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Dr Jeffrey Hogan

Senior Lecturer

School of Mathematical and Physical Sciences (Mathematics)

Career Summary

Biography

Biography

I was awarded the BSc (Hons) in 1985 and the PhD in 1990 (under the supervision of Professors John Price and Michael Cowling) from the University of New South Wales. After completing my study, I held postdoctoral positions at the University of Texas at Austin (1989-91) with Professor John Gilbert, Flinders University (1991-93) with Professor Garth Gaudry and Macquarie University (1993-2000) with Professor Alan McIntosh. I then moved to the University of Arkansas in Fayetteville where I held an Associate Professorship, and gained tenure and promotion to Associate Professor in 2006. In 2009, I took up my current position as Senior Lecturer at the University of Newcastle.

Research

Broadly speaking, I work in pure, applied and computational harmonic analysis. My past and present projects include:

  • Uncertainty Principles for the Fourier transform on locally compact groups
  • Singular integrals and wavelet frames
  • Sampling theory in Fourier and wavelet analysis
  • Clifford-Fourier theory
  • Bandlimited and bandpass prolate functions in one- and higher dimensions
  • Applications of optimisation in the construction of one- and multi-dimensional wavelets

Research Collaboration

I have active collaborations with:

  • Professor Joseph Lakey (New Mexico State University)
  • Dr Matthew Tam (University of Goettingen)
  • Dr Peter Massopust (Technical University of Munich)
  • Professor Brigitte Forster (University of Passau)
  • Dr Daniel Abreu (Acoustics Research Institute, Vienna)
  • Dr Jose-Luis Romero (University of Vienna)
  • Dr Mark Craddock (University of Technology Sydney)

Teaching

Since arrival at UON, I have taught across the undergraduate mathematics curriculum, including courses in first-year calculus, multivariable calculus, linear algebra, mathematical modelling, differential equations, complex analysis, numerical analysis and my favourite -- Fourier analysis.

Administration

Administrative duties at UON have included:

  • Deputy Head of School of Mathematical and Physical Sciences: 2015 -- present
  • Acting Head of Mathematics Discipline: July 2017 - July 2018
  • MAPS HDR Coordinator: January 2017  -- present
  • Bachelor of Mathematics Convenor: 2009 -- 2012


Qualifications

  • PhD, University of New South Wales
  • Bachelor of Science, University of New South Wales

Keywords

  • Clifford analysis
  • Fourier analysis
  • signal processing
  • singular integrals
  • wavelets

Fields of Research

Code Description Percentage
010106 Lie Groups, Harmonic and Fourier Analysis 75
010399 Numerical and Computational Mathematics not elsewhere classified 15
010499 Statistics not elsewhere classified 10

Professional Experience

UON Appointment

Title Organisation / Department
Senior Lecturer University of Newcastle
School of Mathematical and Physical Sciences
Australia

Academic appointment

Dates Title Organisation / Department
1/07/2006 - 1/12/2008 Associate Professor University of Arkansas
Department of Mathematical Sciences
United States
1/08/2000 - 1/07/2006 Assistant Professor University of Arkansas
Department of Mathematical Sciences
United States
15/07/1993 - 31/08/2000 Research Associate MACCS, Macquarie University
Australia
1/09/1991 - 1/06/1993 Research Associate Flinders University
Australia
1/08/1989 - 1/08/1991 Lecturer University of Texas At Austin
Department of Mathematics
United States
1/03/1985 - 1/07/1989 Tutor The University of New South Wales
School of Mathematical Sciences
Australia
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Publications

For publications that are currently unpublished or in-press, details are shown in italics.


Book (7 outputs)

Year Citation Altmetrics Link
2013 Hogan J, AMSI International Conference on Harmonic Analysis and Applications (Macquarie University, February 2011), Centre for Mathematics and its Applications, Mathematical Sciences Institute, the Australian National University, Canberra, 147 (2013)
2013 Hogan J, AMSI International Conference on Harmonic Analysis and Applications (Macquarie University, February 2011), Centre for Mathematics and its Applications, Mathematical Sciences Institute, the Australian National University, Canberra, 147 (2013)
2012 Hogan JA, Lakey JD, Duration and Bandwidth Limiting: Prolate Functions, Sampling, and Applications, Birkhauser, New York, 258 (2012) [A1]
Citations Scopus - 14
2012 Hogan JA, Lakey JD, Preface (2012)
2005 Hogan JA, Lakey JD, Time-frequency and time-scale methods: Adaptive decompositions, uncertainty principles, and sampling (2005) [A1]
Citations Scopus - 13
2005 Hogan JA, Lakey JD, Preface (2005)
2002 Gilbert JE, Han YS, Hogan JA, Lakey JD, Weiland D, Weiss G, Smooth Molecular Decompositions of Functions and Singular Integral Operators, American Mathematical Society, Newport, Rhode Island, 74 (2002) [A1]
Show 4 more books

