Low Complexity Spectral Analysis of Heart-Rate-Variability through a Wavelet based FFT

In this paper, a low complexity system for spectral analysis of heart rate variability (HRV) is presented. The main idea of the proposed approach is the implementation of the Fast-Lomb periodogram that is a ubiquitous tool in spectral analysis, using a wavelet based Fast Fourier transform. Interestingly we show that the proposed approach enables the classification of processed data into more and less significant based on their contribution to output quality. Based on such a classification a percentage of less-significant data is being pruned leading to a significant reduction of algorithmic complexity with minimal quality degradation. Indeed, our results indicate that the proposed system can achieve up-to 45% reduction in number of computations with only 4.9% average error in the output quality compared to a conventional FFT based HRV system.

Analyse selbsterregter Strömungsfelder im Verdichter-Leitrad durch Kopplung von Particle Image Velocimetry und Hitzdrahtanemometrie mittels Fast Fourier Transformation

Der Einsatz der Particle Image Velocimetry (PIV) zur Analyse selbsterregter Strömungsphänomene und das dafür notwendige Auswerteverfahren werden in dieser Arbeit beschrieben. Zur Untersuchung von solchen Mechanismen, die in Turbo-Verdichtern als Rotierende Instabilitäten in Erscheinung treten, wird auf Datensätze zurückgegriffen, die anhand experimenteller Untersuchungen an einem ringförmigen Verdichter-Leitrad gewonnen wurden. Die Rotierenden Instabilitäten sind zeitabhängige Strömungsphänomene, die bei hohen aerodynamischen Belastungen in Verdichtergittern auftreten können. Aufgrund der fehlenden Phaseninformation kann diese instationäre Strömung mit konventionellen PIV-Systemen nicht erfasst werden. Die Kármánsche Wirbelstraße und Rotierende Instabilitäten stellen beide selbsterregte Strömungsvorgänge dar. Die Ähnlichkeit wird genutzt um die Funktionalität des Verfahrens anhand der Kármánschen Wirbelstraße nachzuweisen. Der mittels PIV zu visualisierende Wirbeltransport erfordert ein besonderes Verfahren, da ein externes Signal zur Festlegung des Phasenwinkels dieser selbsterregten Strömung nicht zur Verfügung steht. Die Methodik basiert auf der Kopplung der PIV-Technik mit der Hitzdrahtanemometrie. Die gleichzeitige Messung mittels einer zeitlich hochaufgelösten Hitzdraht-Messung ermöglicht den Zeitpunkten der PIV-Bilder einen Phasenwinkel zuzuordnen. Hierzu wird das Hitzdrahtsignal mit einem FFT-Verfahren analysiert, um die PIV-Bilder entsprechend ihrer Phasenwinkel zu gruppieren. Dafür werden die aufgenommenen Bilder auf der Zeitachse der Hitzdrahtmessungen markiert. Eine systematische Analyse des Hitzdrahtsignals in der Umgebung der PIV-Messung liefert Daten zur Festlegung der Grundfrequenz und erlaubt es, der markierten PIV-Position einen Phasenwinkel zuzuordnen. Die sich aus den PIV-Bildern einer Klasse ergebenden Geschwindigkeitskomponenten werden anschließend gemittelt. Aus den resultierenden Bildern jeder Klasse ergibt sich das zweidimensionale zeitabhängige Geschwindigkeitsfeld, in dem die Wirbelwanderung der Kármánschen Wirbelstraße ersichtlich wird. In hierauf aufbauenden Untersuchungen werden Zeitsignale aus Messungen in einem Verdichterringgitter analysiert. Dabei zeigt sich, dass zusätzlich Filterfunktionen erforderlich sind. Im Ergebnis wird schließlich deutlich, dass die Übertragung der anhand der Kármánschen Wirbelstraße entwickelten Methode nur teilweise gelingt und weitere Forschungsarbeiten erforderlich sind.

