Change search
Refine search result
1 - 32 of 32
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Rows per page
  • 5
  • 10
  • 20
  • 50
  • 100
  • 250
Sort
  • Standard (Relevance)
  • Author A-Ö
  • Author Ö-A
  • Title A-Ö
  • Title Ö-A
  • Publication type A-Ö
  • Publication type Ö-A
  • Issued (Oldest first)
  • Issued (Newest first)
  • Created (Oldest first)
  • Created (Newest first)
  • Last updated (Oldest first)
  • Last updated (Newest first)
  • Disputation date (earliest first)
  • Disputation date (latest first)
  • Standard (Relevance)
  • Author A-Ö
  • Author Ö-A
  • Title A-Ö
  • Title Ö-A
  • Publication type A-Ö
  • Publication type Ö-A
  • Issued (Oldest first)
  • Issued (Newest first)
  • Created (Oldest first)
  • Created (Newest first)
  • Last updated (Oldest first)
  • Last updated (Newest first)
  • Disputation date (earliest first)
  • Disputation date (latest first)
Select
The maximal number of hits you can export is 250. When you want to export more records please use the Create feeds function.
  • 1.
    Boggiatto, Paolo
    et al.
    Univ Turin, Dept Math, I-10123 Turin, TO, Italy.
    Oliaro, Alessandro
    Univ Turin, Dept Math, I-10123 Turin, TO, Italy.
    Wahlberg, Patrik
    Univ Turin, Dept Math, I-10123 Turin, TO, Italy.
    The wave front set of the Wigner distribution and instantaneous frequency2012In: Journal of Fourier Analysis and Applications, ISSN 1069-5869, E-ISSN 1531-5851, Vol. 18, no 2, p. 410-438Article in journal (Refereed)
    Abstract [en]

    We prove a formula expressing the gradient of the phase function of a function f : R-d bar right arrow C as a normalized first frequency momentof the Wigner distribution for fixed time. The formula holds when f is the Fourier transform of a distribution of compact support, or when f belongs to a Sobolev space Hd/2+1+epsilon(R-d) where epsilon > 0. The restriction of the Wigner distribution to fixed time is well defined provided a certain condition on its wave front set is satisfied. Therefore we first need to study the wave front set of the Wigner distribution of a tempered distribution.

  • 2.
    Cappiello, Marco
    et al.
    Universtiy of Torino, Italy.
    Schulz, René
    Leibniz Universität Hannover, Germany.
    Wahlberg, Patrik
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Conormal distributions in the Shubin calculus of pseudodifferential operators2018In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 59, no 2, article id 021502Article in journal (Refereed)
    Abstract [en]

    We characterize the Schwartz kernels of pseudodifferential operators of Shubin type by means of a Fourier-Bros-Iagolnitzer transform. Based on this, we introduce as a generalization a new class of tempered distributions called Shubin conormal distributions. We study their transformation behavior, normal forms, and microlocal properties.

  • 3.
    Carypis, Evanthia
    et al.
    University of Turin, Italy.
    Wahlberg, Patrik
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Propagation of exponential phase space singularities for Schrödinger equations with quadratic Hamiltonians2017In: Journal of Fourier Analysis and Applications, ISSN 1069-5869, E-ISSN 1531-5851, Vol. 23, no 3, p. 530-571Article in journal (Refereed)
    Abstract [en]

    We study propagation of phase space singularities for the initial value Cauchy problem for a class of Schrödinger equations. The Hamiltonian is the Weyl quantization of a quadratic form whose real part is non-negative. The equations are studied in the framework of projective Gelfand–Shilov spaces and their distribution duals. The corresponding notion of singularities is called the Gelfand–Shilov wave front set and means the lack of exponential decay in open cones in phase space. Our main result shows that the propagation is determined by the singular space of the quadratic form, just as in the framework of the Schwartz space, where the notion of singularity is the Gabor wave front set.

