Analysis of financial indices by means of the windowed Fourier transform

The goal of this study is to analyze the dynamical properties of financial data series from nineteen worldwide stock market indices (SMI) during the period 1995–2009. SMI reveal a complex behavior that can be explored since it is available a considerable volume of data. In this paper is applied the window Fourier transform and methods of fractional calculus. The results reveal classification patterns typical of fractional order systems.

Analysis of financial data series using fractional Fourier transform and multidimensional scaling

The goal of this study is the analysis of the dynamical properties of financial data series from worldwide stock market indexes during the period 2000–2009. We analyze, under a regional criterium, ten main indexes at a daily time horizon. The methods and algorithms that have been explored for the description of dynamical phenomena become an effective background in the analysis of economical data. We start by applying the classical concepts of signal analysis, fractional Fourier transform, and methods of fractional calculus. In a second phase we adopt the multidimensional scaling approach. Stock market indexes are examples of complex interacting systems for which a huge amount of data exists. Therefore, these indexes, viewed from a different perspectives, lead to new classification patterns.

The comb signal and its Fourier transform

SignalProcessing, Vol. 81, nº 3

Application of Continuous Wavelet Transform to the Analysis of the Modulus of the Fractional Fourier Transform Bands for Resolving Two Component Mixture

In this paper, the fractional Fourier transform (FrFT) is applied to the spectral bands of two component mixture containing oxfendazole and oxyclozanide to provide the multicomponent quantitative prediction of the related substances. With this aim in mind, the modulus of FrFT spectral bands are processed by the continuous Mexican Hat family of wavelets, being denoted by MEXH-CWT-MOFrFT. Four modulus sets are obtained for the parameter a of the FrFT going from 0.6 up to 0.9 in order to compare their effects upon the spectral and quantitative resolutions. Four linear regression plots for each substance were obtained by measuring the MEXH-CWT-MOFrFT amplitudes in the application of the MEXH family to the modulus of the FrFT. This new combined powerful tool is validated by analyzing the artificial samples of the related drugs, and it is applied to the quality control of the commercial veterinary samples.

Transmission Fourier transform infrared microspectroscopy allows simultaneous assessment of cutin and cell-wall polysaccharides of Arabidopsis petals.

A procedure for the simultaneous analysis of cell-wall polysaccharides, amides and aliphatic polyesters by transmission Fourier transform infrared microspectroscopy (FTIR) has been established for Arabidopsis petals. The combination of FTIR imaging with spectra derivatization revealed that petals, in contrast to other organs, have a characteristic chemical zoning with high amount of aliphatic compounds and esters in the lamina and of polysaccharides in the stalk of the petal. The hinge region of petals was particular rich in amides as well as in vibrations potentially associated with hemicellulose. In addition, a number of other distribution patterns have been identified. Analyses of mutants in cutin deposition confirmed that vibrations of aliphatic compounds and esters present in the lamina were largely associated with the cuticular polyester. Calculation of spectrotypes, including the standard deviation of intensities, allowed detailed comparison of the spectral features of various mutants. The spectrotypes not only revealed differences in the amount of polyesters in cutin mutants, but also changes in other compound classes. For example, in addition to the expected strong deficiencies in polyester content, the long-chain acyl CoA synthase 2 mutant showed increased intensities of vibrations in a wavelength range that is typical for polysaccharides. Identical spectral features were observed in quasimodo2, a cell-wall mutant of Arabidopsis with a defect in pectin formation that exhibits increased cellulose synthase activity. FTIR thus proved to be a convenient method for the identification and characterization of mutants affected in the deposition of cutin in petals.

Applications of Fourier transform infrared spectroscopy

This article summarizes the basic principles of Fourier Transform Infrared Spectroscopy, with examples of methodologies and applications to different field sciences.

On the inverse windowed Fourier transform

The inversion problem concerning the windowed Fourier transform is considered. It is shown that, out of the infinite solutions that the problem admits, the windowed Fourier transform is the "optimal" solution according to a maximum-entropy selection criterion.