Chapter (16 outputs)

Year Citation Altmetrics Link
2017 Hogan JA, Lakey JD, 'Frame properties of shifts of prolate and bandpass prolate functions', Frames and other bases in abstract and function spaces. Novel Methods in Harmonic Analysis, Birkhauser Basel, New York 215-235 (2017) [B1]
Citations Scopus - 1
2012 Hogan JA, Morris AJ, 'Translation-invariant Clifford operators', , Australian National University 48 (2012) [E3]
2012 Hogan JA, Lakey JD, 'Thomson¿s multitaper method and applications to channel modeling', Applied and Numerical Harmonic Analysis 91-127 (2012)

© Springer Science+Business Media, LLC 2012. One of the most basic applications of Fourier analysis is power spectrum estimation. Some historical comments on this age-old problem ... [more]

© Springer Science+Business Media, LLC 2012. One of the most basic applications of Fourier analysis is power spectrum estimation. Some historical comments on this age-old problem can be found in review articles by Robinson [279] and Benedetto [23], and in Percival and Walden¿s book [264]. We refer to Appendix A for basic definitions and properties, and references for stochastic processes. In the problem of estimating a wide-sense stationary random process from data, one has only finitely many samples, often of a single realization of the process, with which to work.

DOI 10.1007/978-0-8176-8307-8_3
2012 Hogan JA, Lakey JD, 'Time-localized sampling approximations', Applied and Numerical Harmonic Analysis 199-221 (2012)

© Springer Science+Business Media, LLC 2012. In this last chapter we explore briefly some connections among sampling and time and band limiting. The chapter begins by pointing out... [more]

© Springer Science+Business Media, LLC 2012. In this last chapter we explore briefly some connections among sampling and time and band limiting. The chapter begins by pointing out a general connection between the samples of eigenfunctions of time and band limiting and the eigenvectors of a certain matrix whose entries are, in essence, the samples of time-localized images of functions that interpolate the samples in the given Paley¿Wiener space. Next, a discrete method is considered for generating eigenfunctions of time¿frequency localizations to unions of sets from their separate localizations. We then reconsider the connection between eigenfunctions and their samples in the concrete context of localization to intervals of the real line, outlining work ofWalter and Shen [347] and of Khare and George [177].Walter and Shen provided L2-estimates for approximate prolate spheroidal wave functions (PSWFs) constructed from interpolation of their sample values within the time-localization interval. We provide a partial sharpening of their estimates by using a slightly enlarged set of samples.

DOI 10.1007/978-0-8176-8307-8_6
2012 Hogan JA, Lakey JD, 'Time and band limiting of multiband signals', Applied and Numerical Harmonic Analysis 129-151 (2012)

© Springer Science+Business Media, LLC 2012. When a = 2OT, the operator POQTcorresponding to single time and frequency intervals has an eigenvalue ¿¿a¿¿1/2, as Theorem 4.1.2 below... [more]

© Springer Science+Business Media, LLC 2012. When a = 2OT, the operator POQTcorresponding to single time and frequency intervals has an eigenvalue ¿¿a¿¿1/2, as Theorem 4.1.2 belowwill show. The norm ¿0(a = 1) of the operator PQ1/2satisfies ¿0(a = 1) = ¿sinc 1[1/2,1/2]¿ > 0.88. The trace of PQ1/2is equal to a = 1, on the one hand and to S¿non the other, so ¿1(a = 1) = 1¿0(a = 1) < 1/2. Suppose that T = 1 and S is a finite, pairwise disjoint union of a frequency intervals I1, ¿, Iaeach of unit length. Then PSQ should have on the order of a eigenvalues of magnitude at least 1/2. Consider now the limiting case in which the frequency intervals become separated at infinity. Any function ¿jthat is concentrated in frequency on Ijwill be almost orthogonal over [T,T], in the separation limit, to any function ¿kthat is frequency-concentrated on Ikwhen j ¿ k.

DOI 10.1007/978-0-8176-8307-8_4
2012 Hogan JA, Lakey JD, 'Duration and bandwidth limiting: Prolate functions, sampling, and applications', Applied and Numerical Harmonic Analysis 1-253 (2012)
Citations Scopus - 6
2012 Hogan JA, Lakey JD, 'Sampling of band-limited and multiband signals', Applied and Numerical Harmonic Analysis 153-198 (2012)

© Springer Science+Business Media, LLC 2012. We provide here an overview of sampling theory that emphasizes real-variable aspects and functional analytic methods rather than analy... [more]

© Springer Science+Business Media, LLC 2012. We provide here an overview of sampling theory that emphasizes real-variable aspects and functional analytic methods rather than analytic function-theoretic ones. While this approach does not justify the most powerful mathematical results, it does provide the basis for practical sampling techniques for band-limited and multiband signals.

