an optimization problem and results in a special linear program.
Journal ArticleDOI
Signal-dependent time-frequency analysis using a radially Gaussian kernel
TL;DR: A signal-dependent kernel that changes shape for each signal to offer improved time-frequency representation for a large class of signals is proposed and an efficient scheme based on Newton's algorithm for finding the optimal kernel is developed.
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