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The discrete Laguerre transform (DLT) belongs to the family of unitary transforms known as Gauss-Jacobi transforms. ... By examining the basis vectors of the transform matrix, the types of signals that can be best represented by the DLT are determined. ... Simulation experiments were run on this type of signal and the performance of the DLT was compared to the DCT for compression of a damped sinusoid, and tracking a sinusoid in white noise in a transform-domain ...doi:10.1109/78.553468 fatcat:f3toa777jfg45lxl5yqafcfn2a
Publication in the conference proceedings of EUSIPCO, Tampere, Finland, 2000 ... In numerous cases, such as signals with few samples or sources of di erent p o wers, this information can be crucial to estimate the source number because the eigenvalues are no longer signi cant. ... That is why w e p r e s e n t t wo methods based on the unitary transformations of C to exploit the inclusion regions. Indeed, a unitary transformation does not modify the eigenvalues. ...doi:10.5281/zenodo.37253 fatcat:mkvf53ex5rdkzduteesvrb6yjy
These transforms are members of a sinusoidal family of unitary transforms intro- duced by A. K. Jain [IEEE Trans. Pattern Anal. Mach. Intell. ... to fast computation of discrete sinusoidal transforms. ...
Our framework offers a unified view that encompasses sinusoidal transforms such as the DCT and a family of orthogonal Haar-like wavelets that is linked analytically to the underlying signal model. ... In this paper, we present a constructive non-Gaussian generalization of this result: the characterization of the optimal orthogonal transform (ICA) for the family of symmetric--stable AR(1) processes. ... However, here we have a model in which we obtain both transform families just by changing the underlying parameters. ...doi:10.1109/tsp.2015.2447494 fatcat:ykclok72rbbp7nbq5rqquwvwja
Publication in the conference proceedings of EUSIPCO, Rhodes, Greece, 1998 ... complexity for this transform  . ... The complexity of the described algorithm is the same as the complexity of fast DCT-IV algorithm using the FFT  (N(n+2 ) =2 m ultiplications and 3N n = 2 additions) which gives the lowest achivable ...doi:10.5281/zenodo.36663 fatcat:nbnp6uv52zazfitqgux35xhela
2003k:94006 94 the unitary transformation to the specific TF characteristics of a system. ... Specifically, we show that the requirements of translation, rotation, and scale- invariance restrict the form of the criterion to essentially a one- parameter family. ...
Implementation of these new tools involves simply preprocessing the signal by a unitary transformation, performing standard processing on the transformed signal, and then (in some cases) transforming the ... Abstruct-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, ... Our approach is based on a special family of "basis changing" operators-the unitary transformations-which convert traditional systems into new systems with different properties  . ...doi:10.1109/78.469861 fatcat:ledxmjlyxfdrrl3qhv7gker7fi
Next, by introducing a generalization of the Bedrosian theorem for the fHT operator, we derive an explicitly understanding of the shifting action of the fHT for the particular family of wavelets obtained ... The representation is based on the shifting action of the group of fractional Hilbert transform (fHT) operators, which extends the notion of arbitrary phase-shifts from sinusoids to finite-energy signals ... The above result (proof provided in Appendix 7.1) signifies that any family of unitary operators that simultaneously commutes with translations and dilations is isomorphic to the fHT group. ...arXiv:0908.3383v1 fatcat:roe56pwrurcaxnvrriiihlchtu
A family of adaptive filtering algorithms for processing signals which have energy concentrated in a relatively small number of component subspaces in the spectral domain is introduced. ... The method is applied to the problem of adaptive line enhancement comb filtering and DFT is used as a transform method. ... If Q is a full rank unitary transform matrix the problem reduces to the ordinary linear least squares adaptive filtering problem. ...doi:10.1109/icassp.1999.756208 dblp:conf/icassp/BegusicLDR99 fatcat:eht6ozpzobh23gvmcwbst4zgwi
Publication in the conference proceedings of EUSIPCO, Tampere, Finland, 2000 ... Orthogonality and completeness of the Laguerre set allows cascading the transform to a second unitary transform, mainly a wavelet transform, while preserving orthogonality and completeness. ... The frequency contents of segments of the signal are modified according to the timevarying warping characteristic, moving from a curve to the next one in the family. ...doi:10.5281/zenodo.37324 fatcat:pxv7u6bj5nbyjf524wo6iuqorq
the modulus of its wavelet transform. ... It relies on a new reformulation of the phase retrieval problem, that involves the holomorphic extension of the wavelet transform. ... by a unitary complex does not change the modulus of its wavelet transform, so we only aim at reconstructing functions up to multiplication by a unitary complex, that is up to a global phase. ...doi:10.1109/tit.2017.2672727 fatcat:vgsl74w3ljfwdbsmun2gti2whm
Circulant orbitals An for a closed-shell system are the orbitals obtained when the N canonical orthonormal Hartree-Fock orbitals At are subjected to a unitary transfornttion which. is the discrete Fourier ... transformation: An = 1/ V^N IeA I(n Il),") where w = exp(21ii/N). ... This research has been aided by grants to the University of North Carolina from the National Science Foundation and the National Institutes of Health. ...doi:10.1073/pnas.78.3.1323 pmid:16592989 pmcid:PMC319121 fatcat:k2gmf56lgrgaxldv2vapehqhy4
The result is a family of resetting shift-shear bases. ... transform of a wavelet basis element to construct a fan basis element. Note that A, maps the complex Fourier-domain sinusoid e'2nf to the chirp function exp [ j 2 r l f J r sign (f)]. ...doi:10.1109/78.258094 fatcat:gqo6n3vaqfcnfaqqgnlsnto5qm
Our approach, Temporal Registration using Optimal Unitary Transformations (TROUT), is based on a novel dissimilarity measure between time series that is easy to compute and automatically identifies optimal ... Clustering of time series data exhibits a number of challenges not present in other settings, notably the problem of registration (alignment) of observed signals. ... alignment by an arbitrary unitary transform. ...arXiv:2012.04756v2 fatcat:vj2e7g2b5nblncfvfa52z3w6da
The fHT is a generalization of the Hilbert transform that extends the quadrature phase-shift action of the latter to arbitrary phase-shifts-a real shift parameter controls this phase-shift action. ... Next, based on the proposed representation and the observation that the fHT operator maps well-localized B-spline wavelets (that resemble Gaussian-windowed sinusoids) into B-spline wavelets of the same ... INTRODUCTION I N this paper, we study the family of fractional Hilbert transforms that generalize the Hilbert transform operator  by extending the phase-shift action cos(ω 0 x) → cos(ω 0 x+θ) of the ...doi:10.1109/icassp.2009.4960306 dblp:conf/icassp/ChaudhuryU09 fatcat:3nkx7vi3lrbofoaferbbsm73ke
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