  • 4.
    Chen, Yuanyuan
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Toft, Joachim
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Wahlberg, Patrik
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    The Weyl product on quasi-Banach modulation spaces2018In: Bulletin of Mathematical Sciences, ISSN 1664-3607, E-ISSN 1664-3615Article in journal (Refereed)
    Abstract [en]

    We study the bilinear Weyl product acting on quasi-Banach modulation spaces. We find sufficient conditions for continuity of the Weyl product and we derive necessary conditions. The results extend known results for Banach modulation spaces.

  • 5.
    Cordero, Elena
    et al.
    University of Turin.
    Tabacco, Anita
    Politecnico di Torino.
    Wahlberg, Patrik
    Università di Torino.
    Schrodinger-type propagators, pseudodifferential operators and modulation spaces2013In: Journal of the London Mathematical Society, ISSN 0024-6107, E-ISSN 1469-7750, Vol. 88, p. 375-395Article in journal (Refereed)
    Abstract [en]

    We prove continuity results for Fourier integral operators with symbols in modulation spaces, acting between modulation spaces. The phase functions belong to a class of non-degenerate generalized quadratic forms that includes Schrödinger propagators and pseudodifferential operators. As a byproduct, we obtain a characterization of all exponents p, q, r1, r2, t1, t2∈[1, ∞] of modulation spaces such that a symbol in Mp, q(ℝ2d) gives a pseudodifferential operator that is continuous from Mr1,r2(ℝd) into Mt1,t2(ℝd).

  • 6.
    Cordero, Elena
    et al.
    Turins universitet.
    Toft, Joachim
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Wahlberg, Patrik
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Sharp results for the Weyl product on modulation spaces2014In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 267, no 8, p. 3016-3057Article in journal (Refereed)
    Abstract [en]

    We give sufficient and necessary conditions on the Lebesgue exponentsfor the Weyl product to be bounded on modulation spaces. The sufficient conditions are obtained as the restriction to N=2 of aresult valid for the N-fold Weyl product. As a byproduct, we obtain sharpconditions for the twisted convolution to be bounded on Wieneramalgam spaces.

  • 7.
    Holst, Anders
    et al.
    1.Department of Mathematics Lund University 221 00 Lund, Sweden.
    Toft, Joachim
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Wahlberg, Patrik
    3.School of Electrical Engineering and Computer Science University of Newcastle Callaghan, NSW 2308, Australia.
    Weyl product algebras and classical modulation spaces2010In: Linear and non-linear theory of generalized functions and its applications / [ed] A. Kaminski, M. Oberguggenberger, S. Pilipovic, Warsaw: Polish Acad. Sci. Inst. Math. , 2010, p. 153-158Conference paper (Refereed)
    Abstract [en]

    We discuss continuity properties of the Weyl product when acting on classical modulation spaces. In particular, we prove that M p,q   is an algebra under the Weyl product when p∈[1,∞]  and 1≤q≤min(p,p ′ )  .

  • 8.
    Oliaro, Alessandro
    et al.
    Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123, Torino (TO), Italy.
    Rodino, Luigi
    Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123, Torino (TO), Italy.
    Wahlberg, Patrik
    Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123, Torino (TO), Italy.
    Almost periodic pseudodifferential operators and Gevrey classes2012In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 191, no 4, p. 725-760Article in journal (Refereed)
    Abstract [en]

    We study almost periodic pseudodifferential operators acting on almost periodic functions G s ap (R d )  of Gevrey regularity index s ≥ 1. We prove that almost periodic operators with symbols of Hörmander type S m ρ,δ   satisfying an s-Gevrey condition are continuous on G s ap (R d )  provided 0 < ρ ≤ 1, δ = 0 and s ρ ≥ 1. A calculus is developed for symbols and operators using a notion of regularizing operator adapted to almost periodic Gevrey functions and its duality. We apply the results to show a regularity result in this context for a class of hypoelliptic operators.