Fourier transform infrared spectroscopy, a new method for rapid determination of total organic and inorganic carbon and biogenic silica concentration in lake sediments

Abstract We demonstrate the use of Fourier transform infrared spectroscopy (FTIRS) to make quantitative measures of total organic carbon (TOC), total inorganic carbon (TIC) and biogenic silica (BSi) concentrations in sediment. FTIRS is a fast and costeffective technique and only small sediment samples are needed (0.01 g). Statistically significant models were developed using sediment samples from northern Sweden and were applied to sediment records from Sweden, northeast Siberia and Macedonia. The correlation between FTIRS-inferred values and amounts of biogeochemical constituents assessed conventionally varied between r = 0.84–0.99 for TOC, r = 0.85– 0.99 for TIC, and r = 0.68–0.94 for BSi. Because FTIR spectra contain information on a large number of both inorganic and organic components, there is great potential for FTIRS to become an important tool in paleolimnology.

A convolution model for energy transport in a therapeutic fast neutron beam

A three-dimensional model has been proposed that uses Monte Carlo and fast Fourier transform convolution techniques to calculate the dose distribution from a fast neutron beam. This method transports scattered neutrons and photons in the forward, lateral, and backward directions and protons, electrons, and positrons in the forward and lateral directions by convolving energy spread kernels with initial interaction available energy distributions. The primary neutron and photon spectrums have been derived from narrow beam attenuation measurements. The positions and strengths of the effective primary neutron, scattered neutron, and photon sources have been derived from dual ion chamber measurements. The size of the effective primary neutron source has been measured using a copper activation technique. Heterogeneous tissue calculations require a weighted sum of two convolutions for each component since the kernels must be invariant for FFT convolution. Comparisons between calculations and measurements were performed for several water and heterogeneous phantom geometries. ^

Experimental evidence for hydrogen-bonded network proton transfer in bacteriorhodopsin shown by Fourier-transform infrared spectroscopy using azide as catalyst.

Experimental evidence for proton transfer via a hydrogen-bonded network in a membrane protein is presented. Bacteriorhodopsin's proton transfer mechanism on the proton uptake pathway between Asp-96 and the Schiff base in the M-to-N transition was determined. The slowdown of this transfer by removal of the proton donor in the Asp-96-->Asn mutant can be accelerated again by addition of small weak acid anions such as azide. Fourier-transform infrared experiments show in the Asp-96-->Asn mutant a transient protonation of azide bound to the protein in the M-to-N transition and, due to the addition of azide, restoration of the IR continuum band changes as seen in wild-type bR during proton pumping. The continuum band changes indicate fast proton transfer on the uptake pathway in a hydrogen-bonded network for wild-type bR and the Asp-96-->Asn mutant with azide. Since azide is able to catalyze proton transfer steps also in several kinetically defective bR mutants and in other membrane proteins, our finding might point to a general element of proton transfer mechanisms in proteins.

Estudo e aplicação da transformada de Fourier na regularização de dados sísmicos na exploração de petróleo

In the oil prospection research seismic data are usually irregular and sparsely sampled along the spatial coordinates due to obstacles in placement of geophones. Fourier methods provide a way to make the regularization of seismic data which are efficient if the input data is sampled on a regular grid. However, when these methods are applied to a set of irregularly sampled data, the orthogonality among the Fourier components is broken and the energy of a Fourier component may "leak" to other components, a phenomenon called "spectral leakage". The objective of this research is to study the spectral representation of irregularly sampled data method. In particular, it will be presented the basic structure of representation of the NDFT (nonuniform discrete Fourier transform), study their properties and demonstrate its potential in the processing of the seismic signal. In this way we study the FFT (fast Fourier transform) and the NFFT (nonuniform fast Fourier transform) which rapidly calculate the DFT (discrete Fourier transform) and NDFT. We compare the recovery of the signal using the FFT, DFT and NFFT. We approach the interpolation of seismic trace using the ALFT (antileakage Fourier transform) to overcome the problem of spectral leakage caused by uneven sampling. Applications to synthetic and real data showed that ALFT method works well on complex geology seismic data and suffers little with irregular spatial sampling of the data and edge effects, in addition it is robust and stable with noisy data. However, it is not as efficient as the FFT and its reconstruction is not as good in the case of irregular filling with large holes in the acquisition.