DOI 10.1007/978-0-8176-8307-8_5
2012 Hogan JA, Lakey JD, 'Numerical aspects of time and band limiting', Applied and Numerical Harmonic Analysis 45-90 (2012)

© Springer Science+Business Media, LLC 2012. This chapter is concerned with the role of the prolates in numerical analysis¿ particularly their approximation properties and applica... [more]

© Springer Science+Business Media, LLC 2012. This chapter is concerned with the role of the prolates in numerical analysis¿ particularly their approximation properties and application in the numerical solution of differential equations. The utility of the prolates in these contexts is due principally to the fact that they form a Markov system (see Defn. 2.1.6) of functions on [-11], a property that stems from their status as eigenfunctions of the differential operator P of (1.6), and allows the full force of the Sturm¿Liouville theory to be applied. The Markov property immediately gives the orthogonality of the prolates on [-11] (previously observed in Sect. 1.2 as the double orthogonality property) and also a remarkable collection of results regarding the zeros of the prolates as well as quadrature properties that are central to applications in numerical analysis.

DOI 10.1007/978-0-8176-8307-8_2
2012 Hogan JA, Lakey JD, 'The bell labs theory', Applied and Numerical Harmonic Analysis 1-43 (2012)

© Springer Science+Business Media, LLC 2012. Duration limiting, or time limiting, refers to restricting a signal by setting its values equal to zero outside of a finite time inter... [more]

© Springer Science+Business Media, LLC 2012. Duration limiting, or time limiting, refers to restricting a signal by setting its values equal to zero outside of a finite time interval or, more generally, outside of a compact set. Bandwidth limiting, or band limiting, refers to restricting a signal by setting its amplitudes equal to zero outside of a finite frequency interval or again, more generally, outside of a compact set. This book addresses primarily the theory of time and band limiting whose core was developed by Landau, Pollak, and Slepian in a series of papers [195, 196, 303, 309] appearing in the Bell System Technical Journal in the early to middle part of the 1960s, and a broader body of work that grew slowly but steadily out of that core up until around 1980, with a resurgence since 2000, due in large part to the importance of time and band limiting in wireless communications. The 1960s Bell Labs theory of time and band limiting is but one aspect of the Bell Labs information theory. The foundations of this encompassing theory were laid, in large part, in Nyquist¿s fundamental papers ¿Certain Topics in Telegraph Transmission Theory¿ [247], which appeared in the Transactions of the American Institute of Electrical Engineers in 1928, and ¿Certain Factors Affecting Telegraph Speed,¿ published in April 1924 in the Bell System Technical Journal, along with Hartley¿s paper ¿Transmission of Information,¿ which also appeared in the Bell System Technical Journal in 1928 [137]. These papers quantified general ideas that were in the air, though certain specific versions were attributed to Kelvin and Wiener among others. Of course, Claude Shannon¿s seminal work, ¿A Mathematical Theory of Communication,¿ which appeared in the Bell System Technical Journal in July and October 1948 [293], is often cited as providing the basis for much of modern communications theory. His sampling theory plays a central role in Chap. 5 of this monograph. The works of Nyquist and Hartley however remain, in some ways, more germane to the study at hand.

DOI 10.1007/978-0-8176-8307-8_1
2008 Hogan JA, Lakey JD, 'Sampling and time-frequency localization of band-limited and multiband signals', Applied and Numerical Harmonic Analysis 275-291 (2008) [B1]

© 2008, Birkhäuser Boston. This chapter develops aspects of previous work ([10] and [11]) that pertain distinctly to band-limited functions. In particular, we discuss some represe... [more]

© 2008, Birkhäuser Boston. This chapter develops aspects of previous work ([10] and [11]) that pertain distinctly to band-limited functions. In particular, we discuss some representation formulas for band-limited functions in terms of periodic nonuniform samples. In the case of multiband signals, periodic nonuniform sampling is often valid at a lower sampling rate than is uniform sampling, as will be discussed. Finally, we will consider some related questions about optimally time- and multiband-limited signals.

DOI 10.1007/978-0-8176-4683-7_13
Citations Scopus - 4
2008 Hogan JA, Lakey JD, 'Periodic nonuniform sampling of bandlimited and multiband signals', Representations, Wavelets, and Frames: A Celebration of the Mathematical Work of Lawrence W.Baggett, Springer, Boston 275-292 (2008) [B2]
2006 Hogan JA, Lakey JD, 'Periodic Nonuniform Sampling in Shift-Invariant Spaces', Applied and Numerical Harmonic Analysis 253-287 (2006) [B1]

© 2006, Birkhäuser Boston. This chapter reviews several ideas that grew out of observations of Djokovic and Vaidyanathan to the effect that a generalized sampling method for bandl... [more]

© 2006, Birkhäuser Boston. This chapter reviews several ideas that grew out of observations of Djokovic and Vaidyanathan to the effect that a generalized sampling method for bandlimited functions, due to Papoulis, could be carried over in many cases to the spline spaces and other shift-invariant spaces. Papoulis¿ method is based on the sampling output of linear, time-invariant systems. Unser and Zerubia formalized Papoulis¿ approach in the context of shift-invariant spaces. However, it is not easy to provide useful conditions under which the Unser-Zerubia criterion provides convergent and stable sampling expansions. Here we review several methods for validating the Unser-Zerubia approach for periodic nonuniform sampling, which is a very special case of generalized sampling. The Zak transform plays an important role.