  • 9.
    Pravda-Starov, Karel
    et al.
    Université de Rennes 1, France.
    Rodino, Luigi
    University of Turin, Italy;RUDN University, Russia.
    Wahlberg, Patrik
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Propagation of Gabor singularities for Schrödinger equations with quadratic Hamiltonians2018In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 291, no 1, p. 128-159Article in journal (Refereed)
    Abstract [en]

    We study propagation of the Gabor wave front set for a Schrödinger equation wit ha Hamiltonian that is the Weyl quantization of a quadratic form with nonnegativereal part. We point out that t he singular space associated with the quadratic formplays a crucial role for the understanding of this propagation. We show that the Gaborsingularities of the solution to the equation for positive times are always contained inthe singular space, and that t hey propagate in this set along the flow of the Hamiltonvector field associated with the imaginary part of the quadratic form. As an applicationwe obtain for the heat equation a sufficient condition on the Gabor wave front set of theinitial datum tempered distribution that implies regularization to Schwartz regularityfor positive times.

  • 10.
    Rodino, Luigi
    et al.
    University of Turin.
    Wahlberg, Patrik
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    The Gabor wave front set2014In: Monatshefte für Mathematik (Print), ISSN 0026-9255, E-ISSN 1436-5081, Vol. 173, no 4, p. 625-655Article in journal (Refereed)
    Abstract [en]

    We define the Gabor wave front set W F-G(u) of a tempered distribution u in terms of rapid decay of its Gabor coefficients in a conic subset of the phase space. We show the inclusion W F-G(a(w) (x, D)u) subset of W F-G(u), u is an element of l'(R-d), a is an element of S-0,0(0), where S-0,0(0) denotes the Hormander symbol class of order zero and parameter values zero. We compare our definition with other definitions in the literature, namely the classical and the global wave front sets of Hormander, and the l-wave front set of Coriasco and Maniccia. In particular, we prove that the Gabor wave front set and the global wave front set of Hormander coincide.

  • 11.
    Schulz, René
    et al.
    Leibniz Universität Hannover, Germany.
    Wahlberg, Patrik
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Microlocal properties of Shubin pseudodifferential and localization operators2016In: Journal of Pseudo-Differential Operators and Applications, ISSN 1662-9981, E-ISSN 1662-999X, Vol. 7, no 1, p. 91-111Article in journal (Refereed)
    Abstract [en]

    We investigate global microlocal properties of localization operators and Shubin pseudodifferential operators. The microlocal regularity is measured in terms of a scale of Shubin-type Sobolev spaces. In particular, we prove microlocality and microellipticity of these operators.

  • 12.
    Schulz, René
    et al.
    Leibniz Universität Hannover, Germany.
    Wahlberg, Patrik
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    The Equality of the homogeneous and the Gabor wave front set2017In: Communications in Partial Differential Equations, ISSN 0360-5302, E-ISSN 1532-4133, Vol. 42, no 5, p. 703-730Article in journal (Refereed)
    Abstract [en]

    We prove that Hörmander’s global wave front set and Nakamura’s homogeneous wave front set of a tempered distribution coincide. In addition we construct a tempered distribution with a given wave front set, and we develop a pseudodifferential calculus adapted to Nakamura’s homogeneous wave front set.

  • 13.
    Toft, Joachim
    et al.
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering. Matematik.
    Holst, Anders
    Matematisk institutionen, Lunds universitet.
    Wahlberg, Patrik
    Department of Mathematics and Statistics, University of Newcastle, Australia.
    Modulation spaces and Weyl product algebras2006Report (Other academic)
  • 14.
    Toft, Joachim
    et al.
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering. Matematik.
    Holst, Anders
    Wahlberg, Patrik
    Weyl product algebras and modulation spaces2007In: Journal of functional analysis, ISSN 0022-1236, Vol. 251, p. 463-491Article in journal (Refereed)
  • 15.
    Toft, Joachim
    et al.
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering. Matematik.
    Wahlberg, Patrik
    Department of Mathematics and Statistics, University of Newcastle, Australia.
    Algebraic properties off the Weyl product on modulation spaces2006Report (Other academic)
  • 16.
    Toft, Joachim
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Wahlberg, Patrik
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Embeddings of alpha-modulation spaces2012In: Pliska Studia Mathematica Bulgarica, ISSN 0204-9805, Vol. 21, p. 25-46Article in journal (Refereed)
  • 17. Wahlberg, Patrik
    A transformation of almost periodic pseudodifferential operators to Fourier multiplier operators with operator-valued symbols2009In: Rendiconti del Seminario Matematico, ISSN 0373-1243, Vol. 67, no 2, p. 247-269Article in journal (Refereed)
    Abstract [en]

