Recently Gabor Muiltipliers have been used to implement time-variant filtering as Gabor Filters.  This idea can be further generalized. To investigate the basic properties of such operators the concept of abstract, i.e. unstructured, frames is used. Such multipliers are operators, where a certain fixed mask, a so-called symbol, is applied to the coefficients of frame analysis , whereafter synthesis is done. The properties that can be found for this case can than be used for all kind of frames, for example regular and irregular Gabor frames, wavelet frames or auditory filterbanks.

 

The basic definition of a frame multiplier follows:
 

As special case of such multipliers such operators for irregular Gabor system will be investigated and implemented. This corresponds to a irregular sampled Short-Time-Fourier-Transformation. As application  an STFT correpsonding to the bark scale can be examined.

This mathematical and basic research-oriented project is important for many other projects like time-frequency-masking or system-identification.

Objective:

Numerous implementations and algorithms for time frequency analysis can be found in literature or on the internet. Most of them are either not well documented or no longer maintained. P. Soendergaard started to develop the Linear Time Frequency Toolbox for MATLAB. It is the goal of this project to find typical applications of this toolbox in acoustic applications, as well as incorporate successful, not-yet-implemented algorithms in STx.

Method:

The linear time-frequency toolbox is a small open-source Matlab toolbox with functions for working with Gabor frames for finite sequences. It includes 1D Discrete Gabor Transform (sampled STFT) with inverse. It works with full-length windows and short windows. It computes the canonical dual and canonical tight windows.

Application:

These algorithms are used for acoustic applications, like formants, data compression, or de-noising. These implementations are compared to the ones in STx, and will be implemented in this software package if they improve its performance.

Partners:

• H. G. Feichtinger et al., NuHAG, Faculty of Mathematics, University of Vienna
• B. Torrésani, Groupe de Traitement du Signal, Laboratoire d'Analyse Topologie et Probabilités, LATP/ CMI, Université de Provence, Marseille
• P. Soendergaard, Department of Mathematics, Technical University of Denmark

Introduction:

As is customary for urban varieties, the varieties of Vienna are predominantly social varieties. Education and social background form the primary factors which define the language behaviour of the speakers.

The Viennese dialect belongs to the Middle Bavarian dialect group. Around the turn of the century, a sound change arose which monophthongized the diphthongs /aɛ/ and /ɑɔ/ to /æ:/ and /ɒ:/ repectively. This sound change was accomplished around 1950. As a result of the Viennese monophthongization, the palatal constriction location became overloaded. As early as the thirties, Kranzmayer observed what he called the "e-confusion", i.e., people stopped to discern the /e/-vowels, "Segen" (blessing) and "sehen" (to see) became homophones: [se:ŋ].

Method:

5 female and 5 male speakers of the Viennese dialect were asked to name pictures, to read sentences, and to speak spontaneously.

Results:

As a consequence of the Viennese monophthongization and the consecutive overcrowding of the palatal constriction location, speakers of the Viennese dialect developed two strategies. One group, in the sense Kranzmayer observed, neutralized /e/ and /ɛ/ to /e/. This neutralization made room for the new palatal vowel /æ/.

The other group, however, preserved /e/ and /ɛ/, but sometimes applied the two vowels incorrectly, i.e., produced /ɛ/ instead of /e/ and the other way round. However, since no neutralization took place, the vowel /i/ is shifted to the pre-palatal constriction location. By this shift, room is created on the palatal bar for the new vowel /æ/.

Group I, consequently, discerns the following vowels:

• palatal: /i:, i, e:, e, æ:/
• velar: /u:, u/
• uvular: /o:, o, ɔ:, ɔ/
• pharyngeal: /ɑ:, ɑ, ɒ:/

Group II discerns the vowels as follows:

• pre-palatal: /i:, i/
• palatal: /e:, e, ɛ:, ɛ, æ:/
• velar: /u:, u/
• uvular: /o:, o, ɔ:, ɔ/
• pharyngeal: /ɑ:, ɑ, ɒ:/

Lip rounding and duration is distinctive for each vowel system.