In this paper we study the error behavior of the well known fast Fourier transform for nonequispaced data (NFFT) with respect to the L2-norm. We compare the arising errors for different window functions and show that the accuracy of the algorithm can be significantly improved by modifying the shape of the window function. Based on the considered error estimates for different window functions we are able to state an easy and efficient method to tune the involved parameters automatically. The numerical examples show that the optimal parameters depend on the given Fourier coefficients, which are assumed not to be of a random structure or roughly of the same magnitude but rather subject to a certain decrease.

Invariant object recognition is maybe the most basic and fundamental property of our visual system. It is the basis of many other cognitive tasks, like motor actions and social interactions. Hence, the theoretical understanding and modeling of invariant object recognition is one of the central problems in computational neuroscience. Indeed, object recognition consists of two different tasks: classification and identification. The focus of this thesis is on object identification under the basic geometrical transformations shift, scaling, and rotation. The visual system can perform shift, size, and rotation invariant object identification. This thesis consists of two parts. In the first part, we present and investigate the VisNet model proposed by Rolls. The generalization problems of VisNet triggered our development of a new neural network model for invariant object identification. Starting point for an improved generalization behavior is the search for an operation that extracts images features that are invariant under shifts, rotations, and scalings. Extracting invariant features guarantees that an object seen once in a specific pose can be identified in any pose. We present and investigate our model in the second part of this thesis.

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.

Master of Science / Department of Civil Engineering / Hani G. Melhem / The objective of this research is to use structure ambient random vibration response to detect damage level and location. The use of ambient vibration is advantageous because excitation is caused by service conditions such as normal vehicle traffic on a highway bridge, train passage on a railroad bridge, or wind loads on a tall building. This eliminates the need to apply a special impact or dynamic load, or interrupt traffic on a bridge in regular service. This research developed an approach in which free vibration of a structure is extracted from the response of this structure to a random excitation in the time domain (acceleration versus time) by averaging out the random component of the response. The result is the free vibration that includes all modes based on the sampling rate on time. Then this free vibration is transferred to the frequency domain using a Fast Fourier Transform (FFT). Variations in frequency response are a function of structural stiffness and member end-conditions. Such variations are used as a measure to identify the change in the structural dynamic properties, and ultimately detect damage. A physical model consisting of a 20 × 20 × 1670 -mm long steel square tube was used to validate this approach. The beam was tested under difference supports conditions varying from a single- to three-span continuous configuration. Random excitation was applied to the beam, and the dynamic response was measured by an accelerometer placed at various locations on the span. A numerical model was constructed in ABAQUS and the dynamic response was obtained from the finite element model subjected to similar excitation as in the physical model. Numerical results were correlated against results from the physical model, and comparison was made between the different span/support configurations. A subsequent step would be to induce damage that simulates loss of stiffness or cracking condition of the beam cross section, and that would be reflected as a change in the frequency and other dynamic properties of the structure. The approach achieved good results for a structure with a limited number of degrees of freedom. Further research is needed for structures with a larger number of degrees of freedom and structures with damage in symmetrical locations relative to the accelerometer position.

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This Master's thesis deals with determination of nucleobases in formamide samples (pure or catalyzed form) after their initiation by high-power density energy events. The theoretical part states the reader to the problems of prebiotic chemistry and acquaints him with the various theories of the origin of the nucleobases. The experimental part deals with the analysis of the samples initiated by Laser System PALS, which was used for the simulation high-power density energy events. For the identification and determination of the final products of laser plasma initiated chemical reactions in the gaseous phase of the samples was used the Fourier Transform Infrared Spectroscopy. The liquid part of the samples and the nucleobases in this part were analyzed by the gas chromatography with the mass detection.

The aim of the thesis is to focus on the different methods of analysis of vibration signals. Focusing on the physical fundamentals of vibrations and a description of their origin in an electrical machine. Describe the vibration sources from mechanical across the electromagnetic to the aerodynamic. Defining the current defects of electric machines and sensors suitable for the measurement of vibrations in an electric machines. Introduction to the methods of analysis of vibration signals in the time and frequency domain. Then using some of these methods for the analysis of vibration signals measured asynchronous motors with different manufacturer defined production defect. The conclusion is composed from the comparison between measured and analyzed results.

