Completed

  • TIFMOFUS: Time-Frequency Methods for Operators and Function Spaces

    Multilateral Scientific and Technological Cooperation in the Danube Region 2017-2018
    Austria, Czech Republic, Republic of Serbia, and Slovak Republic
    Project duration: 01.01.2017 - 31.12.2018

    Project website: nuhag.eu/tifmofus

  • Time Frequency Virtual Acoustics (TF-VA)

    Objectives:

    In the context of binaural virtual acoustics, a sound source is positioned in a free-field 3-D space around the listener by filtering it via head-related transfer functions (HRTFs). In a real-time application, numerous HRTFs need to be processed. The long impulse responses of the HRTFs require a high computational power, which is difficult to directly implement on current processors in situations involving more than a few simultaneous sources.

    Technically speaking, an HRTF is a linear time-invariant (LTI) system. An LTI system can be implemented in the time domain by direct convolution or recursive filtering. This approach is computationally inefficient. A computationally efficient approach consists of implementing the system in the frequency domain; however, this approach is not suitable for real-time applications since a very large delay is introduced. A compromise solution of both approaches is provided by a family of segmented-FFT methods, which permits a trade-off between latency and computational complexity. As an alternative, the sub-band method can be applied as a technique to represent linear systems in the time-frequency domain. Recent work has showed that the sub-band method offers an even better tradeoff between latency and computational complexity than segmented-FFT methods. However, the sub-band analysis is still mathematically challenging and its optimum configuration is dependant on the application under consideration.

    Methods:

    TF-VA involves developing and investigating new techniques for configuring the sub-band method by using advanced optimization methods in a functional analysis context. As a result, an optimization technique that minimizes the computational complexity of the sub-band method will be obtained.

    Two approaches will be considered: The first approach designs the time-frequency transform for minimizing the complexity of each HRTF. In the second approach, we will design a unique time-frequency transform, which will be used for a joint implementation of all HRTFs of a listener. This will permit an efficient implementation of interpolation techniques while moving sources spatially in real-time. The results will be evaluated in subjective localization experiments and in terms of localization models.

    Status:

    • Main participator: Damian Marelli (University of Newcastle, Australia)
    • Co-applicants: Peter Balazs, Piotr Majdak
    • Project begin: November 2011
    • Funding: Lise-Meitner-Programm of the Austrian Science Fund (FWF) [M 1230-N13]
  • Vowel Systems in Comparison

    Objective:

    This project describes vowel systems of several languages acoustically and compares them. The project's main interest is focused on languages with acoustically insufficient descriptions thus far, e.g. Albanian, Romanian, Ful, Mandinka, or Crioulo.

    Method:

    Selected speakers are asked to perform a reading task and to speak spontaneously. Vowels in all positions are segmented, labeled, and analyzed. Formant frequencies (F1, F2, F3) are extracted and the vowel systems are defined.

    Language specificity affects not only the number of vowels and their features, but also the extent of variability and stability of certain vowels. A given vowel of language A might be quite stable, whereas the same vowel might exert high variability in language B. In the same way, vowels might be discerned differently. For example, pre-palatal /i/ and mid-palatal /e/ are discerned by F3 in Standard Austrian German (see diagram on SAG), whereas both mid-palatal /i/ and /e/ are predominantly discerned by F2 in Modern Standard Albanian (see diagram on MSA).

    Application:

    In forensic speaker identification, thorough descriptions of the languages in question are often needed in order to conduct a thorough comparison.

  • Vowel Tensity in Standard Austrian and Standard German

    FWF DACH I 536-G20: 2011-2013
    Cooperation with the Institute of Phonetics and Speech Processing, LMU Munich.

    Project leader (Austria): Sylvia Moosmüller
    Project leader (Germany): Jonathan Harrington

    Objective:

    Across languages, the distinction between so-called tense and lax vowels, e.g., Miete - Mitte ("rent" - "center") or Höhle - Hölle ("cave" - "hell"), is encountered in many languages. However, many different articulatory adjustments might cause this distinction, and these are language-specific.

    In the current project, we address this issue by analysing high tense and lax vowel pairs of the type bieten - bitten ("to offer" - "to request"), Hüte - Hütte ("hats" - "hut"), and Buße - Busse ("penance" - "busses") in two related language varieties: Standard Austrian German (SAG) and Standard German German (SGG). Previous studies suggest that high lax vowel pairs like bitten, Hütte, or Busse tend to approximate their respective tense cognates bieten, Hüte, and Buße.