DOI 10.1007/0-8176-4504-7_12
Citations Scopus - 6
2005 Hogan J, Lakey JD, 'Non-Translation-Invariance in Principal Shift-Invariant Spaces', , World Scientific Publishing, Hackensack, New Jersey, USA 471-485 (2005) [E1]
2001 Hogan JA, Lakey JD, 'Embeddings and uncertainty principles for generalized modulation spaces', Modern Sampling Theory: Mathematics and Applications, Birkhauser, Boston 73-105 (2001)
2001 Hogan JA, Axelsson A, Grognard R, McIntosh A, 'Harmonic analysis of Dirac operators on bounded domains', Clifford analysis and its applications, Kluwer, Netherlands 231-246 (2001)
1998 Hogan JA, Lakey JD, Gilbert JE, 'Fourier and wavelet characterizations of massless Hardy spaces', Dirac operators in analysis, Addison Wesley Longman, Harlow, Essex, UK 25-40 (1998)
Show 13 more chapters

Journal article (25 outputs)

Year Citation Altmetrics Link
2017 Hogan JA, Massopust P, 'Quaternionic B-splines', Journal of Approximation Theory, 224 43-65 (2017) [C1]
DOI 10.1016/j.jat.2017.09.003
2017 Franklin DJ, Hogan JA, Larkin KG, 'Hardy, Paley-Wiener and Bernstein spaces in Clifford analysis', COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 62 1314-1328 (2017) [C1]
DOI 10.1080/17476933.2016.1250411
2017 Hogan JA, Lakey JD, 'On the Numerical Evaluation of Bandpass Prolates II', JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 23 125-140 (2017) [C1]
DOI 10.1007/s00041-016-9465-y
Citations Scopus - 3Web of Science - 1
2016 Hogan JA, Lakey JD, 'Frame expansions of bandlimited signals using prolate spheroidal wave functions', Sampling Theory in Signal and Image Processing, 15 139-153 (2016) [C1]

© 2016 SAMPLING PUBLISHING. We consider methods to compute duals of frames for Paley¿Wiener spaces generated by shifts of certain prolate spheroidal wave functions. In particular,... [more]

© 2016 SAMPLING PUBLISHING. We consider methods to compute duals of frames for Paley¿Wiener spaces generated by shifts of certain prolate spheroidal wave functions. In particular, we consider methods to compute frame expansions restricted to subband-limited functions. Methods to compute dual frame generators are also provided in the case of corresponding frames for spaces of bandpass-limited signals.

2015 Hogan JA, Lakey JD, 'Frame properties of shifts of prolate spheroidal wave functions', Applied and Computational Harmonic Analysis, 39 21-32 (2015) [C1]

© 2014 Elsevier Inc. Abstract We provide conditions on a shift parameter and number of basic prolate spheroidal wave functions with a fixed bandwidth and time concentrated to a fi... [more]

© 2014 Elsevier Inc. Abstract We provide conditions on a shift parameter and number of basic prolate spheroidal wave functions with a fixed bandwidth and time concentrated to a fixed duration such that the shifts of the basic prolates form a frame or a Riesz basis for the Paley-Wiener space consisting of all square integrable functions with the given bandlimit.

DOI 10.1016/j.acha.2014.08.003
Citations Scopus - 13Web of Science - 9
2014 Ogburn DX, Waters CL, Sciffer MD, Hogan JA, Abbott PC, 'A finite difference construction of the spheroidal wave functions', COMPUTER PHYSICS COMMUNICATIONS, 185 244-253 (2014) [C1]
DOI 10.1016/j.cpc.2013.07.024
Citations Scopus - 7Web of Science - 7
Co-authors Murray Sciffer, Colin Waters
2014 Hogan JA, Kroger J, Lakey JD, 'Time and bandpass limiting and an application to EEG', Sampling Theory in Signal and Image Processing, 13 295-313 (2014) [C1]
Citations Scopus - 2
2013 Craddock MJ, Hogan JA, 'The Fractional Clifford-Fourier Kernel', JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 19 683-711 (2013) [C1]
DOI 10.1007/s00041-013-9274-5
Citations Scopus - 3Web of Science - 3
2013 Hogan JA, Lakey JD, 'Letter to the Editor: On the Numerical Evaluation of Bandpass Prolates', Journal of Fourier Analysis and Applications, 19 439-446 (2013) [C1]

This letter provides a technique for numerical evaluation of certain eigenfunctions of the integral kernel operator corresponding to time truncation of a square-integrable functio... [more]

This letter provides a technique for numerical evaluation of certain eigenfunctions of the integral kernel operator corresponding to time truncation of a square-integrable function to a finite interval, followed by frequency limiting to frequencies in an annular band. © 2013 Springer Science+Business Media New York.