Estudo e aplicação da transformada de Fourier na regularização de dados sísmicos na exploração de petróleo

In the oil prospection research seismic data are usually irregular and sparsely sampled along the spatial coordinates due to obstacles in placement of geophones. Fourier methods provide a way to make the regularization of seismic data which are efficient if the input data is sampled on a regular grid. However, when these methods are applied to a set of irregularly sampled data, the orthogonality among the Fourier components is broken and the energy of a Fourier component may "leak" to other components, a phenomenon called "spectral leakage". The objective of this research is to study the spectral representation of irregularly sampled data method. In particular, it will be presented the basic structure of representation of the NDFT (nonuniform discrete Fourier transform), study their properties and demonstrate its potential in the processing of the seismic signal. In this way we study the FFT (fast Fourier transform) and the NFFT (nonuniform fast Fourier transform) which rapidly calculate the DFT (discrete Fourier transform) and NDFT. We compare the recovery of the signal using the FFT, DFT and NFFT. We approach the interpolation of seismic trace using the ALFT (antileakage Fourier transform) to overcome the problem of spectral leakage caused by uneven sampling. Applications to synthetic and real data showed that ALFT method works well on complex geology seismic data and suffers little with irregular spatial sampling of the data and edge effects, in addition it is robust and stable with noisy data. However, it is not as efficient as the FFT and its reconstruction is not as good in the case of irregular filling with large holes in the acquisition.

Determinations of stress wave velocity in a timber pole using wavelet transform

This paper presents an application of Wavelet Transfonn (WT) for determination of stress wave velocity for Non-destructive Testing of timber utility poles in service. For surface Non-destructive Testing (NDT), the hammer impact, which produces generally broadband frequency excitation, is used to generate stress wave. Moreover, due to practicality the impact location for field testing of a utility pole is on the side of the pole and 1.5 m above ground level. And the geometry of utility pole could not guarantee non-dispersive longitudinal wave. All of these issues have resulted in lack of accuracy and reliability of results from surface NDT in field testing. In recognition of such problem, this research explores methods to reliably calculate desired wave velocity by isolating wave mode and studying dispersive nature of utility pole. Fast Fourier Transfonn (FFT) is firstly conducted to determine the suitable frequency from a stress wave data. Then WT is applied on the wave data mentioned to perfonn time-frequency analysis. Velocity can be detennined by time history data of desired frequency from WT results which will be compared with the available analytical solution for longitudinal wave velocity. The results of the investigation showed that wavelet transfonn analysis can be a reliable signal processing tool for non-destructive testing in tenns of velocity detennination, which in tum also helps to detennine the embedded length of the timber pole.

Rapid quantification of methamphetamine: using Attenuated Total Reflectance Fourier Transform Infrared Spectroscopy (ATR-FTIR) and Chemometrics

In Australia and increasingly worldwide, methamphetamine is one of the most commonly seized drugs analysed by forensic chemists. The current well-established GC/MS methods used to identify and quantify methamphetamine are lengthy, expensive processes, but often rapid analysis is requested by undercover police leading to an interest in developing this new analytical technique. Ninety six illicit drug seizures containing methamphetamine (0.1% - 78.6%) were analysed using Fourier Transform Infrared Spectroscopy with an Attenuated Total Reflectance attachment and Chemometrics. Two Partial Least Squares models were developed, one using the principal Infrared Spectroscopy peaks of methamphetamine and the other a Hierarchical Partial Least Squares model. Both of these models were refined to choose the variables that were most closely associated with the methamphetamine % vector. Both of the models were excellent, with the principal peaks in the Partial Least Squares model having Root Mean Square Error of Prediction 3.8, R2 0.9779 and lower limit of quantification 7% methamphetamine. The Hierarchical Partial Least Squares model had lower limit of quantification 0.3% methamphetamine, Root Mean Square Error of Prediction 5.2 and R2 0.9637. Such models offer rapid and effective methods for screening illicit drug samples to determine the percentage of methamphetamine they contain.

