Prof. Dr. Götz Pfander

Götz Pfander
Personal Information

Born August 20th 1970, in Mainz, Germany.

Married to Tijana Janjic Pfander, three children, Mila, born in 2003, Sava, born in 2006, and Teodora, born 2014. 
 

Education

PhD in Mathematics awarded on August 20th, 1999, for thesis titled Periodic waveletgrams and periodicity detection. Advisor John J. Benedetto, University of Maryland at College Park.

Recipient Department of Mathematics Dissertation Fellowship, University of Maryland, spring 1999.

Master of Arts in Mathematics, University of Maryland, College Park, May 22nd, 1998.

Studies of Mathematics at the University of Maryland, College Park, fall 1995 --- summer 1999.

Recipient Freie Universität exchange stipend to spend academic year 95/96 at University of Maryland.

Studies of Mathematics and Psychology (minor subject) at Johannes Gutenberg Universität Mainz, fall 1991 --- summer 1993, and Freie Universität Berlin, fall 1993 --- summer 1995.
 

Previous Professorships

Assistant Professor of Mathematics at Jacobs University Bremen September 2002 - August 2009.

College Master of College III, Jacobs University Bremen, September 2007 - December 2011.

Associate Professor of Mathematics at Jacobs University Bremen since September 2009.

Visiting Professor of Mathematics at Massachusetts Institute of Technology, January 2012 - August 2012.

John von Neumann Visiting Professor at Technical University Munich, January 2014 - June 2014.

Lehrstuhlvertretung Wissenschaftliches Rechnen / Informatik, Katholische Universität Eichstätt, September 2014 - Januar 2015.

Associate Professor of Mathematics at Jacobs University Bremen, continuation, February 2015 - January 2016. 
 

Fellowships and Postdoctoral Appointments

Time--frequency analysis of operators with bandlimited symbol, Max Kade Fellowship to visit University of Maryland January 2004 --- August 2004.

Smart Modem: Advanced xDSL Technology for QoS, investigator. Principal investigator Kurt Jetter, project financed jointly by the German Federal Ministry of Education and Research and Siemens AG, Universität Hohenheim, September 1999 --- August 2002.

Health monitoring systems for jet engines, investigator. Principal investigator John J. Benedetto, project was based on my PhD thesis research and funded by the Maryland Industrial Partnership / NASA, 1999--2001. Received funding during the summer 1999.

Signal and Image processing based on the uncertainty principle, irregular sampling and finite fields, investigator. Principal investigator John J. Benedetto, funded by the US Air Force Office of Scientific Research, 1996 --- 1999. Received funding during the summer 1998.

Employment as Teaching Assistant at Freie Universität Berlin, October 1994 --- July 1995, and at University of Maryland, September 1995 --- December 1998. 

Research

Underlying principles

One of the traditional goals in numerical harmonic and functional analysis, is the development of efficient methods to assemble (synthesize) or decompose (analyse) functions or operators into well-understood basic building blocks. Analysis relies on the understanding of appropriately chosen basic components and on determining the weight of each component in a given signal. For example, a picture can be decomposed into patches of red, green, and blue of varying intensities. The dual operation is signal synthesis. Using the same building blocks as in the analysis step, we can assemble or reassemble signals and transformations of our liking. Returning to our example, we could, starting from scratch, draw a picture by choosing patches of red, green, and blue and intensities freely.


In digital communications, synthesis and analysis are applied in succession. To transmit digital data through a medium, an analog signal is formed using a synthesis step. Here, the digital information is embedded in the weights. The receiver then performs an analysis of the obtained signal to extract the weights and with it the digital data. The principal objective is to design building blocks that are robust against disturbances present in transmission channels.

Within the past decade, mathematical contributions to these objectives had an tremendous impact on signal processing and communications engineering: wavelet bases were designed to analyze images (jpeg2000), and Gabor systems are currently used to transmit data through wired or wireless channels (OFDM). A wavelet basis consists of functions, which are all equal in shape but which are translated (shifted in time or space) or stretched copies of each other. The building blocks in Gabor theory on the other hand are functions, which are modulated (frequency-shifted) and translated (shifted in time or space) copies of each other.
In recent years, our research within the framework described above focused on time--frequency analysis of operators and Gabor analysis, and their applications in communications engineering. (For educational material, visit the website of the Summer Academy of the Jacobs University Bremen: Progress in Mathematics for Communication Systems.)