DOI 10.1007/s00041-012-9257-y
Citations Scopus - 4Web of Science - 2
2012 Hogan JA, Morris AJ, 'Quaternionic wavelets', Numerical Functional Analysis and Optimization, 33 1031-1062 (2012) [C1]
Citations Scopus - 6Web of Science - 5
2012 Lakey JD, Hogan JA, 'On the numerical computation of certain eigenfunctions of time and multiband limiting', Numerical Functional Analysis and Optimization, 33 1095-1111 (2012) [C1]
DOI 10.1080/01630563.2012.682133
Citations Web of Science - 1
2010 Hogan JA, Izu S, Lakey JD, 'Sampling approximations for time- and bandlimiting', Sampling Theory in Signal and Image Processing, 9 91-117 (2010) [C1]
Citations Scopus - 9
2009 Hogan JA, Lakey J, 'Non-translation-invariance and the synchronization problem in wavelet sampling', Acta Applicandae Mathematicae, 107 373-398 (2009) [C1]
DOI 10.1007/s10440-009-9480-y
Citations Scopus - 10Web of Science - 9
2007 Hogan J, 'Frame-based non uniform sampling in paley-wiener spaces', Journal of Applied Functional Analysis, 2 361-400 (2007) [C1]
2006 Hogan JA, Lakey JD, 'Hardy's theorem and rotations', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 134 1459-1466 (2006) [C1]
DOI 10.1090/S0002-9939-05-08098-6
Citations Scopus - 2Web of Science - 3
2006 Hogan JA, Lakey JD, 'On uncertainty bounds and growth estimates for fractional fourier transforms', Applicable Analysis: an international journal, 85 891-899 (2006) [C1]
2005 Hogan JA, Lakey JD, 'Sampling and oversampling in shift-invariant and multiresolution spaces 1: Validation of sampling schemes', INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING, 3 257-281 (2005) [C1]
DOI 10.1142/S0219691305000798
Citations Web of Science - 4
2005 Gilbert JE, Hogan JA, Lakey JD, 'BMO, boundedness of affine operators, and frames', APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 18 3-24 (2005) [C1]
DOI 10.1016/j.acha.2004.05.005
Citations Scopus - 4Web of Science - 5
2001 Kirkup H, Pitman AJ, Hogan J, Brierley G, 'An Initial Analysis of River Discharge and Rainfall in Coastal New South Wales, Australia Using Wavelet Transforms', Australian Geographical Studies, 39 313-334 (2001)
DOI 10.1111/1467-8470.00149
2000 Gilbert JE, Hogan JA, Lakey JD, 'Characterization of Hardy spaces by singular integrals and 'divergence-free' wavelets', PACIFIC JOURNAL OF MATHEMATICS, 193 79-105 (2000)
DOI 10.2140/pjm.2000.193.79
2000 Hogan JA, Li C, McIntosh A, Zhang K, 'Global Higher Integrability of Jacobians on Bounded Domains', Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, 17 193-218 (2000)
1997 Hogan JA, Gilbert JE, Lakey JD, 'Atomic decomposition of divergence-free Hardy spaces', Mathematics Moravica, Special Volume 33-52 (1997)
1995 HOGAN JA, LAKEY JD, 'EXTENSIONS OF THE HEISENBERG-GROUP BY DILATIONS AND FRAMES', APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2 174-199 (1995)
DOI 10.1006/acha.1995.1013
Citations Scopus - 14Web of Science - 13
1993 HOGAN JA, 'A QUALITATIVE UNCERTAINTY PRINCIPLE FOR UNIMODULAR GROUPS OF TYPE-I', TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 340 587-594 (1993)
DOI 10.2307/2154667
Citations Scopus - 15Web of Science - 12
1988 Hogan JA, 'Weighted norm inequalities for the Fourier transform on connected locally compact groups', Pacific Journal of Mathematics, 131 277-290 (1988)
Show 22 more journal articles

Conference (13 outputs)