    We present results for pseudodifferential operators on Rd whose symbol a(·,x)is almost periodic (a.p.) for each x ∈ Rd and belongs to a Hörmander class Smr,d. We studya linear transformation a 7→ U(a) from a symbol a(x,x) to a frequency-dependent matrixU(a)(x)l,l′ , indexed by (l,l′) ∈ L×L where L is a countable set in Rd . The map a 7→ U(a) transforms symbols of a.p. pseudodifferential operators to symbols of Fourier multiplieroperators acting on vector-valued function spaces. We show that the map preserves operatorpositivity and identity, respects operator composition and respects adjoints.

  • 18.
    Wahlberg, Patrik
    Univ Turin, Dipartimento Matemat, I-10123 Turin, TO, Italy.
    Locally stationary stochastic processes and Weyl symbols of positive operators2011In: Positivity (Dordrecht), ISSN 1385-1292, E-ISSN 1572-9281, Vol. 15, no 1, p. 105-134Article in journal (Refereed)
    Abstract [en]

    The paper treats locally stationary stochastic processes. A connection with the Weyl symbols of positive operators is observed and explored. We derive necessary conditions on the two functions that constitute the covariance function of a locally stationary stochastic process, some of which use this connection to time-frequency analysis and pseudodifferential operators. Finally, we discuss briefly the subclass of Cohen's class of time-frequency representations having separable kernels, which is related to locally stationary stochastic processes.

  • 19.
    Wahlberg, Patrik
    Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
    On time-frequency analysis and pseudo-differential operators for vector-valued functions2008Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis treats different aspects of time-frequency analysis and pseudodifferential operators, with particular emphasis on techniques involving vector-valued functions and operator-valued symbols. The vector (Banach) space is either motivated by an application as in Paper I, where it is a space of stochastic variables, or is part of a general problem as in Paper II, or arises naturally from problems for scalar-valued operators and function spaces, as in Paper V. Paper III and IV fall outside this framework and treats algebraic aspects of time-frequency analysis and pseudodifferential operators for scalar-valued symbols and functions that are members of modulation spaces. Paper IV builds upon Paper III and applies the results to a filtering problem for second-order stochastic processes.

    Paper I treats the Wigner distribution of a Gaussian weakly harmonizable stochastic process defned on Rd. Paper II extends recent continuity results for pseudodifferential and localization operators, with symbols in modulation spaces, to the vector/operator-framework, where the vector space is a Hilbert or a Banach space. In Paper III we give algebraic results for the Weyl product acting on modulation spaces. We give suffcient conditions for a weighted modulation space to be an algebra under theWeyl product, and we also give necessary conditions for unweighted modulation spaces. In Paper IV we discretize the results of Paper III by means of a Gabor frame delined by a Gaussian function. Finally, Paper V deals with pseudodifferential operators with symbols that are almost periodic in the first variable. We show that such operators may be transformed to Fourier multiplier operators with operator- valued symbols such that the transformation preserves positivity and operator composition.

  • 20.
    Wahlberg, Patrik
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Propagation of polynomial phase space singularities for Schrödinger equations with quadratic Hamiltonians2018In: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 122, no 1, p. 107-140Article in journal (Refereed)
    Abstract [en]

    We study propagation of phase space singularities for a Schrödinger equation with a Hamiltonian that is the Weyl quantization of a quadratic form with non-negative real part. Phase space singularities are measured by the lack of polynomial decay of given order in open cones in the phase space, which gives a parametrized refinement of the Gabor wave front set. The main result confirms the fundamental role of the singular space associated to the quadratic form for the propagation of phase space singularities. The singularities are contained in the singular space, and propagate in the intersection of the singular space and the initial datum singularities along the flow of the Hamilton vector field associated to the imaginary part of the quadratic form.

