The master's thesis focuses on the study of algorithms dealing with noise separation from musical signal. The first chapter is an introduction into methods which are used for noise removal of the musical signal. Furthermore, this chapter describes theory to the issue, specifically a description of transformations for converting from time to frequency domain, and finally thresholding method of spectral coefficients is explained in detail. The aim of the second chapter is an analysis of the proposed algorithm, which is engaged in testing. From the beginning fast algorithms of gradual transformation are described and then a detailed description of the algorithm as a whole. Later, this chapter deals with the selection of audio recordings and with preparation of these recordings for the actual testing. Finally, testing of audio samples is presented in the third chapter of this thesis. This chapter also concludes comparison of individual transformations, achieved results and review of algorithm.

Aus dem Streubild der Kleinwinkelstreuung kann im Allgemeinen, die die Streuvertei-lung erzeugende Struktur nicht eindeutig rekonstruiert werden. Die Ursache dafür wird erörtert und die damit verbundenen Einschränkungen bei der rechnerischen Auswertung der Streukurven an Beispielen veranschaulicht. Dies geschieht an Streukurven, die mit bekannten Größenverteilungen berechnet wurden. Weiterhin wird untersucht, welche Fit- Ansätze sich zur Auswertung der Kleinwinkelstreuexperimente am besten eignen. Als Fit- Ansätze wurden Reihenentwicklungen nach Trigonometrischen- und Polynomfunkti-onen und eine theoretisch motivierte Funktion verwendet. Neben dem entscheidenden Vergleich mit der Streukurve der Ausgangsfunktion werden die Ergebnisse auch den Rechnungen gegenübergestellt, die mit der weit verbreiteten Glatter- Methode erzielt werden.

We describe an implementation of a multi-threaded NFFT (nonequispaced fast Fourier transform) software library and present the used parallelization approaches. Besides the NFFT kernel, the NFFT on the two-sphere and the fast summation based on NFFT are also parallelized. Thereby, the parallelization is based on OpenMP and the multi-threaded FFTW library. Furthermore, benchmarks for various cases are performed. The results show that an efficiency higher than 0.50 and up to 0.79 can still be achieved at 12 threads.

We present a MPI based software library for computing the fast Fourier transforms on massively parallel, distributed memory architectures. Similar to established transpose FFT algorithms, we propose a parallel FFT framework that is based on a combination of local FFTs, local data permutations and global data transpositions. This framework can be generalized to arbitrary multi-dimensional data and process meshes. All performance relevant building blocks can be implemented with the help of the FFTW software library. Therefore, our library offers great flexibility and portable performance. Likewise FFTW, we are able to compute FFTs of complex data, real data and even- or odd-symmetric real data. All the transforms can be performed completely in place. Furthermore, we propose an algorithm to calculate pruned FFTs more efficiently on distributed memory architectures. For example, we provide performance measurements of FFTs of size 512^3 and 1024^3 up to 262144 cores on a BlueGene/P architecture.

We present an efficient method to compute the electrostatic fields, torques and forces in dipolar systems, which is based on the fast Fourier transform for nonequispaced data (NFFT). We consider 3d-periodic, 2d-periodic, 1d-periodic as well as 0d-periodic (open) boundary conditions. The method is based on the corresponding Ewald formulas, which immediately lead to an efficient algorithm only in the 3d-periodic case. In the other cases we apply the NFFT based fast summation in order to approximate the contributions of the nonperiodic dimensions in Fourier space. This is done by regularizing or periodizing the involved functions, which depend on the distances of the particles regarding the nonperiodic dimensions. The final algorithm enables a unified treatment of all types of periodic boundary conditions, for which only the precomputation step has to be adjusted.

The computation of the Coulomb potentials and forces in charged particle systems under 3d-periodic boundary conditions is possible in an efficient way by utilizing the Ewald summation formulas and applying the fast Fourier transform (FFT). In this paper we consider the particle-particle NFFT (P2NFFT) approach, which is based on the fast Fourier transform for nonequispaced data (NFFT) and compare the error behaviors regarding different window functions, which are used in order to approximate the given continuous charge distribution by a mesh based charge density. While typically B-splines are applied in the scope of particle mesh methods, we consider for the first time also an approximation by Bessel functions. We show how the resulting root mean square errors in the forces can be predicted precisely and efficiently. The results show that if the parameters are tuned appropriately the Bessel window function can keep up with the B-spline window and is in many cases even the better choice with respect to computational costs.

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Die ständig steigende Rechenleistung von PCs und Workstations ermöglicht es, die spektralen Varianzen direkt durch Fouriertransformation einer Zeitreihe zu schätzen. Dabei ist ein geeignetes Fenster auszuwählen. Die Nichtbeachtung dieser Tatsache führt zwangsläufig zum Rechteckfenster und zum Verschmieren der Information über den ganzen Spektralbereich. Von den hier untersuchten Fenstern hat das Hanning-Fenster die besten Eigenschaften mit dem stärksten Abfall im benachbarten Frequenzbereich. Analog der Fensterung von Auto- und Kreuzkorrelationsfunktion im Frequenzraum wird das Hanning-Fenster für die Fouriertransformation einer Meßreihe im Frequenzraum angegeben. / Due to the permanent grow in PC and workstation power it is possible to estimate the spectral variances directly by the Fourier transform of a time series. Thereby one has to choose an appropriate data window. Ignoring this leads to an unsuited square window function where the spectral power in one frequency bin contains leakage from frequency components that are bins away. From the window functions we tested here, the Hanning window has best properties with minimum leakage. Analogous to windowing of the auto- and crosscorrelation function in the frequency domain we give also the Hanning window for the Fourier transform of time series in the frequency domain.