Evidence for the adsorption of molecules at special sites located at copper/zinc oxide interfaces. Part 2. -- A fourier-transform infrared spectroscopy study of methanol adsorption on reduced and oxidised Cu/ZnO/SiO2 catalysts

FTIR spectra are reported of methanol adsorbed at 295 K on ZnO/SiO 2, on reduced Cu/ZnO/SiO2 and on Cu/ZnO/SiO2 which had been preoxidised by exposure to nitrous oxide. Methanol on ZnO/SiO2 gave methoxy species on ZnO and SiO, in addition to both strongly and weakly physisorbed methanol on SiO2. The corresponding adsorption of methanol on reduced Cu/ZnO/SiO2 also gave methoxy species on Cu and a small amount of bridging formate. Reaction of methanol with a reoxidised Cu/ZnO/SiO2 catalyst resulted in an enhanced quantity of methoxy species on Cu. Heating adsorbed species on Cu/ZnO/SiO2 at 393 K led to the loss of methoxy groups on Cu and the concomitant formation of formate species on both ZnO and Cu. The comparable reaction on a reoxidised Cu/ZnO/SiO2 catalyst gave an increased amount of formate species on ZnO and this correlated with an increased quantity of methoxy groups lost from Cu. An explanation is given in terms of adsorption of formate and formaldehyde species at special sites located at the copper/zinc oxide interface.

Evidence for the adsorption of molecules at special sites located at copper/zinc oxide interfaces: Part 1. -- A Fourier-transform infrared study of formic acid and formaldehyde adsorption on reduced and oxidised Cu/ZnO/SiO2 catalysts

Fourier-transform infrared (FTIR) spectra are reported of formic acid and formaldehyde on ZnO/SiO2, reduced Cu/ZnO/SiO2 and reoxidised Cu/ZnO/SiO2 catalyst. Formic acid adsorption on ZnO/SiO2 produced mainly bidentate zinc formate species with a lesser quantity of unidentate zinc formate. Formic acid on reduced Cu/ZnO/SiO2 catalyst resulted not only in the formation of bridging copper formate structures but also in an enhanced amount of formate relative to that for ZnO/SiO2 catalyst. Formic acid on reoxidised Cu/ZnO/SiO2 gave unidentate formate species on copper in addition to zinc formate moieties. The interaction of formaldehyde with ZnO/SiO2 catalyst resulted in the formation of zinc formate species. The same reaction on reduced Cu/ZnO/SiO2 catalyst gave bridging formate on copper and a remarkable increase in the quantity of formate species associated with the zinc oxide. Adsorption of formaldehyde on a reoxidised Cu/ZnO/SiO2 catalyst produced bridging copper formate and again an apparent increase in the concentration of zinc formate species. An explanation in terms of the adsorption of molecules at special sites located at the interface between copper and zinc oxide is given.

A combined temperature-programmed reaction spectroscopy and Fourier-transform infrared spectroscopy study of CO2/H2 and CO/CO2/H2 interactions with model ZnO/SiO2, Cu/SiO2 and Cu/ZnO/SiO2 methanol-synthesis catalysts

The reaction of CO2 and H2 with ZnO/SiO2 catalyst at 295 K gave predominantly hydrogencarbonate on zinc oxide and a small quantity of formate was evolved after heating at 393 K. Elevation of the reaction temperature to 503 K enhanced the rate of formation of zinc formate species. Significantly these formate species decomposed at 573 K almost entirely to CO2 and H2. Even after exposure of CO2-H2 or CO-CO2-H2 mixtures to highly defected ZnO/SiO2 catalyst, the formate species produced still decomposed to give CO2 and H2. It was concluded that carboxylate species which were formed at oxygen anion vacancies on polar Zn planes were not significantly hydrogenated to formate. Consequently it was proposed that the non-polar planes on zinc oxide contained sites which were specific for the synthesis of methanol. The interaction of CO2 and H2 with reduced Cu/ZnO/SiO2 catalyst at 393 K gave copper formate species in addition to substantial quantities of formate created at interfacial sites between copper and zinc oxide. It was deduced that interfacial formate species were produced from the hydrogenation of interfacial bidentate carbonate structures. The relevance of interfacial formate species in the methanol synthesis reaction is discussed. Experiments concerning the reaction of CO2-H2 with physical mixtures of Cu/SiO2 and ZnO/SiO2 gave results which were simply characteristic of the individual components. By careful consideration of previous data a detailed proposal regarding the role of spillover hydrogen is outlined. Admission of CO to a gaseous CO2-H2 feedstock resulted in a considerably diminished amount of formate species on copper. This was ascribed to a combination of over-reduction of the surface and site-blockage.