Year Citation Altmetrics Link
2017 Hogan JA, Lakey J, 'Sampling in Paley-Wiener spaces, uncertainty and the prolate spheroidal wavefunctions', Proceedings of the AMSI/AustMS 2014 Workshop in Harmonic Analysis and its Applications, Sydney, Australia (2017) [E1]
2017 Hogan JA, Lakey JD, 'Riesz bounds for prolate shifts', 2017 INTERNATIONAL CONFERENCE ON SAMPLING THEORY AND APPLICATIONS (SAMPTA), Tallinn, ESTONIA (2017) [E1]
2017 Hogan JA, Lakey JD, 'Bandpass pseudo prolate shift frames and Riesz bases', 2017 INTERNATIONAL CONFERENCE ON SAMPLING THEORY AND APPLICATIONS (SAMPTA), Tallinn, ESTONIA (2017) [E1]
2015 Hogan JA, Lakey JD, 'Prolate shift frames and their duals', 2015 International Conference on Sampling Theory and Applications, SampTA 2015, Washington, DC (2015) [E1]
DOI 10.1109/SAMPTA.2015.7148862
Citations Scopus - 2
2015 Hogan JA, Lakey JD, 'Wavelet frames generated by bandpass prolate functions', 2015 International Conference on Sampling Theory and Applications, SampTA 2015 (2015) [E1]

© 2015 IEEE. We refer to eigenfunctions of the kernel corresponding to truncation in a time interval followed by truncation in a frequency band as bandpass prelates (BPPs). We pro... [more]

© 2015 IEEE. We refer to eigenfunctions of the kernel corresponding to truncation in a time interval followed by truncation in a frequency band as bandpass prelates (BPPs). We prove frame bounds for certain families of shifts of bandpass prolates, and we numerically construct dual frames for finite dimensional analogues. In the continuous case, the corresponding families produce wavelet frames for the space of square-integrable functions.

DOI 10.1109/SAMPTA.2015.7148863
Citations Scopus - 4Web of Science - 1
2013 Hogan JA, Lakey JD, 'Sampling aspects of approximately time-limited multiband and bandpass signals', Proceedings of the 10th International Conference on Sampling Theory and Applications (SampTA 2013), Bremen, Germany (2013) [E1]
2001 Hogan JA, Lakey JD, 'Sampling and aliasing without translation-invariance', Proceedings of the 2001 International Conference on Sampling Theory and Applications, Orlando, Florida (2001)
2000 Hogan JA, Lakey J, 'Sampling for shift-invariant and wavelet subspaces', WAVELET APPLICATIONS IN SIGNAL AND IMAGE PROCESSING VIII PTS 1 AND 2, SAN DIEGO, CA (2000)
DOI 10.1117/12.408622
Citations Scopus - 2
1999 Hogan JA, Lakey JD, 'Sharp embeddings for modulation spaces and the Poisson summation formula', Proceedings of the 1999 International Workshop on Sampling Theory and Applications, Loen, Norway (1999)
1997 Hogan JA, Lakey JD, Gilbert JE, 'Wavelet subspaces for sampling and extrapolation', Proceedings of SAMPTA, Aveiro, Portugal (1997)
1996 Gilbert JE, Hogan JA, Lakey JD, 'Frame decompositions of form-valued Hardy spaces', CLIFFORD ALGEBRAS IN ANALYSIS AND RELATED TOPICS, UNIV ARKANSAS, FAYETTEVILLE, AR (1996)
Citations Scopus - 3Web of Science - 2
1996 Croft MJ, Hogan JA, 'Wavelet-based signal extrapolation', ISSPA 96 - FOURTH INTERNATIONAL SYMPOSIUM ON SIGNAL PROCESSING AND ITS APPLICATIONS, PROCEEDINGS, VOLS 1 AND 2, GOLD COAST, AUSTRALIA (1996)
Citations Scopus - 4
1988 Hogan JA, 'A qualitative uncertainty principle for locally compact abelian groups', Proceedings of the Centre for Mathematical Analysis, Australian National University, Australian National University (1988)
Show 10 more conferences
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Grants and Funding

Summary

Number of grants 5
Total funding $616,120

Click on a grant title below to expand the full details for that specific grant.


20171 grants / $13,500

Multichannel Image and Signal Analysis: Phase and Geometry$13,500

For research visits between the participants to work on current research in which methods of Clifford analysis are applied to problems of multidimensional, multichannel signal and image analysis.