A sampling theory for operators and channel measurements
[Translate to Englisch:] A sampling theory for operators and channel measurements

The so-called classical sampling theorem states that a bandlimited function can be recovered from its samples as long as a sufficiently dense sampling grid is used. In the recently developed sampling theory for operators, bandlimited functions are replaced by pseudodifferential operators that have band-limited Kohn--Nirenberg symbols. We showed, for example, that if the bandlimitation is described by a bounded Jordan domain of measure less than one, then the operator can be recovered through its action on a distribution defined on an appropriately chosen sampling grid. Further, an operator band-limited to a Jordan domain of measure larger than one cannot be recovered through its action on any tempered distribution whatsoever, pointing towards a fundamental difference to the classical sampling theorem where a large bandwidth can always be compensated through a sufficiently fine sampling grid. The dichotomy depending on the size of the bandlimitation in phase space is a manifestation of Heisenberg's uncertainty principle.

 

Figure: Our operator sampling results apply to all pseudodifferential operators whose Kohn- Nirenberg symbol is bandlimited to a Jordan domain of area less than one (e.g., the grey region). These results extend Shannon's sampling theorem which is equivalent to the identifiability of operators whose Kohn-Nirenberg symbol is bandlimited to a segment of the frequency shift axis (red) and the fact that time-invariant operators can be identified from their action on the impulse. The latter holds since the Kohn-Nirenberg symbols of time-invariant operators are bandlimited to the time shift axis (green).

Collaborators: John Benedetto, Yoon Mi Hong, Werner Kozek, David Walnut, Peter Rashkov
Publications: 13,14,15,16,19,23,25,28,31,32,34 

Sparse time-frequency representations
[Translate to Englisch:] Sparse time-frequency representations

Efficient algorithms aiming at the recovery of signals and operators from a restricted number of measurements must be based on some a-priori , information about the object under investigation. In a large body of recent work, the signal or operator at hand is assumed to have a sparse representation in a given dictionary. A typical example in this realm is the recovery of vectors that are sparse in the Euclidean basis, that is, of vectors which have a limited number of nonzero components at unknown locations. Such a vector is to be determined efficiently by a small number of linear measurements which are given by inner products with appropriately chosen analysis vectors. The difficulty in this body of work lies in the fact that sparsity conditions as those mentioned above are met by collections of linear subspaces of signal or operator spaces, collections whose unions are nonlinear. To circumvent a combinatorial and therefore unfeasible exhaustive search, efficient alternatives such as $\ell_1$-minimization (Basis Pursuit) have been proposed in the sparse representations and compressed sensing literature. In this work, we consider sparse representations in terms of time--frequency shift dictionaries, and investigate recovery conditions similar to the ones for Gaussian, Bernoulli and Fourier measurements.

 

Figure: Empirical verifcation of Basis Pursuit recovery using a Gabor system with random window in the noisy setting (25 dB signal to noise ratio). Contours of the fitted logistic regression model (gray), the 93% success rate contour (dash), and 1/(2 log n) (solid). See publication 13.

Collaborators: Holger Rauhut, Jared Tanner
Publications: 21,25,30 

Pulse design and time-variant communication channel models
[Translate to Englisch:] Pulse design and time-variant communication channel models

Our goal is the mathematical analysis and optimisation of orthogonal frequency division multiplexing (OFDM) schemes in view of transmission stability in time-invariant, but also wireless and other time variant environments. In fact, one of the cornerstones of our work is the analysis of the perturbation stability of different bases when used in wireless communication channels. For example, we derived estimates which relate the worst case distortion of a function to the functions time-frequency concentration and the time variant channel operators spreading support.

 

Further, we continue our work on the modelling of narrowband finite lifelength systems such as wireless radio communications by smooth and compactly supported spreading functions. Our results include the exact implementation of certain classes of so-called underspread operators and the derivation of a fast algorithm for computing the matrix representation of a channel operator with respect to pulseshaped OFDM bases.

Another line of research within this realm considers the analysis and reduction of the crest factor (equivalently, the peak to average ratio of OFDM signals. Figure: Construction of a channel spreading function whose operator causes a large distortion to a function with time-frequency support G.

