ARI guest talk by Neil Kristofer Dizon - University of Newcastle

24. July 2019

14.30

Seminar Room, Wohllebengasse 12-14 / Ground Floor

### Abstract

The multiresolution analysis (MRA) is a theoretically systematic way of constructing orthonormal wavelet bases for ${L}^{2}\left({ℝ}^{n},ℂ\right)$. Relying heavily on complex analysis, Daubechies used the MRA to derive a special class of compactly supported smooth orthogonal wavelets on the line. Alternatively, Franklin, Hogan, and Tam developed techniques which have been successful in reproducing the Daubechies' wavelets using optimization and projection methods, effectively bypassing the role of complex analysis. The same techniques have been applied to produce nonseparable examples of compactly supported smooth orthogonal wavelets on the plane.

In this talk, we discuss the extensions of these constructions to allow for the optimization of wavelets' cardinality and symmetry. Additionally, we present an alternative approach to achieve cardinality and symmetry on the line by solving an optimization problem arising from a quadrature mirror filter construction using the Zak transform. Finally, we discuss the possibility of extending these techniques to construct quaternionic wavelets.

(Abstract_pdf)

## Upcoming Events

#### HSCR19

The 3rd International Workshop on the
History of Speech Communication Research

13. - 14. September 2019

Vienna, Austria

#### Improving speech technology with the open source VOiCES dataset

ARI guest talk by Michael R. Lomnitz

19. September 2019

14.30

Seminar Room, Wohllebengasse 12-14 / Ground Floor

#### SSW10

The 10th ISCA Speech Synthesis Workshop

20. - 22. September 2019

Vienna, Austria

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