Funding body: Bayerische Forschunsallianz

Funding body Bayerische Forschunsallianz
Project Team

Prof. Brigitte Forster, Dr Jeffrey Hogan, Dr Peter Massopust

Scheme Bayerischen Hochshulforderprogramms zur Ahnbahnung und Vertiefung internationaler Forschnungskooperationen
Role Investigator
Funding Start 2017
Funding Finish 2017
GNo
Type Of Funding International - Competitive
Category 3IFA
UON N

20161 grants / $593,620

Relaxed reflection methods for feasibility and matrix completion problems$593,620

Funding body: ARC (Australian Research Council)

Funding body ARC (Australian Research Council)
Project Team Laureate Professor Jon Borwein, Doctor Jeffrey Hogan, Associate Professor Russell Luke, Associate Professor Brailey Sims
Scheme Discovery Projects
Role Lead
Funding Start 2016
Funding Finish 2018
GNo G1500027
Type Of Funding Aust Competitive - Commonwealth
Category 1CS
UON Y

20141 grants / $2,000

Faculty PVC Conference Assistance Grant 2014$2,000

Funding body: University of Newcastle - Faculty of Science & IT

Funding body University of Newcastle - Faculty of Science & IT
Project Team Doctor Jeffrey Hogan
Scheme PVC Conference Assistance Grant
Role Lead
Funding Start 2014
Funding Finish 2014
GNo G1401195
Type Of Funding Internal
Category INTE
UON Y

20131 grants / $2,000

Faculty PVC Conference Assistance Grant 2013$2,000

Funding body: University of Newcastle - Faculty of Science & IT

Funding body University of Newcastle - Faculty of Science & IT
Project Team Doctor Jeffrey Hogan
Scheme PVC Conference Assistance Grant
Role Lead
Funding Start 2013
Funding Finish 2013
GNo G1401161
Type Of Funding Internal
Category INTE
UON Y

20101 grants / $5,000

Hypercomplex Signal Processing$5,000

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Doctor Jeffrey Hogan
Scheme New Staff Grant
Role Lead
Funding Start 2010
Funding Finish 2010
GNo G1000074
Type Of Funding Internal
Category INTE
UON Y
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Research Supervision

Number of supervisions

Completed3
Current4

Current Supervision

Commenced Level of Study Research Title Program Supervisor Type
2018 PhD Higher-dimensional Prolate Spheroidal Wave Functions PhD (Mathematics), Faculty of Science, The University of Newcastle Principal Supervisor
2017 PhD Optimisation in the Construction of Multidimensional Wavelets PhD (Mathematics), Faculty of Science, The University of Newcastle Principal Supervisor
2017 PhD Supply Food Optimisation PhD (Statistics), Faculty of Science, The University of Newcastle Co-Supervisor
2016 PhD An Exploration of Generalised Convexity on Semigroups and Semimodules PhD (Mathematics), Faculty of Science, The University of Newcastle Principal Supervisor

Past Supervision

Year Level of Study Research Title Program Supervisor Type
2018 PhD Projection Algorithms for Non-separable Wavelets and Clifford Fourier Analysis PhD (Mathematics), Faculty of Science, The University of Newcastle Principal Supervisor
2018 PhD Random Walks On Groups PhD (Mathematics), Faculty of Science, The University of Newcastle Co-Supervisor
2014 PhD Fourier and Wavelet Analysis of Clifford-Valued Functions PhD (Mathematics), Faculty of Science, The University of Newcastle Principal Supervisor
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Research Projects

Prolate functions : bandlimited and bandpass signal processing 2009 -

Prolate functions have maximal energy concentration among all signals of a fixed bandlimit and have found many applications in signal processing, especially as taper functions for spectral estimation algorithms. This is due to their ``spectral accumulation'' properties. In this project, we

  1. construct bandpass prolates whose spectra are supported on a union of intervals on the line.
  2. construct prolate functions on graphs.
  3. develop the required aspects of Clifford analysis to enable the construction of bandlimited and bandpass prolates in higher dimensions.

Publications

Hogan JA, Lakey JD, Time-frequency and time-scale methods: Adaptive decompositions, uncertainty principles, and sampling (2005) [A1]

Hogan JA, Lakey JD, 'Sampling and time-frequency localization of band-limited and multiband signals', Applied and Numerical Harmonic Analysis 275-291 (2008) [B1]

Hogan JA, Lakey JD, Duration and Bandwidth Limiting: Prolate Functions, Sampling, and Applications, Birkhauser, New York, 258 (2012) [A1]

Hogan JA, Lakey JD, 'Numerical aspects of time and band limiting', Applied and Numerical Harmonic Analysis 45-90 (2012)

Lakey JD, Hogan JA, 'On the numerical computation of certain eigenfunctions of time and multiband limiting', Numerical Functional Analysis and Optimization, 33 1095-1111 (2012) [C1]

Hogan JA, Lakey JD, 'Time-localized sampling approximations', Applied and Numerical Harmonic Analysis 199-221 (2012)

Hogan JA, Lakey JD, 'Letter to the Editor: On the Numerical Evaluation of Bandpass Prolates', Journal of Fourier Analysis and Applications, 19 439-446 (2013) [C1]

Hogan JA, Kroger J, Lakey JD, 'Time and bandpass limiting and an application to EEG', Sampling Theory in Signal and Image Processing, 13 295-313 (2014) [C1]

Hogan JA, Lakey JD, 'Frame properties of shifts of prolate spheroidal wave functions', Applied and Computational Harmonic Analysis, 39 21-32 (2015) [C1]