Collaborators: Niklas Grip, Kurt Jetter, Werner Kozek, Georg Zimmermann
Publications: 4,6,7,9,10,18,22,28 

Gabor frames on the real line
[Translate to Englisch:] Gabor Frames on the real Line

Within Gabor frame theory proper, we have addressed a number of structural questions. In one of our recent results, we point out that Gabor systems generated by a continuous and compactly supported prototype function, and frequency-shift parameters 2, 3, . . . do not form frames. This result was a surprise for us, as it had been generally assumed that any "nice" window g and "reasonable" choice of time- and frequency-shift parameters yield Gabor frames. Our observation demonstrates that even for window functions that are perfectly natural in approximation theory and wavelet theory, the Gabor frame parameters have to be chosen extremely carefully.

 

In our work on Gabor multipliers we proved, in the case of identical analysis and synthesis windows, we proved, that the generating operators for such multipliers are either Riesz bases (exact frames) or not frames for their closed linear spans. The same dichotomy conclusion is valid for general rank one operators under mild and natural conditions.
An additional research interest is the construction of Gabor frames of functions for arbitrary time-frequency lattices or irregular discrete sets in the time-frequency plane. Orthonormal bases have been constructed for arbitrary time-frequency lattices but they consist of characteristic functions which are poorly localized in frequency. Hence, the fundamental problem of constructing Gabor frames or Riesz bases of well behaved functions for arbitrary lattices remains open.
Figure: Illustration of lattice parameters (1/a,1/b) so that the rank one operators that compose a Gabor multiplier with respect to the characteristic function on the unit interval fails (in red) to be Riesz basis in the space of Hilbert-Schmidt operators.

Collaborators: John Benedetto, Karlheinz Groenenig, A.J.E.M. Janssen, Norbert Kaiblinger
Publications: 11,14,28 

Uncertainty principles and time-frequency analysis on finite Abelian groups
[Translate to Englisch:] Uncertainty principles and time-frequency analysis on finite Abelian groups

Uncertainty principles establish restrictions on how well localized the Fourier transform of a well localized function can be and vice versa. In the case of a function defined on a finite Abelian group, localization is generally expressed through the cardinality of the support of the function. A classical result on uncertainty states that the product of the number of nonzero entries in a vector representing a nontrivial function on an Abelian group and the number of nonzero entries in its Fourier transform is not smaller than the order of the group. This result has been improved for any nontrivial Abelian group by Meshulam.

 

In our work, we established corresponding results for joint time-frequency representations, that is, to obtain restrictions on the minimal cardinality of the support of joint time-frequency representations of functions defined on finite Abelian groups. Applications of our results range from sparse matrix identification to the construction of a generic class of Gabor frames which are maximally robust to erasures.

Figure: Illustration of the uncertainty principle for vectors of finite Abelian groups. We display in red those support size pairs achievable by a vector on the group (Z_2)^4 and its Fourier transform. Results are based on numerical experiments.

Collaborators: Jim Lawrence, Felix Krahmer, Peter Rashkov, David Walnut
Publications: 12,20,24,26,27,29,33 

Wavelet periodicity detection
[Translate to Englisch:] Wavelet periodicity detection

The theory of periodic wavelet transforms developed here is motivated by the problem of epileptic seizure prediction based on the analysis of electrical potential time series derived from brain activity of patients before and during an epileptic seizure.

 

A central theorem in the theory is the characterization of wavelets having time and scale periodic wavelet transforms. We showed that such wavelets are precisely generalized Haar wavelets plus a logarithmic term. This theorem could not only be quantified to analyze seizure prediction, but could also provide a technique to address a large class of periodicity detection problems. An essential step in this quantification is the geometric and linear algebra construction of a generalized Haar wavelet associated with a given periodicity. This gives rise to an algorithm for periodicity detection based on the periodicity of wavelet transforms defined by generalized Haar wavelets and implemented by wavelet averaging methods. The algorithm detects periodicities embedded in significant noise.


Collaborators: John Benedetto, Alfredo Nava-Tudela
Publications: 0,1,2,3,5,8

Matlab code: Periodicity detection tools (based on my thesis)
PerMat - Pertubation Matrices
Matlab package to compute with functions defined on the integers

Please contact me if you are interested in using these tools!