    The research questions were investigated by a) comparing the tense and lax vowel pairs in SAG and SGG, b) by investigating whether high lax vowel pairs approximate their tense cognates in SAG, c) by investigating whether the high vowel pairs in SAG are distinguished by quality, by quantity, or by quantity relations with the following consonant, and d) by investigating whether an ongoing sound change can be observed in SAG, with young SAG speakers exhibiting a higher degree to merge the vowels than old SAG speakers.

    Main Results:

    SGG speakers clearly distinguish the high vowel pairs by quality, whereas speaker-specific strategies can be observed in SAG, with some speakers distinguishing high tense and lay vowel pairs by quality, others merging the quality contrast, but restricting the merger to velar contexts only, and still others merging high tense and lax vowels alltogether. In case of distinction, the differences between high tense and high lax vowels are less pronounced in SAG than in SGG and still less pronounced in the speech of young SAG speakers as compared to old SAG speakers. The same result was observed for quantity distinctions: All speakers differentiate the high vowel pairs by quantity, meaning that the tense vowels of the type bieten, Hüte, and Buße are longer than their respective lax cognates. Again, the differences are most pronounced in SGG and least pronounced in the speech of the young SAG speakers, meaning that the tense vowels of the type bieten, Hüte, and Buße are truncated in the speech of young SAG speakers as compared to old SAG speakers and SGG speakers. Results on the quantity interactions of vowel + consonant sequences prove quantifying aspects in SAG. Again, some age-specific differences emerged insofar as overall, young SAG speakers have shorter durations than old SAG speakers. However, they maintain the timing relations observed for the old SAG speakers. Results on perception strongly suggest that SAG speakers make use of quantity cues in order to distinguish the vowel pairs, whereas SGG speakers rather rely on cues connected with quality. Generally, it can be concluded that quantity distinctions are more relevant in SAG than in SGG.

    Project Related Publications:

    Harrington, Jonathan, Hoole, Philip, & Reubold, Ulrich.(2012). A physiological analysis of high front, tense-lax vowel pairs in Standard Austrian and Standard German.Italian Journal of Linguistics, 24, 158-183.

    Brandstätter, Julia & Moosmüller, Sylvia. (in print).Neutralisierung der hohen Vokale in der Wiener Standardsprache – A sound change in progress? In M. Glauninger & A. Lenz (Eds.), Standarddeutsch in Österreich – Theoretische und empirische Ansätze.Vienna: Vandenhoeck & Ruprecht.

    Brandstätter, Julia, Kaseß, Christian H., & Moosmüller, Sylvia (accepted). Quality and quantity in high vowels in Standard Austrian German. In: A. Leemann, M-J. Kolly & V. Dellwo (Eds.), Trends in phonetics and phonology in German-speaking Europe. Zurich: Peter Lang.

    Cunha, Conceição, Harrington, Jonathan, Moosmüller, Sylvia, & Brandstätter, Julia (accepted). The influence of consonantal context on the tense-lax contrast in two standard varieties of German. In: A. Leemann, M-J. Kolly & V. Dellwo (Eds.), Trends in phonetics and phonology in German-speaking Europe.Zurich: Peter Lang.

    Moosmüller, Sylvia. (in print). Methodisches zur Bestimmung der Standardaussprache in Österreich. In: M. Glauninger & A. Lenz (Eds.), Standarddeutsch in Österreich – Theoretische und empirische Ansätze. Vienna: Vandenhoeck & Ruprecht (=Wiener Arbeiten zur Linguistik).

    Moosmüller, Sylvia & Brandstätter, Julia.(in print). Phonotactic Information in the temporal organisation of Standard Austrian German and the Viennese Dialect. Language Sciences.

  • Wavelet Approaches in the Fast Multipole Method

    Objective:

    Beside the Fast Multipole Method wavelet based approaches are of increasing interest for the fast calculation of large matrices.

    Method:

    The first part of the project is the implementation of the wavelet method for the compression of the data. Next step is the investigation whether wavelet and FMM approaches can be used together and whether an additional speed up is possible.

    Application:

    The aim of the project is the development of an algorithm that allows for a fast calculation of large matrices. The final aim is the possibilities to handle large acoustic problems numerically.

