
Associate Professor Jeffrey Hogan
Associate Professor
School of Mathematical and Physical Sciences (Mathematics)
- Email:jeff.hogan@newcastle.edu.au
- Phone:(02) 4921 7235
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, and gained tenure and promotion to Associate Professor in 2006. In 2009 I accepted a position 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 |
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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 |
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Associate Professor | University of Newcastle School of Mathematical and Physical Sciences Australia |
Academic appointment
Dates | Title | Organisation / Department |
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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 |
Publications
For publications that are currently unpublished or in-press, details are shown in italics.
Book (7 outputs)
Year | Citation | Altmetrics | Link | ||
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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)
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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)
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2012 |
Hogan JA, Lakey JD, Duration and Bandwidth Limiting: Prolate Functions, Sampling, and Applications, Birkhauser, New York, 258 (2012) [A1]
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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]
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2005 | Hogan JA, Lakey JD, Preface (2005) | ||||
Show 4 more books |
Chapter (15 outputs)
Year | Citation | Altmetrics | Link | |||||
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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]
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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Show 12 more chapters |
Journal article (26 outputs)
Year | Citation | Altmetrics | Link | ||||||||
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2018 |
Hogan JA, Lakey JD, 'An Analogue of Slepian Vectors on Boolean Hypercubes', Journal of Fourier Analysis and Applications, (2018) © 2018, Springer Science+Business Media, LLC, part of Springer Nature. Analogues of Slepian vectors are defined for finite-dimensional Boolean hypercubes. These vectors are the mo... [more] © 2018, Springer Science+Business Media, LLC, part of Springer Nature. Analogues of Slepian vectors are defined for finite-dimensional Boolean hypercubes. These vectors are the most concentrated in neighborhoods of the origin among bandlimited vectors. Spaces of bandlimited vectors are defined as spans of eigenvectors of the Laplacian of the hypercube graph with lowest eigenvalues. A difference operator that almost commutes with space and band limiting is used to initialize computation of the Slepian vectors.
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2017 |
Hogan JA, Massopust P, 'Quaternionic B-splines', Journal of Approximation Theory, 224 43-65 (2017) [C1]
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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]
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2017 |
Hogan JA, Lakey JD, 'On the Numerical Evaluation of Bandpass Prolates II', JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 23 125-140 (2017) [C1]
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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. |
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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.
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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]
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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]
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2013 |
Craddock MJ, Hogan JA, 'The Fractional Clifford-Fourier Kernel', JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 19 683-711 (2013) [C1]
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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.
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2012 |
Hogan JA, Morris AJ, 'Quaternionic wavelets', Numerical Functional Analysis and Optimization, 33 1031-1062 (2012) [C1]
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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]
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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]
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2009 |
Hogan JA, Lakey J, 'Non-translation-invariance and the synchronization problem in wavelet sampling', Acta Applicandae Mathematicae, 107 373-398 (2009) [C1]
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2006 |
Hogan JA, Lakey JD, 'Hardy's theorem and rotations', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 134 1459-1466 (2006) [C1]
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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]
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2005 |
Gilbert JE, Hogan JA, Lakey JD, 'BMO, boundedness of affine operators, and frames', APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 18 3-24 (2005) [C1]
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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)
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Show 23 more journal articles |
Conference (13 outputs)
Year | Citation | Altmetrics | Link | |||||
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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]
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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.
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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] | |||||||
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)
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Show 10 more conferences |
Grants and Funding
Summary
Number of grants | 5 |
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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
Funding body: Bayerische Forschunsallianz
Funding body | Bayerische Forschunsallianz |
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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) |
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Project Team | Laureate Professor Jon Borwein, Associate Professor 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 |
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Project Team | Associate Professor 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 |
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Project Team | Associate Professor 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 |
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Project Team | Associate Professor Jeffrey Hogan |
Scheme | New Staff Grant |
Role | Lead |
Funding Start | 2010 |
Funding Finish | 2010 |
GNo | G1000074 |
Type Of Funding | Internal |
Category | INTE |
UON | Y |
Research Supervision
Number of supervisions
Current Supervision
Commenced | Level of Study | Research Title | Program | Supervisor Type |
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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 |
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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 |
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
- construct bandpass prolates whose spectra are supported on a union of intervals on the line.
- construct prolate functions on graphs.
- 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 |
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PhD Faculty of Science |
Higher-dimensional Prolate Spheroidal Wave Functions |
Collaborators
Name | Organisation |
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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:
- Wavelets on the line with improved properties (near-cardinality, near-symmetry, etc).
- 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) |
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Project Team | Laureate Professor Jon Borwein, Associate Professor Jeffrey Hogan, Associate Professor Russell Luke, Associate Professor Brailey Sims |
Scheme | Discovery Projects |
Students
Program | Research Title |
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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 |
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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 |
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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 | |
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United States | 38 | |
Australia | 34 | |
Canada | 1 | |
Germany | 1 |
News
ARC Discovery Projects funding success
November 4, 2015
Associate Professor Jeffrey Hogan
Position
Associate Professor
School of Mathematical and Physical Sciences
Faculty of Science
Focus area
Mathematics
Contact Details
jeff.hogan@newcastle.edu.au | |
Phone | (02) 4921 7235 |
Fax | (02) 4921 6898 |
Office
Room | SR243 |
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Building | Mathematics Building |
Location | Callaghan University Drive Callaghan, NSW 2308 Australia |