Publikations

2019

2018

2017

2016

2015

  • Volltext
    Pfander, Götz E. ; Zheltov, P.:
    Estimation of Overspread Scattering Functions.
    In: IEEE Transactions on Signal Processing. 63 (Mai 2015) 10. - S. 2451-2463.
    ISSN 1053-587X ; 1941-0476
    10.1109/TSP.2015.2403309
    (Peer-Review-Journal)
  • Sampling Theory, a Renaissance - Compressive Sensing and Other Developments.
    Hrsg.: Pfander, Götz E.
    Basel : Birkhäuser, 2015. - 532 S. - (Applied and Numerical Harmonic Analysis)
    ISBN 978-3-319-19748-7
  • Walnut, David ; Pfander, Götz E. ; Kailath, Thomas:
    Cornerstones of Sampling of Operator Theory.
    In: Balan Radu ; Begué Matthew ; Benedetto John J. ; Czaja Wojciech (Hrsg.): Excursions in Harmonic Analysis. - Cham : Birkhäuser, 2015. - S. 291-332. - (Applied and Numerical Harmonic Analysis ; 4)
    ISBN 978-3-319-20188-7 ; 978-3-319-20187-0
    https://doi.org/10.1007/978-3-319-20188-7_12
    (Begutachteter Beitrag / peer-reviewed paper)
  • Pfander, Götz E. ; Walnut, David:
    Regular operators sampling for parallelograms.
    In: Proceedings on the International Conference on Sampling Theory and Applications (SampTA), May 25 - 29, 2015, Washington DC. - Piscataway, New Jersey : IEEE, 2015
    ISBN 978-1-4673-7353-1 ; 1-4673-7353-2 ; 978-1-4673-7353-1
    10.1109/SAMPTA.2015.7148847
    (Begutachteter Beitrag / peer-reviewed paper)
  • Pfander, Götz E. ; Walnut, David:
    Regular operator sampling for parallelograms.
    In: Proceedings on the International Conference on Sampling Theory and Applications (SampTA), May 25 - 29, 2015, Washington DC. - Piscataway, New Jersey : IEEE, 2015. - S. 44-47
    ISBN 978-1-4673-7353-1 ; 1-4673-7353-2 ; 978-1-4673-7353-1
    https://doi.org/10.1109/SAMPTA.2015.7148847
    (Begutachteter Beitrag / peer-reviewed paper)
  • Cabrelli, Carlos ; Molter, Ursula ; Pfander, Götz E.:
    An Amalgam Balian-Low Theorem for symplectic lattices of rational density.
    In: Proceedings on the International Conference on Sampling Theory and Applications (SampTA), May 25 - 29, 2015, Washington DC. - Piscataway, New Jersey : IEEE, 2015. - S. 134-138
    ISBN 978-1-4673-7353-1 ; 1-4673-7353-2 ; 978-1-4673-7353-1
    https://doi.org/10.1109/SAMPTA.2015.7148866
    (Begutachteter Beitrag / peer-reviewed paper)
  • Salanevich, Palina ; Pfander, Götz E.:
    Polarization based phase retrieval for time-frequency structured measurements.
    In: Proceedings on the International Conference on Sampling Theory and Applications (SampTA), May 25 - 29, 2015, Washington DC. - Piscataway, New Jersey : IEEE, 2015. - S. 187-191
    ISBN 978-1-4673-7353-1 ; 1-4673-7353-2 ; 978-1-4673-7353-1
    https://doi.org/10.1109/SAMPTA.2015.7148847
    (Begutachteter Beitrag / peer-reviewed paper)

2014

2013

2012

2011

2010

2009

2008

2007

2006

2005

2003

2002

2001

2000

  • Pfander, Götz E.:
    Generalized Haar wavelets and frames.
    In: Aldroubi, Akram ; Laine, Andrew F. ; Unser, Michael A. (Hrsg.): Proceedings of SPIE, Wavelet Applications in Signal and Image Processing VIII. - Bellingham, USA : SPIE, 2000
    ISBN 978-0819437648
    10.1117/12.408641
    (Begutachteter Beitrag / peer-reviewed paper)
  • Kozek, Werner ; Pfander, Götz E. ; Zimmermann, Georg:
    Perturbation stability of various coherent Riesz families.
    In: Aldroubi, Akram ; Laine, Andrew F. ; Unser, Michael A. (Hrsg.): Proceedings of SPIE, Wavelet Applications in Signal and Image Processing VIII. - Bellingham, USA : SPIE, 2000. - S. 411-419
    ISBN 978-0819437648
    10.1117/12.408627
    (Begutachteter Beitrag / peer-reviewed paper)
  • Kozek, Werner ; Pfander, Götz E. ; Ungermann, Jörn ; Zimmermann, Georg:
    A comparative study of various MCM schemes.
    In: Proceedings of the 5th International OFDM-Workshop 2000, Technische Universität Hamburg-Harburg. - Hamburg, 2000. - 20.1-20.4
    (Begutachteter Beitrag / peer-reviewed paper)