  • 21.
    Wahlberg, Patrik
    Univ Turin, Dipartimento Matemat, I-10123 Turin, TO, Italy.
    Regularization of kernels for estimation of the Wigner spectrum of Gaussian stochastic processes2010In: Probability and Mathematical Statistics, ISSN 0208-4147, Vol. 30, no 2, p. 369-381Article in journal (Refereed)
    Abstract [en]

    We study estimation of the Wigner time-frequency spectrum of Gaussian stochastic processes. Assuming the covariance belongs to the Feichtinger algebra, we construct an estimation kernel that gives a mean square error arbitrarily close to the infimum over kernels in the Feichtinger algebra.

  • 22.
    Wahlberg, Patrik
    Department of Mathematics, University of Turin, Via Carlo Alberto 10, 10123, Turin, Italy.
    Representations of almost periodic pseudodifferential operators and applications in spectral theory2012In: Journal of Pseudo-Differential Operators and Applications, ISSN 1662-9981, E-ISSN 1662-999X, Vol. 3, no 1, p. 81-119Article in journal (Refereed)
    Abstract [en]

    The paper concerns algebras of almost periodic pseudodifferential operators on Rd with symbols in Hörmander classes. We study three representations of such algebras, one of which was introduced by Coburn, Moyer and Singer and the other two inspired by results in probability theory by Gladyshev. Two of the representations are shown to be unitarily equivalent for nonpositive order. We apply the results to spectral theory for almost periodic pseudodifferential operators acting on L 2 and on the Besicovitch Hilbert space of almost periodic functions.

  • 23.
    Wahlberg, Patrik
    Lund University.
    The random Wigner distribution of Gaussian stochastic processes with covariance in S0(R2d)2005In: Journal of Function Spaces and Applications, ISSN 0972-6802, E-ISSN 1758-4965, Vol. 3, no 2, p. 163-181Article in journal (Refereed)
    Abstract [en]

    The paper treats time-frequency analysis of scalar-valued zero mean Gaussian stochastic processes on ℝd. We prove that if the covariance function belongs to the Feichtinger algebra S0(ℝ2d) then: (i) the Wigner distribution and the ambiguity function of the process exist as finite variance stochastic Riemann integrals, each of which defines a stochastic process on ℝ2d, (ii) these stochastic processes on ℝ2d are Fourier transform pairs in a certain sense, and (iii) Cohen's class, ie convolution of the Wigner process by a deterministic function Φ∈C(ℝ2d), gives a finite variance process, and if Φ∈S0(ℝ2d) then W∗Φ can be expressed multiplicatively in the Fourier domain.

  • 24.
    Wahlberg, Patrik
    Deparment of Electroscience, Lund university.
    The Wigner distribution of Gaussian weakly harmonizable stochastic processes2006In: Pseudo-differential operators and related topics operator theory: Advances and Applications / [ed] P. Boggiatto, L. Rodino, J. Toft, M.W. Wong, Basel: Birkhäuser Verlag, 2006, p. 211-226Chapter in book (Refereed)
    Abstract [en]

    The paper treats the Wigner distribution of scalar-valued stochastic processes defined on ℝd. We show that if the process is Gaussian and weakly harmonizable then a stochastic Wigner distribution is well defined. The special case of stationary processes is studied, in which case the Wigner distribution is weakly stationary in the time variable and the variance is equal to the deterministic Wigner distribution of the covariance function.

  • 25.
    Wahlberg, Patrik
    The University of Newcastle.
    Vector-valued modulation spaces and localization operators with operator-valued symbols2007In: Integral equations and operator theory, ISSN 0378-620X, E-ISSN 1420-8989, Vol. 59, no 1, p. 99-128Article in journal (Refereed)
    Abstract [en]

    We study the short-time Fourier transformation, modulation spaces, Gabor representations and time-frequency localization operators, for functions and tempered distributions that have as range space a Banach or a Hilbert space. In the Banach space case the theory of modulation spaces contains some modifications of the scalar-valued theory, depending on the Banach space. In the Hilbert space case the modulation spaces have properties similar to the scalar-valued case and the Gabor frame theory essentially works. For localization operators in this context symbols are operator-valued. We generalize two results from the scalar-valued theory on continuity on certain modulation spaces when the symbol belongs to an L p,q space and M , respectively. The first result is true for any Banach space as range space, and the second result is true for any Hilbert space as range space.

