Brad Osgood
Professor of Electrical Engineering and, by courtesy, in Education
Bio
Osgood is a mathematician by training and applies techniques from analysis and geometry to various engineering problems. He is interested in problems in imaging, pattern recognition, and signal processing.
Academic Appointments
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Professor, Electrical Engineering
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Professor (By courtesy), Graduate School of Education
Program Affiliations
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Science, Technology and Society
Professional Education
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PhD, Michigan (1980)
Research Interests
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Math Education
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Technology and Education
2024-25 Courses
- Introduction to Matrix Methods
ENGR 108 (Win) - The Fourier Transform and Its Applications
EE 261 (Aut) -
Independent Studies (18)
- Curricular Practical Training for Electrical Engineers
EE 290A (Aut, Win, Spr, Sum) - Curricular Practical Training for Electrical Engineers
EE 290B (Aut, Win, Spr, Sum) - Curricular Practical Training for Electrical Engineers
EE 290C (Aut, Win, Spr, Sum) - Curricular Practical Training for Electrical Engineers
EE 290D (Aut, Win, Spr, Sum) - Curricular Practical Training for Electrical Engineers
EE 290E (Aut, Win, Spr, Sum) - Curricular Practical Training for Electrical Engineers
EE 290F (Aut, Win, Spr, Sum) - Curricular Practical Training for Electrical Engineers
EE 290G (Aut, Win, Spr, Sum) - Curricular Practical Training for Electrical Engineers
EE 290H (Aut, Sum) - Electrical Engineering Instruction
EE 195 (Aut, Win, Spr) - Master's Research
CME 291 (Aut, Win, Spr, Sum) - Master's Thesis and Thesis Research
EE 300 (Aut, Win, Spr, Sum) - Special Studies and Reports in Electrical Engineering
EE 191 (Aut, Win, Spr, Sum) - Special Studies and Reports in Electrical Engineering
EE 391 (Aut, Win, Spr, Sum) - Special Studies and Reports in Electrical Engineering (WIM)
EE 191W (Aut, Win, Spr, Sum) - Special Studies in Engineering
ENGR 299 (Aut, Win, Spr, Sum) - Special Studies or Projects in Electrical Engineering
EE 190 (Aut, Win, Spr, Sum) - Special Studies or Projects in Electrical Engineering
EE 390 (Aut, Win, Spr, Sum) - Writing of Original Research for Engineers
ENGR 199W (Aut, Win, Spr, Sum)
- Curricular Practical Training for Electrical Engineers
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Prior Year Courses
2022-23 Courses
- Introduction to Matrix Methods
ENGR 108 (Win) - The Fourier Transform and Its Applications
EE 261 (Aut)
2021-22 Courses
- Introduction to Matrix Methods
ENGR 108 (Win) - The Fourier Transform and Its Applications
EE 261 (Aut)
- Introduction to Matrix Methods
Stanford Advisees
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Doctoral Dissertation Reader (AC)
Ethan Liang, Aya Mouallem, Giray Ogut -
Doctoral Dissertation Advisor (AC)
Chien-yi Chang -
Master's Program Advisor
Justin Chang -
Doctoral (Program)
Sreela Kodali, Parth Nobel, Marina Qian, Sarah Zou
All Publications
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Fast DFT Computation for Signals With Structured Support
IEEE TRANSACTIONS ON INFORMATION THEORY
2024; 70 (2): 1498-1524
View details for DOI 10.1109/TIT.2023.3329804
View details for Web of Science ID 001166812100025
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Best Möbius Approximations of Convex and Concave Mappings
COMPUTATIONAL METHODS AND FUNCTION THEORY
2023
View details for DOI 10.1007/s40315-023-00517-0
View details for Web of Science ID 001122792300001
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On convolution, convex, and starlike mappings
STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA
2022; 67 (2): 431-440
View details for DOI 10.24193/subbmath.2022.2.17
View details for Web of Science ID 000810067300018
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Computing the Discrete Fourier Transform of signals with spectral frequency support
IEEE. 2021: 2381-2386
View details for DOI 10.1109/ISIT45174.2021.9518104
View details for Web of Science ID 000701502202080
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Convolution Idempotents With a Given Zero-Set
IEEE TRANSACTIONS ON SIGNAL PROCESSING
2020; 68: 4773–81
View details for DOI 10.1109/TSP.2020.3016137
View details for Web of Science ID 000566329600007
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Some results on convolution idempotents
IEEE. 2020: 1462-1467
View details for Web of Science ID 000714963401091
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Discrete Sampling: A Graph Theoretic Approach to Orthogonal Interpolation
IEEE TRANSACTIONS ON INFORMATION THEORY
2019; 65 (12): 8119–30
View details for DOI 10.1109/TIT.2019.2934688
View details for Web of Science ID 000512370800028
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A NOTE ON CONVEX CONFORMAL MAPPINGS
