An Algorithm for the Continuous Morlet Wavelet Transform

This article consists of a brief discussion of the energy density over time or frequency that is obtained with the wavelet transform. Also an efficient algorithm is suggested to calculate the continuous transform with the Morlet wavelet. The energy values of the Wavelet transform are compared with the power spectrum of the Fourier transform. Useful definitions for power spectra are given. The focus of the work is on simple measures to evaluate the transform with the Morlet wavelet in an efficient way. The use of the transform and the defined values is shown in some examples.Comment: 15 pages, 4 figures, revised for MSS

Wavelet transformation of structure bourne sound signals for dispersion characterisation and source localisation

Die Arbeit behandelt die Definition eines speziellen Wavelet, um die Biegewellen Impulsantwort zu analysieren. Dieses Wavelet eröffnet die Möglichkeit direkt die Dispersion des Impulses zu untersuchen. Das Ziel ist eine Quelle zu lokalisieren oder Materialparameter zu bestimmen. Die Arbeit behandelt zusätzlich eine Diskussion der zeit- und frequenzabhängigen Energiedichte, die mit Hilfe der Wavelettransformation gewonnen wird. Es wird ein effizienter Algorithmus zur Berechnung der kontinuierlichen Wavelettransformation mit dem Morletwavelet vorgestellt. Die Energiegrößen der Wavelettransformation werden mit dem Leistungsspektrum der Fouriertransformation verglichen. Es wird eine Definition von Leistungsspektren, die mit der Wavelettransformation gewonnen wurden, angegeben. Das Ziel dieses Abschnitts ist die Morlet Wavelettransformation effizient auszuführen. Die Anwendung der Transformation und der definierten Größen wird in Beispielen vorgeführt. Ein weiterer Teil der Arbeit ist die Herleitung einer analytischen Funktion der Impulsantwort für unendliche Balken und Platten mit einer impulsartigen Kraftanregung im Koordinatenursprung. Diese Funktionen werden zur Zeitumkehr der Impulsantwort und Auswertung der Zeit-Frequenzverteilung angewendet. Die Impulsantwort für unendlichen Balken und Platten, die der Eulerschen Biegetheorie genügen wird hergeleitet und eine Interpretation bezüglich der Energieerhaltung und der Mobilität angegeben. Aufbauend auf diesen Ergebnissen wird ein neues Wavelet, das Biegewavelet, definiert, das der Analyse der Impulsantworten dienen soll. Es wird ein Überblick über die mathematischen Eigenschaften des Wavelets gegeben und ein Algorithmus zur Extrahierung der Dispersion mit Hilfe eines Genetischen Algorithmus vorgestellt. Die Anwendung des Wavelets wird in einem Beispiel vorgestellt. In einem Experiment wird die Impulsantwort eines endlichen Balkens und einer Platte gemessen und mit den theoretischen Funktionen verglichen. Die Signale vor der ersten Reflektion des Impulses zeigten eine gute Übereinstimmung mit der Theorie. Die Transformation mit dem Biegewavelet wird auf die experimentellen Signale angewendet und gezeigt, dass es möglich ist auf diesem Weg eine Quelle exakt zu lokalisieren.The work addresses the definition of a wavelet that is adapted to analyse a flexural impulse response. The wavelet gives the opportunity to directly analyse the dispersion characteristics of a pulse. The aim is to localize a source or to measure material parameters. The work also consists of a brief discussion of the energy density over time or frequency that is obtained with the wavelet transform. An efficient algorithm is suggested to calculate the continuous transform with the Morlet wavelet. The energy values of the Wavelet transform are compared with the power spectrum of the Fourier transform. Useful definitions for power spectra obtained with the Wavelet transform are given. The focus of this part is on simple measures to evaluate the transform with the Morlet wavelet in an efficient way. The use of the transform and the defined values is shown in examples. Part of the work is the response functions for infinite beams and plates with a force excitation at the origin of the coordinate system and its application to time reversal and time frequency analysis. The response function for Euler-Bernoulli beams and plates is derived. Interpretation concerning energy conservation and mobility are given. Based on the results is the definition of a new wavelet, the bending wavelet, which is meant to analyse the flexural impulse response. An overview of the mathematical properties of the bending wavelet is presented. An algorithm to extract the dispersion characteristics with the use of genetic algorithms is outlined. The application of the wavelet is shown in an example. The impulse response of a finite beam is measured in an experiment and compared with that predicted theoretically. The experimental data before the first reflection of the pulse showed good agreement with the theory. The transform with the bending wavelet is performed with the measured impulse response. It is shown that one is able to localize a source with the use of the bending wavelet

Investigations on the mode of action of gephyronic acid, an inhibitor of eukaryotic protein translation from myxobacteria.

The identification of inhibitors of eukaryotic protein biosynthesis, which are targeting single translation factors, is highly demanded. Here we report on a small molecule inhibitor, gephyronic acid, isolated from the myxobacterium Archangium gephyra that inhibits growth of transformed mammalian cell lines in the nM range. In direct comparison, primary human fibroblasts were shown to be less sensitive to toxic effects of gephyronic acid than cancer-derived cells. Gephyronic acid is targeting the protein translation system. Experiments with IRES dual luciferase reporter assays identified it as an inhibitor of the translation initiation. DARTs approaches, co-localization studies and pull-down assays indicate that the binding partner could be the eukaryotic initiation factor 2 subunit alpha (eIF2α). Gephyronic acid seems to have a different mode of action than the structurally related polyketides tedanolide, myriaporone, and pederin and is a valuable tool for investigating the eukaryotic translation system. Because cancer derived cells were found to be especially sensitive, gephyronic acid could potentially find use as a drug candidate

Inhibition of translation in two <i>in vitro</i> systems.

<p>(a) GA (■) inhibited the translation in a rabbit reticulocyte lysate more efficiently than cycloheximide (●). The error bars show standard deviations. (b) GA also inhibited a wheat germ lysate translation system. Here, the relative standard deviations were < 5%. The error bars do not exceed the square symbols. All experiments were run in triplicates.</p

Bicistronic reporter systems in KB-3-1 cells allowing to compare cap-dependent translation directly to cap-independent in the same environment.

<p>GA inhibited the translation of the polio IRES sequence (a) but not that of the CrPV IRES (b). DMDA-pateamine A which targets eIF4A also inhibited the polio IRES and not the CrPV IRES mediated translation. Cycloheximide, which targets the elongation phase, inhibited translation from both IRES sequences. All experiments were run in triplicates. The error bars show standard deviations.</p

Activity of GA in primary and transformed cells.

<p>Human dermal fibroblasts (NHDF; □) and cancerous KB-3-1 cells (■) were incubated with different concentrations of GA and measured for viability after 48 hours. NHDFs were less sensitive than KB-3-1 cancer cells.</p

DARTS approach with GA.

<p>KB-3-1 cell lysates incubated with different concentrations of GA were subjected to pronase digestion. After SDS-PAGE protein bands were stained with Coomassie Brilliant Blue. A lysate treated with cycloheximide served as negative control. GA partially protected a protein at 36 kDa (see arrow) from digestion that is not protected by cycloheximide.</p

Inhibition of a luciferase signal in KB-3-1 reporter cells.

<p>GA (■) inhibits the production of <i>Renilla</i> luciferase in the cells to the same extend as cycloheximide (●). The experiments were run in triplicates. The error bars show standard deviations.</p

The chemical structure of gephyronic acid 1.

<p>The chemical structure of gephyronic acid 1.</p