  • 26.
    Wahlberg, Patrik
    et al.
    Univ. of Newcastle.
    Hansson, Maria
    Lund University.
    Kernels and multiple windows for estimation of the Wigner-Ville spectrum of Gaussian locally stationary processes2007In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 55, no 1, p. 73-84Article in journal (Refereed)
    Abstract [en]

    This paper treats estimation of the Wigner-Ville spectrum (WVS) of Gaussian continuous-time stochastic processes using Cohen's class of time-frequency representations of random signals. We study the minimum mean square error estimation kernel for locally stationary processes in Silverman's sense, and two modifications where we first allow chirp multiplication and then allow nonnegative linear combinations of covariances of the first kind. We also treat the equivalent multitaper estimation formulation and the associated problem of eigenvalue-eigenfunction decomposition of a certain Hermitian function. For a certain family of locally stationary processes which parametrizes the transition from stationarity to nonstationarity, the optimal windows are approximately dilated Hermite functions. We determine the optimal coefficients and the dilation factor for these functions as a function of the process family parameter.

  • 27.
    Wahlberg, Patrik
    et al.
    Lund University.
    Lantz, Göran
    University Hospital HUG.
    Approximate time-variable coherence analysis of multichannel signals2002In: Multidimensional systems and signal processing, ISSN 0923-6082, E-ISSN 1573-0824, Vol. 13, no 3, p. 237-264Article in journal (Refereed)
    Abstract [en]

    We present a new method for signal extraction from noisy multichannel epileptic seizure onset EEG signals. These signals are non-stationary which makes time-invariant filtering unsuitable. The new method assumes a signal model and performs denoising by filtering the signal of each channel using a time-variable filter which is an estimate of the Wiener filter. The approximate Wiener filters are obtained using the time-frequency coherence functions between all channel pairs, and a fix-point algorithm. We estimate the coherence functions using the multiple window method, after which the fix-point algorithm is applied. Simulations indicate that this method improves upon its restriction to assumed stationary signals for realistically non-stationary data, in terms of mean square error, and we show that it can also be used for time-frequency representation of noisy multichannel signals. The method was applied to two epileptic seizure onset signals, and it turned out that the most informative output of the method are the filters themselves studied in the time-frequency domain. They seem to reveal hidden features of the epileptic signal which are otherwise invisible. This algorithm can be used as preprocessing for seizure onset EEG signals prior to time-frequency representation and manual or algorithmic pattern classification.

  • 28.
    Wahlberg, Patrik
    et al.
    Univ Newcastle, Sch Elect Engn & Comp Sci, Callaghan, NSW 2308, Australia.
    Schreier, Peter
    Univ Newcastle, Sch Elect Engn & Comp Sci, Callaghan, NSW 2308, Australia.
    Gabor discretization of the Weyl product for modulation spaces and filtering of nonstationary stochastic processes2009In: Applied and Computational Harmonic Analysis, ISSN 1063-5203, E-ISSN 1096-603X, Vol. 26, no 1, p. 97-120Article in journal (Refereed)
    Abstract [en]

    We discretize the Weyl product acting on symbols of modulation spaces, using a Gabor frame defined by a Gaussian function. With one factor fixed. the Weyl product is equivalent to a matrix multiplication on the Gabor coefficient level. If the fixed factor belongs to the weighted Sjostrand space M omega(infinity,1), then the matrix has polynomial or exponential off-diagonal decay, depending oil the weight omega. Moreover, if its operator is invertible on L(2), the inverse matrix has similar decay properties. The results are applied to the equation for the linear minimum mean square error filter for estimation of a nonstationary second-order stochastic process from a noisy observation. The resulting formula for the Gabor coefficients of the Weyl symbol for the optimal filter may be interpreted as a time-frequency version of the filter for wide-sense stationary processes, known as the noncausal Wiener filter.

