Proceedings ArticleDOI
New dimensions in wavelet analysis
Richard G. Baraniuk,Douglas L. Jones +1 more
- Vol. 5, pp 137-140
TLDR
A new class of signal analysis tools that generalizes the popular wavelet and short-time Fourier transforms is introduced and provides a systematic method for designing new representations with properties useful for certain types of signals.Abstract:
A new class of signal analysis tools that generalizes the popular wavelet and short-time Fourier transforms is introduced. The class allows skews and rotations of the analyzing wavelet in the time-frequency plane, in addition to the time and frequency translations and scalings used by conventional transforms. In addition to providing a unifying framework for studying existing time-frequency representations, the general class provides a systematic method for designing new representations with properties useful for certain types of signals. >read more
Citations
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Journal ArticleDOI
The chirplet transform: physical considerations
Steve Mann,Simon Haykin +1 more
TL;DR: The proposed chirplets are generalizations of wavelets related to each other by 2-D affine coordinate transformations in the time-frequency plane, as opposed to wavelets, which are related to Each other by 1-D affirmations in thetime domain only.
Journal ArticleDOI
Unitary equivalence: a new twist on signal processing
TL;DR: The utility of the unitary equivalence concept for uniting seemingly disparate approaches proposed in the literature is illustrated by generalizing linear time-invariant systems, orthonormal basis and frame decompositions, and joint time-frequency and time-scale distributions.
Journal ArticleDOI
The Weyl correspondence and time-frequency analysis
R.G. Shenoy,T.W. Parks +1 more
TL;DR: The authors show that convolving the Wigner distribution with a general smoothing function is equivalent to evaluating a weighted sum of spectrograms, and relates smoothing of the Wigninger distribution to the "multiple window" technique pioneered by Thomson (1982).
Journal ArticleDOI
Shear madness: new orthonormal bases and frames using chirp functions
TL;DR: The authors take a first step in this direction by deriving two new families of orthonormal bases and frames employing elements that shear, or chirp, in the time-frequency plane, in addition to translate and scale.
Journal ArticleDOI
Wigner-based formulation of the chirplet transform
TL;DR: Using the Wigner distribution, a matrix formulation is derived and analyzed for the chirplet transform, a signal analysis tool that generalizes the wavelet and short-time Fourier transforms.
References
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TL;DR: A review and tutorial of the fundamental ideas and methods of joint time-frequency distributions is presented with emphasis on the diversity of concepts and motivations that have gone into the formation of the field.
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Continuous and discrete wavelet transforms
Christopher Heil,David F. Walnut +1 more
TL;DR: This paper is an expository survey of results on integral representations and discrete sum expansions of functions in $L^2 ({\bf R})$ in terms of coherent states, focusing on Weyl–Heisenberg coherent states and affine coherent states.
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On the locus and spread of pseudo-density functions in the time-frequency plane
TL;DR: In this article, a general principle is formulated according to which the various pseudo-density functions of f should be concentrated around the curve (t, phi prime) and a more detailed qualitative analysis of the behavior of the Wigner distribution of f around this curve is included.
Proceedings ArticleDOI
Affine smoothing of the Wigner-Ville distribution
Patrick Flandrin,Olivier Rioul +1 more
TL;DR: 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.