Στην εργασία χρησιμοποιούνται σήματα καρδιακού ρυθμού, τα οποία αντιστοιχούν σε φυσιολογικές και οξαιμικές περιπτώσεις.Στην συνέχεια αυτά τα σήματα τα επεξεργαζόμαστε με διάφορες τεχνικές. Στόχος της εργασίας αυτής είναι ο διαχωρισμός των δυο αυτών ομάδων. / In this thesis are used signals of cardiac rythm, that correspond in physiologic and oxidemic cases.Then we processed these signals with various techniques.Target of this thesis is the segregation of this two teams.

The established methodologies for studying computational complexity can be applied to the new problems posed by very large-scale integrated (VLSI) circuits. This thesis develops a ''VLSI model of computation'' and derives upper and lower bounds on the silicon area and time required to solve the problems of sorting and discrete Fourier transformation. In particular, the area A and time T taken by any VLSI chip using any algorithm to perform an N-point Fourier transform must satisfy AT2 ≥ c N2 log2 N, for some fixed c > 0. A more general result for both sorting and Fourier transformation is that AT2x = Ω(N1 + x log2x N) for any x in the range 0 < x < 1. Also, the energy dissipated by a VLSI chip during the solution of either of these problems is at least Ω(N3/2 log N). The tightness of these bounds is demonstrated by the existence of nearly optimal circuits for both sorting and Fourier transformation. The circuits based on the shuffle-exchange interconnection pattern are fast but large: T = O(log2 N) for Fourier transformation, T = O(log3 N) for sorting; both have area A of at most O(N2 / log1/2 N). The circuits based on the mesh interconnection pattern are slow but small: T = O(N1/2 loglog N), A = O(N log2 N).

[Truncated abstract] This thesis presents three different methods to investigate flexural wave propagation and scattering, power flow and transmission efficiencies, and dynamic stress concentration and fatigue failures in structural dynamics. The first method is based on the acoustical wave propagator (AWP) technique, which is the main part described in this thesis. Through the numerical implementation of the AWP, the complete information of the vibrating structure can be obtained including displacement, velocity, acceleration, bending moments, strain and stresses. The AWP technique has been applied to systems consisting of a one-dimensional stepped beam, a two-dimensional thin plate, a thin plate with a sharp change of section, a heterogeneous plate with multiple cylindrical patches, and a Mindlin?s plate with a reinforced rib. For this Mindlin?s plate structure, through the comparison of the results obtained by Mindlin?s thick plate theory and Kirchhoff?s classical thin plate theory, the difference of theoretical predicted results is investigated. As part of these investigations, reflection and transmission coefficients, power flow and transmission efficiencies in a onedimensional stepped beam, and power flow in a two-dimensional circular plate structure, are studied. In particular, this technique has been successfully extended to investigate wave propagation and scattering, and dynamic stress concentration at discontinuities. Potential applications are fatigue failure prediction and damage detection in complex structures. The second method is based on experimental techniques to investigate the structural response under impact loads, which consist of the waveform measuring technique in the time domain by using the WAVEVIEW software, and steady-state measurements by using the Polytec Laser Scanning Vibrometer (PLSV) in the frequency domain. The waveform measuring technique is introduced to obtain the waveform at different locations in the time domain. These experimental results can be used to verify the validity of predicted results obtained by the AWP technique. Furthermore, distributions of dynamic strain and stress in both near-field (close to discontinuities) and far-field regions are investigated for the study of the effects of the discontinuities on reflection and transmission coefficients in a one-dimensional stepped beam structure. Experimental results in the time domain can be easily transferred into those in the frequency domain by the fast Fourier transformation, and compared with those obtained by other researchers. This PLSV technique provides an accurate and efficient tool to investigate mode shape and power flow in some coupled structures, such as a ribbed plate. Through the finite differencing technique, autospectral and spatial of dynamic strain can be obtained. The third method considered uses the travelling wave solution method to solve reflection and transmission coefficients in a one-dimensional stepped beam structure in the time domain. In particular, analytical exact solutions of reflection and transmission coefficients under the given initial-value problem are derived. These analytical solutions together with experimental results can be used to compare with those obtained by the AWP technique.