  • WaveletMulAc: Analytical and Numerical Properties of Wavelet Multipliers

    Objective:

    Gabor multipliers are an efficient time-variant filtering tool used implicitly in many engineering applications in signal processing. For these operators, the result of a Gabor transform (the sampled version of the Short Time Fourier Transform) is multiplied by a fixed function (the time-frequency mask or symbol). The result is then synthesized.

    Transforms other than the Gabor transform, particularly the wavelet transform, are more suitable for certain applications. The concept of multipliers can easily be extended in this case. This results in the introduction of operators called wavelet multipliers, which will be investigated in detail in this project. The project aims to precisely define wavelet multipliers' mathematical properties and optimize their use in applications.

    Method:

    The problem will be approached using modern wavelet theory, harmonic analysis tools, and numeric tools. Formulation and demonstration of analytic statements will be conducted jointly with systematic numeric experiments in order to study the properties of wavelet multipliers.

    The following topics will be investigated in the project:

    • Eigenvalues and eigenvectors of wavelet multipliers
    • Invertibility and injectivity of wavelet multipliers
    • Reproducing kernel invariance
    • Discretization and implementation of wavelet multiplier
    • Best approximation of operators by wavelet multipliers and identification of wavelet multipliers

    Application:

    The applications of wavelet multipliers in signal processing are numerous and include any application requiring time-variant filtering. Some applications of wavelet multipliers will be investigated further in the parallel projects:

    • Mathematical Modeling of Auditory Time-Frequency Masking Functions
    • Improvement of Head-Related Transfer Function Measurements
    • Advanced Method of Sound Absorption Measurements

    Publications:

    • Anaïk Olivero: "Expérimentation des multiplicateurs temps-échelle" (On the time-scale multipliers) Master thesis under the supervision of R. Kronland-Martinet and B. Torrésani, June 2008
  • WavletMul: Wavelet Multipliers and their Application to Reflection Measurements

    Objective:

    Time-variant filters are gaining more importance in today's signal processing applications. Also, there wavelet analysis has numerous applications. The goal of this project is to investigate time-variant systems based on wavelet analysis.

    Method:

    The concept of multipliers can be easily extended to wavelet frames. This means the coefficients of a wavelet analysis are multiplied by a fixed symbol and then resynthesized. The influence of the special structures of these sequences on the resulting operators will be investigated.

    The theory of Pseudo-Differential Operators (PDO) can be translated to the wavelet case. How operators of interest in the investigation of multipliers, like the Kohn-Nirenberg correspondence, are translated to this case is of particular interest. Natural starting points for the research are:

    Use dilations in the definition of the spreading function instead of modulation.

    Define a special wavelet kernel function by using a weak formulation:

    < K f , g > = < k , Wg f >

    Application:

    A very useful application for this project is an analysis-modification-synthesis system based on the wavelet analysis. With some language manipulation, this could be called a "Wavelet Phase Vocoder".

    The application investigated in this project is the measurement of reflection coefficients. The wavelet analysis is preferable for signals containing transient parts. It is essential to separate the impulse responses of different reflections in order to calculate the absorption coefficient of a sound-proof wall. The impulse responses can be easily separated in a scalogram, and they can be extracted by using a wavelet multiplier.

    Project-completion:

    This project ended on 28.02.2008 and is incorporated into the 'High Potential'-Project of the WWTF, MULAC.

  • Weighted and Controlled Frames

    Objective:

    Weighted and controlled frames were introduced to speed up the inversion algorithm for the frame matrix of a wavelet frame. In this project, these kinds of frames are investigated further.

    Method:

    The frame multiplier concept is closely linked to the weighted frames concept. The frame operator of the weighted frame is simply a frame multiplier of the original frame. This project aims to explore this synergy. Finding an efficient way to invert the frame operator by applying weights to a given frame would be especially interesting. Weights are searched, for which the frame bounds are as "tight" as possible, meaning the spectrum is more concentrated. The first numerical experiments to find optimal weights have been conducted.

    Application:

    Weighted frames have already been applied to wavelets on the sphere. Also, the original work by Duffin and Schaefer dealt with the problem of finding such weights for a sequence of exponentials.

    Partners:

    • J. P. Antoine, Unité de physique théorique et de physique mathématique – FYMA