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
2019; 147 (6): 2655–59
View details for DOI 10.1090/proc/14429
View details for Web of Science ID 000468244300031
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LP relaxations and Fuglede's conjecture
IEEE. 2018: 2525–29
View details for Web of Science ID 000448139300507
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CONCAVE CONFORMAL MAPPINGS AND PRE-VERTICES OF SCHWARZ-CHRISTOFFEL MAPPINGS
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
2012; 140 (10): 3495-3505
View details for Web of Science ID 000309487600017
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Discrete Sampling and Interpolation: Universal Sampling Sets for Discrete Bandlimited Spaces
IEEE TRANSACTIONS ON INFORMATION THEORY
2012; 58 (7): 4176-4200
View details for DOI 10.1109/TIT.2012.2193871
View details for Web of Science ID 000305575000008
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SCHWARZIAN NORMS AND TWO-POINT DISTORTION
PACIFIC JOURNAL OF MATHEMATICS
2011; 254 (1): 101-116
View details for Web of Science ID 000301281400007
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SCHWARZIAN DERIVATIVES OF CONVEX MAPPINGS
ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA
2011; 36 (2): 449-460
View details for DOI 10.5186/aasfm.2011.3628
View details for Web of Science ID 000295069400005
- Schwarzian Norms and two-point distortion Paci c J. Math 2011; 254-1: 101–116
- On a Theorem of Haimo regarding concave mappings Annales Univ. Marie Curie-Sklodowska, Mathematica 2011; 65 (2): 17-28
- Schwarzian derivatives of convex mappings Ann. Acad. Sci. Fenn. 2011; 36: 449–460
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Injectivity Criteria for Holomorphic Curves in C-n
PURE AND APPLIED MATHEMATICS QUARTERLY
2011; 7 (1): 223-251
View details for Web of Science ID 000274659100009
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OSCILLATION OF SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY
2009; 79 (1): 161-169
View details for DOI 10.1017/S0004972708001202
View details for Web of Science ID 000265053300016
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TWO-POINT DISTORTION THEOREMS FOR HARMONIC MAPPINGS
ILLINOIS JOURNAL OF MATHEMATICS
2009; 53 (4): 1061-1075
View details for Web of Science ID 000207877200005
- Falling factorials, generating functions, and conjoint ranking tables Journal of Integer Sequences 2009; 12
- Schwarzian derivatives and uniform local univalence Comp. Methods in Function Theory. 2008; 8 (1): 21–34
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Schwarzian derivative criteria for valence of analytic and harmonic mappings
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY
2007; 143: 473-486
View details for DOI 10.1017/SO305004107000394
View details for Web of Science ID 000251403400017
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Univalence criteria for lifts of harmonic mappings to minimal surfaces
JOURNAL OF GEOMETRIC ANALYSIS
2007; 17 (1): 49-74
View details for Web of Science ID 000245341000004
- A generalization of Nehari's p-criterion for univalence Complex Variables and Elliptic Equations 2007; 52: 225– 233
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Schwarzian derivatives of analytic and harmonic functions
International Conference on Complex and Hormonic Analysis
DESTECH PUBLICATIONS, INC. 2007: 25–33
View details for Web of Science ID 000253414500004
- Applied Calculus John Wiley & Sons, New York. 2006
- Single and Multivariable Calculus John Wiley & Sons, New York. 2005
- Ellipses, near ellipses, and harmonic Möbius transformations 2005
- Calculus John Wiley & Sons, New York. 2005
- Multivariable Calculus John Wiley & Sons, New York. 2005
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Ellipses, near ellipses, and harmonic Mobius transformations
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
2005; 133 (9): 2705-2710
View details for Web of Science ID 000230031500031
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Optimal variable-density K-SPACE sampling in MRI
2nd IEEE International Symposium on Biomedical Imaging
IEEE. 2004: 237–240
View details for Web of Science ID 000227671300060
- Curvature properties of planar harmonic mappings Comp. Methods in Function Theory 2004; 4: 127– 142
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The Schwarzian derivative for harmonic mappings
JOURNAL D ANALYSE MATHEMATIQUE
2003; 91: 329-351
View details for Web of Science ID 000189382800014
- Recent progress on the geometry of univalence criteria Cont. Math. vol. 1999; 240: 75– 87
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The Schwarzian derivative, conformal connections, and Mobius structures
JOURNAL D ANALYSE MATHEMATIQUE
1998; 76: 163-190
View details for Web of Science ID 000079338000007
- Quasiconformal mappings and analysis: A collection of papers honoring F. W. Gehring Papers from the International Symposium held in Ann Arbor, MI, August 1995. edited by Duren, P., Heinonen, J., Osgood, B. Springer-Verlag, New York. 1998