1998

  • Benedetto, John ; Pfander, Götz E.:
    Wavelet periodicity detection algorithms.
    In: Aldroubi, Akram ; Laine, Andrew F. ; Unser, Michael A. (Hrsg.): Proceedings of SPIE, Wavelet Applications in Signal and Image Processing VI. - Bellingham, USA : SPIE, 1998. - S. 48-55
    10.1117/12.328148
    (Begutachteter Beitrag / peer-reviewed paper)

1997

  • Benedetto, John ; Pfander, Götz E.:
    Wavelet detection of periodic behaviour in EEG and ECoG Data.
    In: Sydow, Achim (Hrsg.): Proceedings of the 15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics, Berlin August 1997. - Berlin : Wissenschaft & Technik, 1997. - S. 75-80
    ISBN 978-3896855503
    (Begutachteter Beitrag / peer-reviewed paper)

Publications until 2015

Books

[B·1] Sampling Theory: A Renaissance - Compressive Sensing and Other Developments
Götz E. Pfander (editor), 
to appear in the Birkhäuser book series Applied and Numerical Harmonic Analysis, July 2015.

Preprints

[U·5] Boundedness of multilinear pseudo-differential operators on modulation spaces,
Shahla Molahajloo, Kasso Okoudjou,, Götz E. Pfander,
submitted. 
BibTex

[U·4] Analyzing the algorithm for proving the restricted invertibility theorem,
Peter G. Casazza, Götz E. Pfander, 
submitted. 
BibTex

[U·3] Cornerstones of Sampling of Operator Theory,
David Walnut, Götz E. Pfander, Thomas Kailath
invited paper, Excursions of Harmonic Analysis IV,R. Balan, M. Begue, J.J. Benedetto, W. Czaja, K. Okoudjou, (eds), Birkäuser Basel.
BibTex

[U·2] Sampling and reconstruction of operators,
Götz E. Pfander, David Walnut, 
submitted. 
BibTex

[U·1] On the stability of sparse convolutions,
Philipp Walk, Peter Jung, Götz E. Pfander, 
submitted.

Journal Publications

[J·30] Time-frequency shift invariance and the Amalgam Balian Low Theorem,
Carlos Cabrelli, Ursula Molter, Götz E. Pfander, 
to appear in Applied and Computational Harmonic Analysis.
Preprint link.
BibTex

[J·29] Estimation of overspread scattering functions,
Götz E. Pfander, Pavel Zheltov,
IEEE Transactions on Signal Processing, 63 (10), 2451-2463, 2015.
BibTex

[J·28] Reconstruction of the scattering function of overspread radar targets,
Onur Oktay, Götz E. Pfander, Pavel Zheltov,
IET Signal Processing, 8 (9), 1018-1024, 2014.
Preprint link.
BibTex

[J·27] Local sampling and approximation of operators with bandlimited Kohn-Nirenberg symbol,
Felix Krahmer, Götz E. Pfander, 
Constructive Approximation, 39 (3), 541 - 572, 2014. 
Preprint link.
BibTex

[J·26] Sampling of stochastic operators,
Götz E. Pfander, Pavel Zheltov,
IEEE Transactions on Information Theory, 60 (4), 2359 - 2372, 2014.
Preprint link.
BibTex

[J·25] Identification of stochastic operators,
Götz E. Pfander, Pavel Zheltov,
Applied and Computational Harmonic Analysis, 36 (2), 256 - 279, 2014.
BibTex

[J·24] Remarks on multivariate Gaussian Gabor frames,
Götz E. Pfander, Peter Rashkov,
Monatshefte für Mathematik, 172 (2), 179-187, 2013.
Preprint link.
BibTex

[J·23] A density criterion for operator identification,
Niklas Grip, Götz E. Pfander, Peter Rashkov,
Sampling Theory in Signal and Image Processing, 12 (1), 1-20, 2013.
Preprint link.
BibTex

