Objective:

During the current project of efficiently calculating a resynthesis window and an iterative scheme for a finite element method algorithm for vibrations in soils and liquids, it became apparent that block matrices are a powerful tool to find numerically efficient algorithms.

Method:

In this project, the focus should be the investigation of the numeric features of block matrices. How can this structure be used to calculate or approximate the inverse of a matrix or its norm? How can this be used to speed up iterative schemes?

Application:

The results should be used for the two projects mentioned below:

• double preconditioning for Gabor frames
• vibrations in random layers

Objective:

In signal processing, synthesis is important in addition to analysis. This is especially true for the modification of data. For the Short-Time Fourier Transformation, the synthesis is often done using a simple overlap add (OLA), which is the sum of the outputs of the filter. Also, the output is re-weighted with the analysis window, such as occurs when using the phase vocoder. It is often presumed that with standard windows this will give satisfactory results.

Aside from Gabor frame theory, if the well-known construction of synthesis windows was possible, it would guarantee perfect reconstruction. However, this method is not used often in signal processing algorithms.

Method:

In this project, we will systematically investigate if and for which parameters the respective OLA synthesis with the original window gives good reconstruction. We will compare it to the reconstruction with the dual window, introducing and motivating it as perfect reconstruction overlap add (PROLA). We will show that this method is always preferable to others and that it can be calculated very efficiently.

Application:

This is currently being implemented in STx. There the phase vocoder will have the option to guarantee perfect reconstruction, either with dual or tight windows.

Partners:

• Department of Mathematics, University of Wisconsin-Eau Claire

Objective:

The Short-Time Fourier Transform (STFT), in its sampled version (the Gabor transform), is a well known, valuable tool for displaying the energy distribution of a signal over the time-frequency plane. The equivalence between Gabor analysis and certain filter banks is a well-known fact. The main task is how to find a Gabor analysis-synthesis system with perfect (or depending on the application, satisfactorily accurate) reconstruction in a numerically efficient way. This is done by using the dual Gabor frame, which implies the need to invert the Gabor frame operator.

Method:

This project incorporates an application of the general idea of preconditioning in the context of Gabor frames. While most (iterative) algorithms aim at a relatively costly exact numeric calculation of the inverse Gabor frame matrix, we will use a "cheap method" to find an approximation. The inexpensive method will be based on (double) preconditioning using diagonal and circulant preconditioners. As a result, good approximations of the true dual Gabor atom can be obtained at low computational costs.

Application:

For a number of applications, such as time stretching without changing the frequency content in audio processing or more complex modifications like psychoacoustical masking, the time domain signal needs to be reconstructed using the time-frequency domain coefficients.

Partners:

• H. G. Feichtinger et al., NuHAG, Facultyof Mathematics, University of Vienna

Publications:

• P. Balazs, H.G. Feichtinger, M. Hampejs, G. Kracher; "Double Preconditioning for Gabor Frames?;  IEEE Transactions on Signal Processing, Vol. 54, No.12, December 2006 (2006), preprint

• P. Balazs, H.G. Feichtinger, M. Hampejs, G. Kracher; "Double Preconditioning for the Gabor Frame Operator?; Proceedings ICASSP '06, May 14-19, Toulouse, DVD (2006)

Project Objective:

The project aims to implement an automatic sound recording system that would allow continuous sound recordings for any length of time (several weeks) without user intervention. The long-term investigation of sound data is used for the observation of noise emission from machines in continuous operation and for the documentation of noise situations. The hardware and system complexity are to be restricted to standard measurement microphones and standard PCs or for continuously running, suitable laptops with external disk storage units.

Method:

The recorder contained in the standard S_TOOLS-STx software package is controlled by the macro programming so that the sound files (about the length of one hour) are generated consecutively with date-and-time specification and then written on the hard disk. The intelligent segmentation algorithms insert automatic "tags" and annotations in real-time or in post-processing. The segmentation data are administrated dynamically and enable the direct inclusion of the recorded sound events in the sound data files, signal analytical processes, and statistical processes. Using the currently available storage units, e.g. disk storage on the scale of 1.28 TByte, continuous measuring (2-canal stereo, 44.1. kHz, 16bit) over a period of 2.5 months is possible.

Application:

For the investigation of noise emissions, e.g. traffic and environmental noise, permanent control stations that measure all sound sources in their time context are needed. Only with a broad analysis of the whole situation can noise pollution and health risks be collected.

Ref.:

PACS: 43.50.Rq; Project: NOIDESc: Deskriptoren zur Bewertung von Lärmsignalen (FFG-809085, bmvit-isb2).