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Peter Balazs | |
---|---|

Born | Tulln an der Donau, Austria | 11 December 1970

Residence | Tulln an der Donau, Austria |

Nationality | Austrian |

Alma mater | University of Vienna |

Awards | Start-Preis |

Scientific career | |

Fields | Mathematics, Signal processing, Acoustics |

Institutions | Acoustics Research Institute, CNRS, Université catholique de Louvain |

Doctoral advisor | Hans Georg Feichtinger |

**Peter Balazs** (born 11 December 1970 in Tulln an der Donau) is an Austrian mathematician working at the Acoustics Research Institute Vienna of the Austrian Academy of Sciences.

**Tulln an der Donau** is a historic town in the Austrian state of Lower Austria, the administrative seat of Tulln District. Because of its abundance of parks and gardens, Tulln is often referred to as *Blumenstadt*.

The **Acoustics Research Institute** (**ARI**) is a non-university research institution of the Austrian Academy of Sciences in Vienna. It was founded in 1972 as 'Kommission für Schallforschung', became a 'Forschungsstelle' in 1994 and since 2000 has the rank of an institute.

The **Austrian Academy of Sciences** is a legal entity under the special protection of the Republic of Austria. According to the statutes of the Academy its mission is to promote the sciences and humanities in every respect and in every field, particularly in fundamental research.

Peter Balazs studied mathematics and physics at the University of Vienna. In 2001, he graduated with honors in mathematics and an M.Sc. thesis on "Polynomials over Groups" ("Polynome über Gruppen"). He successfully defended his PhD thesis and graduated (with distinction) in June 2005. His PhD thesis is titled, "Regular and Irregular Gabor Multiplier with Application to Psychoacoustic Masking".

**Mathematics** includes the study of such topics as quantity, structure, space, and change.

**Physics** is the natural science that studies matter, its motion, and behavior through space and time, and that studies the related entities of energy and force. Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves.

The **University of Vienna** is a public university located in Vienna, Austria. It was founded by Duke Rudolph IV in 1365 and is the oldest university in the German-speaking world. With its long and rich history, the University of Vienna has developed into one of the largest universities in Europe, and also one of the most renowned, especially in the Humanities. It is associated with 20 Nobel prize winners and has been the academic home to a large number of scholars of historical as well as of academic importance.

Peter Balazs has been part of the Acoustics Research Institute since 1999. His PhD thesis was written at NuHaG^{ [1] } (Numerical Harmonic Analysis Group), Faculty of Mathematics, University of Vienna. The cooperation formed during his thesis also resulted in him becoming a fellow of the HASSIP (Harmonic Analysis and Statistics for Signal and Image Processing) EU network. He joined the LATP (Laboratoire d'Analyse, Topologie, Probabilités), CMI and LMA, CNRS Marseille from November 2003 to April 2004 and in March, May and June 2006. He also worked with the FYMA, UCL, Louvain-La-Neuve in August 2005.

For the project FLAME (Frames and Linear Operators for Acoustical Modeling and Parameter Estimation) Peter Balazs 2011 was honored with the high reputed Start-Preis.^{ [2] }^{ [3] } He is director of the Acoustics Research Institute since 2012.

The **Start-Preis** is the highest Austrian award for young scientists.

Peter Balazs has published 27 journal and 25 conference papers,^{ [4] } a selection of which is presented below (in chronological order):

- 2006 P. Balazs, H.G. Feichtinger, M. Hampejs, G. Kracher; "Double Preconditioning for Gabor Frames”; IEEE Transactions on Signal Processing, Vol. 54, No.12, pp. 4597-4610 (2006)
- 2007 P. Balazs, "Basic Definition and Properties of Bessel Multipliers", Journal of Mathematical Analysis and Applications, Volume 325, Issue 1, pp. 571-585,
- 2007 P. Majdak, P. Balazs, B.Laback, "Multiple Exponential Sweep Method for Fast Measurement of Head Related Transfer Functions", Journal of the Audio Engineering Society, Vol. 55, No. 7/8, pp. 623 - 637
- 2008 P. Balazs, "Matrix Representation of Operators Using Frames", Sampling Theory in Signal and Image Processing, Vol. 7, No. 1, pp. 39-54
- 2010 P. Balazs, B. Laback, G. Eckel, W. Deutsch, "Time-Frequency Sparsity by Removing Perceptually Irrelevant Components Using a Simple Model of Simultaneous Masking", IEEE Transactions on Audio, Speech and Language Processing, Vol. 18 (1), pp. 34-49
- 2010 D. Marelli, P. Balazs, "On Pole-Zero Model Estimation Methods Minimizing a Logarithmic Criterion for Speech Analysis", IEEE Transactions on Audio, Speech and Language Processing, Volume 18 (2), pp. 237 - 248
- 2011 J. P. Antoine, P. Balazs, "Frames and Semi Frames", Journal of Physics A: Mathematical and Theoretical, vol. 44, 205201
- 2012 D. Stoeva, P. Balazs, "Invertibility of Multipliers", Applied and Computational Harmonic Analysis, Vol. 33 (2), pp. 292-299

**Hans Georg Feichtinger** is an Austrian mathematician. He is Professor in the mathematical faculty of the University of Vienna. He is editor-in-chief of the Journal of Fourier Analysis and Applications (JFAA) and associate editor to several other journals. He is one of the founders and head of the Numerical Harmonic Analysis Group (NuHAG) at University of Vienna. Today Feichtinger's main field of research is harmonic analysis with a focus on time-frequency analysis.

- ↑ http://www.univie.ac.at/nuhag-php/home/
- ↑ "Archived copy". Archived from the original on 2011-08-27. Retrieved 2011-06-22.
- ↑ http://science.orf.at/stories/1684300/
- ↑ http://www.balazs.at/wissenen.html

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A **fast Fourier transform** (**FFT**) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). Fourier analysis converts a signal from its original domain to a representation in the frequency domain and vice versa. The DFT is obtained by decomposing a sequence of values into components of different frequencies. This operation is useful in many fields, but computing it directly from the definition is often too slow to be practical. An FFT rapidly computes such transformations by factorizing the DFT matrix into a product of sparse factors. As a result, it manages to reduce the complexity of computing the DFT from
, which arises if one simply applies the definition of DFT, to
, where
is the data size. The difference in speed can be enormous, especially for long data sets where *N* may be in the thousands or millions. In the presence of round-off error, many FFT algorithms are much more accurate than evaluating the DFT definition directly. There are many different FFT algorithms based on a wide range of published theories, from simple complex-number arithmetic to group theory and number theory.

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