[J·22] The restricted isometry property for time-frequency structured random matrices,
Götz E. Pfander, Holger Rauhut, Joel Tropp,
Probability Theory and Related Fields, 156, (3-4), 707-737, 2013.
Preprint link.
BibTex

[J·21] Sampling of Operators,
Götz E. Pfander,
Journal of Fourier Analysis and Applications, 19 (3), 612-650, 2013.
Preprint link.
BibTex

[J·20] Boundedness of pseudo-differential operators on L^p, Sobolev, and modulation spaces,
Shahla Molahajloo, Götz E. Pfander,
Mathematical Modelling of Natural Phenomena 8 (1), 175-192, 2013.
Preprint link.
BibTex

[J·19] Infinite dimensional restricted invertibility,
Peter G. Casazza, Götz E. Pfander,
Journal of Functional Analysis 263 (12), 3784-3803, 2012.
Preprint link.
BibTex

[J·18] A geometric construction of tight Gabor frames with multivariate compactly supported smooth windows,
Götz E. Pfander, Peter Rashkov, Yang Wang
Journal of Fourier Analysis and Applications 18(2), 223-239, 2012.
Preprint link.
BibTex

[J·17] Irregular and multi-channel sampling of operators,
Yoon Mi Hong, Götz E. Pfander,
Applied and Computational Harmonic Analysis (ACHA), 29 (2) 214-231, 2010.
Preprint link.
BibTex

[J·16] Sparsity in time-frequency representations,
Götz E. Pfander, Holger Rauhut,
Journal of Fourier Analysis and Applications, 11(6), pp. 715-726, 2010.
Preprint link.
BibTex

[J·15] On the invertibility of rectangular bi-infinite matrices and applications in time-frequency analysis,
Götz E. Pfander,
Linear Algebra and Applications, 429 (1), 331-345, 2008.
Preprint link.
BibTex

[J·14] Identification of matrices having a sparse representation,
Götz E. Pfander, Holger Rauhut, Jared Tanner,
IEEE Transactions on Signal Processing, 56 (11), 5376-5388, 2008.
Preprint link.
BibTex

[J·13] Uncertainty in time--frequency representations on finite Abelian groups,
Felix Krahmer, Götz E. Pfander, Peter Rashkov,
Applied and Computational Harmonic Analysis (ACHA), 25 (2) 209-225, 2008.
Preprint link.
BibTex

[J·12] Measurement of time-varying multiple-input multiple-output channels,
Götz E. Pfander,
Applied and Computational Harmonic Analysis (ACHA), 24 (3) 393-401, 2008.
Preprint link.
BibTex

[J·11] A discrete model for the effcient analysis of time-varying narrowband communication Channels,
Niklas Grip, Götz E. Pfander,
Multidimensional Systems and Signal Processing, 19 (1), pp. 3-40, 2008.
Preprint link.
BibTex

[J·10] Note on sparsity in signal recovery and in matrix identification,
Götz E. Pfander
The Open Applied Mathematics Journal, 1, pp. 21-22, 2007.
BibTex

[J·9] Measurement of time variant linear channels,
Götz E. Pfander, David Walnut,
IEEE Transactions on Information Theory, 52 (11), pp. 4808-4820, 2006.
Preprint link.
BibTex

[J·8] Operator identification and Feichtinger's algebra,
Götz E. Pfander, David Walnut,
Sampling Theory in Signal and Image Processing (STSIP), 5 (2), pp. 183-200, 2006.
Preprint link.
BibTex

[J·7] Frame expansions for Gabor multipliers,
John Benedetto, Götz E. Pfander,
Applied and Computational Harmonic Analysis (ACHA), 20 (1), pp. 26-40, 2006.
Preprint link.
BibTex

[J·6] Identification of operators with bandlimited symbols,
Werner Kozek, Götz E. Pfander,
SIAM Journal of Mathematical Analysis, 37 (3), pp. 867-888, 2006.
Preprint link.
BibTex

[J·5] Linear independence of Gabor systems in finite dimensional vector spaces,
James Lawrence, Götz E. Pfander, David Walnut,
Journal of Fourier Analysis and Applications, 11(6), pp. 715-726, 2005.
Preprint link.
BibTex