- John domains and a univalence criterion of Ahlfors Results in Mathematics 1998; 33: 203–207
- Coefficients of small univalent functions Results in Mathematics 1998; 33: 79–86
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Old and new on the Schwarzian derivative
International Symposium on Quasiconformal Mappings and Analysis
SPRINGER-VERLAG. 1998: 275–308
View details for Web of Science ID 000071070900014
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Finding complete conformal metrics to extend conformal mappings
INDIANA UNIVERSITY MATHEMATICS JOURNAL
1998; 47 (4): 1273-1291
View details for Web of Science ID 000080328700004
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General univalence criteria in the disk: Extensions and extremal function
ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA
1998; 23 (1): 101-132
View details for Web of Science ID 000072494700006
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Functions with prescribed quasisymmetry quotients
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
1997; 125 (7): 2195-2197
View details for Web of Science ID A1997XK30200042
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Weak Schwarzians, bounded hyperbolic distortion, and smooth quasisymmetric functions
JOURNAL D ANALYSE MATHEMATIQUE
1996; 68: 209-252
View details for Web of Science ID A1996VB89800010
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John domains, quasidisks, and the Nehari class
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK
1996; 471: 77-114
View details for Web of Science ID A1996UA55800004
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AN EXTENSION OF A THEOREM OF GEHRING AND POMMERENKE
ISRAEL JOURNAL OF MATHEMATICS
1995; 91 (1-3): 393-407
View details for Web of Science ID A1995RW43300022
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AHLFORS-WEILL EXTENSIONS OF CONFORMAL-MAPPINGS AND CRITICAL-POINTS OF THE POINCARE METRIC
COMMENTARII MATHEMATICI HELVETICI
1994; 69 (4): 659-668
View details for Web of Science ID A1994PX78300008
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SHARP DISTORTION-THEOREMS ASSOCIATED WITH THE SCHWARZIAN DERIVATIVE
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
1993; 48: 289-298
View details for Web of Science ID A1993MG28800008
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THE SCHWARZIAN DERIVATIVE AND CONFORMAL MAPPING OF RIEMANNIAN-MANIFOLDS
DUKE MATHEMATICAL JOURNAL
1992; 67 (1): 57-99
View details for Web of Science ID A1992JF98400004
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THE SCHWARZIAN DERIVATIVE AND CONFORMALLY NATURAL QUASI-CONFORMAL EXTENSIONS FROM ONE-DIMENSION TO 2-DIMENSION TO 3-DIMENSIONS
MATHEMATISCHE ANNALEN
1992; 292 (2): 267-280
View details for Web of Science ID A1992HE21800005
- The Möbius connection in the bundle of conformal 2-jets Idaho State Conf. on Vector Bundles in Complex Di . Geom. 1992
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A GENERALIZATION OF NEHARIS UNIVALENCE CRITERION
COMMENTARII MATHEMATICI HELVETICI
1990; 65 (2): 234-242
View details for Web of Science ID A1990DJ38800004
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MODULI SPACE, HEIGHTS AND ISOSPECTRAL SETS OF PLANE DOMAINS
ANNALS OF MATHEMATICS
1989; 129 (2): 293-362
View details for Web of Science ID A1989T724800004
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EXTREMALS OF DETERMINANTS OF LAPLACIANS
JOURNAL OF FUNCTIONAL ANALYSIS
1988; 80 (1): 148-211
View details for Web of Science ID A1988Q237800011
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COMPACT ISOSPECTRAL SETS OF SURFACES
JOURNAL OF FUNCTIONAL ANALYSIS
1988; 80 (1): 212-234
View details for Web of Science ID A1988Q237800012
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COMPACT ISOSPECTRAL SETS OF PLANE DOMAINS
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
1988; 85 (15): 5359-5361
Abstract
Any isospectral family of two-dimensional Euclidean domains is shown to be compact in the C(infinity) topology. Previously Melrose, using heat invariants, was able to establish the C(infinity) compactness of the curvature of the boundary curves. The additional ingredient used in this paper to obtain the compactness of the domains is the behavior of the determinant of the Laplacian near the boundary of the moduli space.
View details for Web of Science ID A1988P574600004
View details for PubMedID 16593960
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THE SCHWARZIAN DISTANCE BETWEEN DOMAINS - A QUESTION
ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA
1987; 12 (2): 313-318
View details for Web of Science ID A1987P181900015
- The quasihyperbolic metric and associated estimates on the hyperbolic metric Jour. d'Analyse Math. 1986; 47: 37–53
- Hyperbolic curvature and conformal mapping Bull. London Math. Soc. 1986; 18: 272–276
- Some properties of f"/f' and the Poincaré metric Indiana Univ. Math. Jour. 1982; 31: 449–461
- Univalence criteria in multiply connected domains Trans. Amer. Math. Soc. 1980; 260: 459–473