Fingermark initial composition and aging using Fourier transform infrared microscopy (μ-FTIR)

This study investigated fingermark residues using Fourier transform infrared microscopy (μ- FTIR) in order to obtain fundamental information about the marks' initial composition and aging kinetics. This knowledge would be an asset for fundamental research on fingermarks, such as for dating purposes. Attenuated Total Reflection (ATR) and single-point reflection modes were tested on fresh fingermarks. ATR proved to be better suited and this mode was subsequently selected for further aging studies. Eccrine and sebaceous material was found in fresh and aged fingermarks and the spectral regions 1000-1850 cm-1 and 2700-3600 cm-1 were identified as the most informative. The impact of substrates (aluminium and glass slides) and storage conditions (storage in the light and in the dark) on fingermark aging was also studied. Chemometric analyses showed that fingermarks could be grouped according to their age regardless of the substrate when they were stored in an open box kept in an air-conditioned laboratory at around 20°C next to a window. On the contrary, when fingermarks were stored in the dark, only specimens deposited on the same substrate could be grouped by age. Thus, the substrate appeared to influence aging of fingermarks in the dark. Furthermore, PLS regression analyses were conducted in order to study the possibility of modelling fingermark aging for potential fingermark dating applications. The resulting models showed an overall precision of ±3 days and clearly demonstrated their capability to differentiate older fingermarks (20 and 34-days old) from newer ones (1, 3, 7 and 9-days old) regardless of the substrate and lighting conditions. These results are promising from a fingermark dating perspective. Further research is required to fully validate such models and assess their robustness and limitations in uncontrolled casework conditions.

Filtros digitais por transformadas de Fourier aplicados em eletroquímica

The electrochemical properties of micro and nano-electrodes are widely investigated due to their low faradaic and capacitive currents, leading to a new generation of smart and implantable devices. However, the current signals obtained in low-dimensional devices are strongly influenced by noise sources. In this paper, we show the evaluation of filters based on Fast Fourier Transform (FFT) and their implementation in a graphical user interface (GUI) in MATLAB®. As a case study, we evaluated an electrochemical reaction process of charge transfer via outer-sphere. Results showed successful removal of most of the noise in signals, thus proving a promising tool for low-scale measurement.

Fourier transform infrared-attenuated total reflectance (FTIR-ATR) spectroscopy and chemometric techniques for the determination of adulteration in petrodiesel/biodiesel blends

We propose an analytical method based on fourier transform infrared-attenuated total reflectance (FTIR-ATR) spectroscopy to detect the adulteration of petrodiesel and petrodiesel/palm biodiesel blends with African crude palm oil. The infrared spectral fingerprints from the sample analysis were used to perform principal components analysis (PCA) and to construct a prediction model using partial least squares (PLS) regression. The PCA results separated the samples into three groups, allowing identification of those subjected to adulteration with palm oil. The obtained model shows a good predictive capacity for determining the concentration of palm oil in petrodiesel/biodiesel blends. Advantages of the proposed method include cost-effectiveness and speed; it is also environmentally friendly.

Application of fourier transform infrared spectroscopy, chemical and chemometrics analyses to the characterization of agro-industrial waste

Agroindustrial waste in general presents significant levels of nutrients and organic matter and has therefore been frequently put to agricultural use. In this context, the objective of this study was to determine the chemical composition, nitrogen, phosphorus, potassium, calcium, magnesium and carbon content, as well as the qualitative characteristics through Fourier transform infrared spectroscopy of four samples of poultry litter and one sample of cattle manure, from the southwestern region of Paraná, Brazil. Results revealed that, in general, the poultry litter presented higher amount of nutrients and carbon than the cattle manure. The infrared spectra allowed identification of the functional groups present and the differences in degree of sample humification. The statistical treatment confirmed the quantitative and qualitative differences revealed.

Development of a New Transform:MRT

Fourier transform methods are employed heavily in digital signal processing. Discrete Fourier Transform (DFT) is among the most commonly used digital signal transforms. The exponential kernel of the DFT has the properties of symmetry and periodicity. Fast Fourier Transform (FFT) methods for fast DFT computation exploit these kernel properties in different ways. In this thesis, an approach of grouping data on the basis of the corresponding phase of the exponential kernel of the DFT is exploited to introduce a new digital signal transform, named the M-dimensional Real Transform (MRT), for l-D and 2-D signals. The new transform is developed using number theoretic principles as regards its specific features. A few properties of the transform are explored, and an inverse transform presented. A fundamental assumption is that the size of the input signal be even. The transform computation involves only real additions. The MRT is an integer-to-integer transform. There are two kinds of redundancy, complete redundancy & derived redundancy, in MRT. Redundancy is analyzed and removed to arrive at a more compact version called the Unique MRT (UMRT). l-D UMRT is a non-expansive transform for all signal sizes, while the 2-D UMRT is non-expansive for signal sizes that are powers of 2. The 2-D UMRT is applied in image processing applications like image compression and orientation analysis. The MRT & UMRT, being general transforms, will find potential applications in various fields of signal and image processing.

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.