[J·4] Note on B-splines, wavelet scaling functions, and Gabor frames,
Karlheinz Gröchenig, Augustus J. E. M. Janssen, Norbert Kaiblinger, Götz E. Pfander,
IEEE Transactions Information Theory, Volume 49, pp. 3318 - 3320, 2003.
Preprint link.
BibTex

[J·3] Perturbation stability of coherent Riesz systems under convolution operators,
Werner Kozek, Götz E. Pfander, Georg Zimmermann,
Applied and Computational Harmonic Analysis, 12 (3), pp. 286-308, 2002.
Preprint link.
BibTex

[J·2] Periodic wavelet transforms and periodicity detection,
John Benedetto, Götz E. Pfander
SIAM Journal on Applied Mathematics, 62 (4), pp. 1329-1368, 2002.
Preprint link.
BibTex

[J·1] The crest factor of trigonometric polynomials. Part 1: Approximation theoretic results,
Kurt Jetter, Götz E. Pfander, Georg Zimmermann,
Revue d'Analyse Numérique et de Théorie de l'Approximation, 30 (2), pp. 179-195, 2001. 
BibTex

Invited Chapters

[C·3] Gabor frames in finite dimensions,
Götz E. Pfander,
Finite Frames: Theory and Applications, Peter G. Casazza and Gitta Kutyniok (editors), Birkhäser Boston, 2013.
Preprint link.
BibTex

[C·2] Efficient Analysis of OFDM Channels,
Niklas Grip, Götz E. Pfander
in OFDM - Concepts for Future Communication Systems, Hermann Rohling (editor), Springer, 2011.
Preprint link.
BibTex

[C·1] Exploring infinity: number sequences in modern art,
Götz E. Pfander, Isabel Wuensche,
Arkhai, 12, pp. 41-66, April 2007.
BibTex

Refereed Conference Proceedings

[P·16] Regular operator sampling for parallelograms,
Götz E. Pfander, David Walnut
Proceedings International Conference on Sampling Theory and Applications, Washington DC, 2015.
Preprint link.
BibTex

[P·15] An Amalgam Balian-Low Theorem for symplectic lattices of rational density,
Carlos Cabrelli, Ursula Molter, Götz E. Pfander,
Proceedings International Conference on Sampling Theory and Applications, Washington DC, 2015.
Preprint link.
BibTex

[P·14] Polarization based phase retrieval for time-frequency structured measurements,
Palina, Salanevich, Götz E. Pfander,
Proceedings International Conference on Sampling Theory and Applications, Washington DC, 2015.
Preprint link.
BibTex

[P·13] Sparse finite Gabor frames for operator sampling,
Götz E. Pfander, David Walnut
Proceedings International Conference on Sampling Theory and Applications, Bremen, 2013.
Preprint link.
BibTex

[P·12] Density criteria in operator identification,
Niklas Grip, Götz E. Pfander, Peter Rashkov,
Proceedings Sampling Theory and Applications, 2.5. - 6.5.2011, Singapore, 2011.

[P·11] Identification and sampling of stochastic operators,
Götz E. Pfander, Pavel Zheltov,
Proceedings Sampling Theory and Applications, 2.5. - 6.5.2011, Singapore, 2011.

[P·10] Linear independence and coherence of Gabor systems in finite dimensional spaces,
Götz E. Pfander,
Proceedings Sampling Theory and Applications, 18.5. - 22.5.2009, Marseille, 2009.

[P·9] Operator identification and sampling,
Götz E. Pfander, David Walnut,
Proceedings Sampling Theory and Applications, 18.5. - 22.5.2009, Marseille, 2009.

[P·8] Irregular and multichannel sampling in operator Paley- Wiener spaces,
Yoon Mi Hong, Götz E. Pfander,
Proceedings Sampling Theory and Applications, 18.5. - 22.5.2009, Marseille, 2009.

[P·7] On the sampling of functions and operators with an application to Multiple--Input Multiple--Output channel identification,
Götz E. Pfander, David F. Walnut
Proceedings SPIE Vol. 6701, Wavelets XII; Dimitri Van De Ville, Vivek K. Goyal, Manos Papadakis, Eds, pp. 67010T-1 - 67010T-14, 2007.
Preprint link.

[P·6] ISI / ICI comparison of DMT and wavelet based MCM schemes for time invariant channels,
Maria Charina, Kurt Jetter, Achim Kehrein, Werner Kozek, Götz E. Pfander, Georg Zimmermann,
in: J.Speidel (ed.), Neue Kommunikationsanwendungen in modernen Netzen ITG-Fachbericht, Vol. 171, VDE-Verlag, Berlin, pp. 109-115, 2002.

[P·5] A comparitive study of various MCM schemes,
W. Kozek, Götz E. Pfander, J. Ungermann and G. Zimmermann,
Proceedings 5th International OFDM-Workshop 2000, Hamburg, Technische Universität Hamburg-Harburg, pp. 20.1-20.4, Hamburg 2000.

[P·4] Generalized Haar wavelets and frames,
Götz E. Pfander,
Proceedings SPIE Vol. 4119, pp. 528-535, Wavelet Applications in Signal and Image Processing VIII; Akram Aldroubi, Andrew F. Laine, Michael A. Unser; Eds, 2000.
Preprint link.

[P·3] Perturbation stability of various coherent Riesz families,
Werner Kozek, Götz E. Pfander, Georg Zimmermann,
Proceedings SPIE Vol. 4119, pp. 411-419, Wavelet Applications in Signal and Image Processing VIII; Akram Aldroubi, Andrew F. Laine, Michael A. Unser; Eds., 2000.
Preprint link.

[P·2] Wavelet periodicity detection algorithms,
John J. Benedetto, Götz E. Pfander
Proceedings of SPIE's 43rd Annual Meeting, San Diego, Vol. 3458, pp. 48-55, 1998.

[P·1] Wavelet detection of periodic behavior in EEG and ECoG Data,
John J. Benedetto, Götz E. Pfander,
Proceedings of the 15th IMACS World Congress, Berlin, Volume 1, pp. 75-80, 1997.

Technical Reports and Miscellaneous

[T·11] SIC-POVMs vs WSSUS: Quantum Information Theory meets Channel Estimation,
Götz E. Pfander, Pavel Zheltov,
Mini-Workshop: Mathematical Physics meets Sparse Recovery, 17-21, 2014.
BibTex

[T·10] The Bourgain Tzafriri restricted invertibility theorem in infinite dimensions,
Peter G. Casazza, Götz E. Pfander,
Operator Algebras and Representation Theory: Frames, Wavelets and Fractals, Oberwolfach Reports 17/2011,
957-960, 2011. 17-21, 2014.
BibTex

[T·9] Identi cation of time-frequency localized operators,
Niklas Grip, Götz E. Pfander, Peter Rashkov,
Technical Report 22, Jacobs University Bremen, 75 pages, 2010.
BibTex

[T·8] Window design for multivariate Gabor frames on lattices,
Götz E. Pfander, Peter Rashkov,
Technical Report 21, Jacobs University Bremen, 46 pages, 2010.
BibTex

[T·7] Applications of the uncertainty principle for finite abelian groups to communications engineering,
Felix Krahmer, Götz E. Pfander, Peter Rashkov,
Proceedings of the Humboldt-Kolleg Modern trends in mathematics and physics, Sept 2008, Varna/Bulgaria, Suppl. to Bulgarian Journal of Physics, 36(2), 54-59, 2009.
BibTex

[T·6] An open question on the existence of Gabor frames in general linear position,
Felix Krahmer, Götz E. Pfander, Peter Rashkov,
Proceedings Dagstuhl Seminar 08492, 30.11. - 05.12.2008, Structured Decompositions and Efficient Algorithms, 2009.
BibTex

[T·5] Support size restrictions on time-frequency representations of functions on finite Abelian groups,
Felix Krahmer, Götz E. Pfander, Peter Rashkov\\ Proceedings of the 79th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), 2008.
BibTex

[T·4] Time varying narrowband communications channels: analysis and implementation,
Niklas Grip, Götz E. Pfander,
Technical Report 12, Jacobs University Bremen, 125 pages, 2007.
BibTex

[T·3] Support size conditions for time-frequency representations on finite Abelian groups,
Felix Krahmer, Götz E. Pfander, Peter Rashkov,
Technical Report 13, Jacobs University Bremen, 42 pages, 2007.
BibTex

[T·2] Signal processing for vibration detection in jet engines,
John Benedetto, Alfredo Nava-Tudela, Götz E. Pfander,
unpublished (2002).
BibTex

[T·1] Periodic waveletgrams and periodicity detection,
Götz E. Pfander,
PhD Thesis, University of Maryland, College Park, August 1999.
BibTex