Hogan JA, Lakey JD, 'Prolate shift frames and their duals', 2015 International Conference on Sampling Theory and Applications, SampTA 2015, Washington, DC (2015) [E1]

Hogan JA, Lakey JD, 'Wavelet frames generated by bandpass prolate functions', 2015 International Conference on Sampling Theory and Applications, SampTA 2015 (2015) [E1]

Hogan JA, Lakey JD, 'Frame expansions of bandlimited signals using prolate spheroidal wave functions', Sampling Theory in Signal and Image Processing, 15 139-153 (2016) [C1]

Hogan JA, Lakey JD, 'Bandpass pseudo prolate shift frames and Riesz bases', 2017 INTERNATIONAL CONFERENCE ON SAMPLING THEORY AND APPLICATIONS (SAMPTA), Tallinn, ESTONIA (2017) [E1]

Hogan JA, Lakey JD, 'Frame properties of shifts of prolate and bandpass prolate functions', Frames and other bases in abstract and function spaces. Novel Methods in Harmonic Analysis, Birkhauser Basel, New York 215-235 (2017) [B1]

Hogan JA, Lakey JD, 'On the Numerical Evaluation of Bandpass Prolates II', JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 23 125-140 (2017) [C1]

Hogan JA, Lakey JD, 'Riesz bounds for prolate shifts', 2017 INTERNATIONAL CONFERENCE ON SAMPLING THEORY AND APPLICATIONS (SAMPTA), Tallinn, ESTONIA (2017) [E1]

Students

Program Research Title
PhD
Faculty of Science
Higher-dimensional Prolate Spheroidal Wave Functions

Collaborators

Name Organisation
Joseph Lakey New Mexico State University, Las Cruces

Multidimensional wavelets 2016 -

Among modern signal processing techniques, wavelets have provided the most important theoretical challenges and technological advances. The by now classical construction methods on the line require techniques from complex analysis that are not available in higher dimensions. In this project, we apply modern techniques of optimisation to the notoriously difficult construction of wavelets in two and higher dimensions. Outputs include:

  1. Wavelets on the line with improved properties (near-cardinality, near-symmetry, etc).
  2. Wavelets on the plane with prescribed regularity.

With a view to applications in the processing of colour images, the team is working towards the development of quaternion-valued wavelets on the plane.

Grants

Relaxed reflection methods for feasibility and matrix completion problems

Funding body: ARC (Australian Research Council)

Funding body ARC (Australian Research Council)
Project Team Laureate Professor Jon Borwein, Doctor Jeffrey Hogan, Associate Professor Russell Luke, Associate Professor Brailey Sims
Scheme Discovery Projects

Students

Program Research Title
PhD
Faculty of Science
Optimisation in the Construction of Multidimensional Wavelets

Clifford splines 2012 -

Spline functions are important components in signal processing algorithms -- they are often used in finite element algorithms for the solution of differential equations and are also used in the smoothing of discrete data in computer graphics. In this project we investigate the application of Clifford-analytic techniques to the construction of multi-channel, multi-variate splines appropriate to the treatment of multi-channel signals such as colour images and video.

Grants

Multichannel Image and Signal Analysis: Phase and Geometry

Funding body: Bayerische Forschunsallianz

Funding body Bayerische Forschunsallianz
Description For research visits between the participants to work on current research in which methods of Clifford analysis are applied to problems of multidimensional, multichannel signal and image analysis.
Scheme Bayerischen Hochshulforderprogramms zur Ahnbahnung und Vertiefung internationaler Forschnungskooperationen

Publications

Hogan JA, Massopust P, 'Quaternionic B-splines', Journal of Approximation Theory, 224 43-65 (2017) [C1]

Collaborators

Name Organisation
Peter Massopust Technical University of Munish

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Research Collaborations

The map is a representation of a researchers co-authorship with collaborators across the globe. The map displays the number of publications against a country, where there is at least one co-author based in that country. Data is sourced from the University of Newcastle research publication management system (NURO) and may not fully represent the authors complete body of work.

Country Count of Publications
United States 38
Australia 34
Canada 1
Germany 1
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News

ARC Discovery Projects funding success

November 4, 2015

Laureate Professor Jon Borwein, Dr Jeffrey Hogan and Professor Dr Russell Luke have been awarded more than $560,000 in ARC Discovery Project funding commenc

Dr Jeffrey Hogan

Position

Senior Lecturer
School of Mathematical and Physical Sciences
Faculty of Science

Focus area

Mathematics

Contact Details

Email jeff.hogan@newcastle.edu.au
Phone (02) 4921 7235
Fax (02) 4921 6898

Office

Room V128
Building Mathematics Building
Location Callaghan
University Drive
Callaghan, NSW 2308
Australia
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