EDICS Number SP--2.3.1 Time-Frequency Signal Analysis Unitary similarity transformations furnish a powerful vehicle for generating infinite generic classes of signal analysis and processing tools based on concepts different from time, frequency, and scale. Implementation of these new tools involves simply preprocessing the signal by a unitary transformation, performing standard processing techniques on the transformed signal, and then (in some cases) transforming the resulting output. The resulting unitarily equivalent systems focus on the critical signal characteristics in large classes of signals and, hence, prove useful for representing and processing signals that are not well matched by current techniques. As specific examples of this procedure, we generalize linear time-invariant systems, orthonormal basis and frame decompositions, and joint time-frequency and time-scale distributions, illustrating the utility of the unitary equivalence concept for uniting seemingly disparate approaches proposed in the literature.
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438
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Theory of communication
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235
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Digital Coding of Waveforms
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116
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Continuous and discrete wavelet transforms
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77
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Time-Frequency Distributions – A Review
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60
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Simple regularity criteria for subdivision schemes
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39
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33
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32
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30
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Improved time-frequency representation of multicomponent signals using exponential kernels
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29
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Time-scale energy distributions: A general class extending wavelet transforms
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22
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The scale representation
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22
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Time-Frequency Representation of Digital Signals and Systems Based on Short-Time Fourier Analysis
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22
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The use of cone-shaped kernels for generalized time–frequency representations of nonstationary signals
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18
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Shear madness: New orthonormal bases and frames using chirp functions, IEEETrans
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16
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A class of affine Wigner functions with extended covariance properties
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16
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Boudreaux-Bartels, "The hyperbolic class of quadratic time-frequency representations. Part I: Constant-Q warping, the hyperbolic paradigm, properties, and members
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14
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Beyond time-frequency analysis: Energy densities in one and many dimensions
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14
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The interference structure of the Wigner distribution and related time-frequency signal representations
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12
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The use of orthogonal transforms for improving performance of adaptive filters
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12
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Warped wavelet bases: Unitary equivalence and signal processing
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11
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11
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Shear madness: Signal-dependent and metaplectic time frequency representations
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10
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The chirplet transform: A generalization of Gabor’s logon transform
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10
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10
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10
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8
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7
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Boudreaux-Bartels, "The power classes of quadratic time-frequency representations: A generalization of the affine and hyperbolic classes
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7
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New dimensions in wavelet analysis
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6
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Time-frequency perspectives: The chirplet transform
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6
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Time-varying filtering and signal estimation using wigner distribution synthesis techniques
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6
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A signal transform covariant to scale changes
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6
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New signal-space orthonormal bases via the metaplectic transform
– Baraniuk, Jones
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6
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FAMlet, To Be or Not To Be a Wavelet
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5
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The Fourier-Mellin transform and mammalian hearing
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5
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Time-frequency design and processing of signals via smoothed Wigner distributions
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4
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A simple Wilson basis with exponential decay
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4
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Scale-invariant Wigner distribution
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4
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Double series representation of bounded signals
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4
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Bilinear time-frequency representations of signals: The shift-scale invariant class
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3
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Representation temps-fr'equence des signaux
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3
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Signal transforms covariant and invariant to operators
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3
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3
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Sur la localisation et la g'eom'etrie des distributions affines
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2
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Affine Wigner distributions
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2
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Time-frequency representations of wideband signals
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2
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An adaptive hyperbolic-class time-frequency representation," m.sc
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2
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Boudreaux-Bartels, "Quadratic time-frequency distributions: the new hyperbolic class and its intersection with the affine class
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