  • 29.
    Wahlberg, Patrik
    et al.
    Univ Turin, Dipartimento Matemat, I-10123 Turin, TO, Italy.
    Schreier, Peter
    Univ Newcastle, Callaghan, NSW 2308, Australia.
    Locally stationary harmonizable complex improper stochastic processes2011In: Journal of Time Series Analysis, ISSN 0143-9782, E-ISSN 1467-9892, Vol. 32, no 1, p. 33-46Article in journal (Refereed)
    Abstract [en]

    This article concerns continuous-time second-order complex-valued improper stochastic processes that are harmonizable and locally stationary in Silverman's sense. We study necessary and sufficient conditions for the property of local stationarity in the time and frequency domains. A sufficient condition by Silverman is generalized and extended to the improper case. We obtain a result on the absolute continuity of the complementary spectral measure with respect to the spectral measure, which is related to a spectral characterization of improper wide-sense stationary processes.

  • 30.
    Wahlberg, Patrik
    et al.
    Univ Turin, Italy.
    Schreier, Peter
    Univ Gesamthsch Paderborn, Germany.
    On the instantaneous frequency of Gaussian stochastic processes2012In: Probability and Mathematical Statistics, ISSN 0208-4147, Vol. 32, no 1, p. 69-92Article in journal (Refereed)
    Abstract [en]

     We study the instantaneous frequency (IF) of continuous-time, complex-valued, zero-mean, proper, mean-square differentiable, non-stationaryGaussian stochastic processes. We compute the probability density function for the IF for fixed time, which generalizes a result known for wide-sense stationary processes to nonstationary processes. For a fixed point in time, the IF has either zero or infinite variance. For harmonizable processes, we obtain as a consequence the result that the mean of the IF, for fixed time, is the normalized first-order frequency moment of the Wigner spectrum.

  • 31.
    Wahlberg, Patrik
    et al.
    Univ Turin, Dipartimento Matemat, I-10123 Turin, Italy.
    Schreier, Peter
    Univ Newcastle, Sch Elect Engn & Comp Sci, Callaghan, NSW 2308, Australia.
    On Wiener filtering of certain locally stationary stochastic processes2010In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 90, no 3, p. 885-890Article in journal (Refereed)
    Abstract [en]

    We study linear minimum mean squared error filters for continuous-time second-order stochastic processes that are locally stationary in Silverman's sense. We show that the optimal filter is rarely locally stationary even when the covariance functions have Gaussian shape. Using Mehler's formula we derive series expansions of the filter kernel for locally stationary covariances that are determined by Gaussians.

  • 32.
    Wahlberg, Patrik
    et al.
    Univ Newcastle, Sch Elect Engn & Comp Sci, Callaghan, NSW 2308, Australia.
    Schreier, Peter
    Univ Newcastle, Sch Elect Engn & Comp Sci, Callaghan, NSW 2308, Australia.
    Spectral relations for multidimensional complex improper stationary and (almost) cyclostationary processes2008In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 54, no 4, p. 1670-1682Article in journal (Refereed)
    Abstract [en]

    We study continuous-time multidimensional widesense stationary (WSS) and (almost) cyclostationary processes in the frequency domain. Under the assumption that the correlation function is uniformly continuous, we prove the existence of a unique sequence of spectral measures, which coincide with the restrictions to certain subdiagonals of the spectral measure in the strongly harmonizable case. Moreover, the off-diagonal measures are absolutely continuous with respect to the diagonal measure. As a consequence, for strongly harmonizable scalar improper almost cyclostationary processes, we obtain representation formulas for the components of the complementary spectral measure and the off-diagonal components of the spectral measure, in terms of the diagonal component of the spectral measure. We apply these results to analytic signals, which produces sufficient conditions for propriety for almost cyclostationary analytic signals.

1 - 32 of 32
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf