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The discrete Laguerre transform: derivation and applications

G. Mandyam, N. Ahmed
1996 IEEE Transactions on Signal Processing  
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

Detection Of The Source Number By The Gerschgorin Disks

Olivier Caspary, Thierry Cecchin
2015 Zenodo  
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

Page 1416 of Mathematical Reviews Vol. , Issue 2000b [page]

2000 Mathematical Reviews  
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.  ... 

Optimality of Operator-Like Wavelets for Representing Sparse AR(1) Processes

Pedram Pad, Michael Unser
2015 IEEE Transactions on Signal Processing  
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

New Fast Trigonometric Transforms

Karen Egiazarian, V.G. Labunets, E.V. Labunets, J. Astola
1998 Zenodo  
Publication in the conference proceedings of EUSIPCO, Rhodes, Greece, 1998  ...  complexity for this transform [11] .  ...  The complexity of the described algorithm is the same as the complexity of fast DCT-IV algorithm using the FFT [11] (N(n+2 ) =2 m ultiplications and 3N n = 2 additions) which gives the lowest achivable  ... 
doi:10.5281/zenodo.36663 fatcat:nbnp6uv52zazfitqgux35xhela

Page 8880 of Mathematical Reviews Vol. , Issue 2003k [page]

2003 Mathematical Reviews  
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.  ... 

Unitary equivalence: a new twist on signal processing

R.G. Baraniuk, D.L. Jones
1995 IEEE Transactions on Signal Processing  
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 [24] .  ... 
doi:10.1109/78.469861 fatcat:ledxmjlyxfdrrl3qhv7gker7fi

On the Shiftability of Dual-Tree Complex Wavelet Transforms [article]

Kunal Narayan Chaudhury, Michael Unser
2009 arXiv   pre-print
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

Spectral line RLS adaptive filtering algorithm

D. Begusic, D. Linebarger, E.M. Dowling, B. Raghothaman
1999 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258)  
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

Signal Transforms For The Detection And Identification Of Signals

Gianpaolo Evangelista
2015 Zenodo  
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

Phase retrieval for wavelet transforms

Irene Waldspurger
2017 IEEE Transactions on Information Theory  
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 for atoms and molecules

R. G. Parr, M.-B. Chen
1981 Proceedings of the National Academy of Sciences of the United States of America  
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

Shear madness: new orthonormal bases and frames using chirp functions

R.G. Baraniuk, D.L. Jones
1993 IEEE Transactions on Signal Processing  
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

Automatic Registration and Clustering of Time Series [article]

Michael Weylandt, George Michailidis
2021 arXiv   pre-print
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 fractional Hilbert transform and dual-tree Gabor-like wavelet analysis

Kunal Narayan Chaudhury, Michael Unser
2009 2009 IEEE International Conference on Acoustics, Speech and Signal Processing  
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 [1] 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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