Introducción a los sistemas lineales y al análisis de Fourier.

Realizado en la Escuela Universitaria de Informática de la Universidad Pontificia de Salamanca, por 4 profesores del centro para las asignaturas de Fundamentos Matemáticos I, Transmisión de Datos y Ampliación de Matemáticas de las titulaciones de Ingeniería Técnica de Informática de Sistemas, Ingeniería de Informática de Gestión e Ingeniería Superior de Informática. Se pretende proporcionar al alumno una justificación concisa de los conceptos matemáticos sobre los que se sustenta el análisis de Fourier y su relación con los sistemas lineales invariantes. Para ello, se desarrolla un material práctico, innovador, gráfico que potencie la compresión de los conceptos teóricos. Para el desarrollo de esta unidad didáctica, se exponen los contenidos, se desarrollan y después vienen una serie de problemas propuestos y resueltos representativos. Como propuesta adicional, se ha creado información estructurada en formato página Web, puesto que facilita la comprensión del alumno, mediante las técnicas más habituales de presentación gráfica o animación. El proyecto ha sido evaluado por unos candidatos seleccionados al principio del proyecto, en la memoria se adjunta el informe de cada uno de ellos.

Linear and nonlinear generalized Fourier transforms

This article presents an overview of a transform method for solving linear and integrable nonlinear partial differential equations. This new transform method, proposed by Fokas, yields a generalization and unification of various fundamental mathematical techniques and, in particular, it yields an extension of the Fourier transform method.

Assessment of the consistency of near-infrared water vapor line intensities using high-spectral-resolution ground-based Fourier transform measurements of solar radiation

Calculations of the absorption of solar radiation by atmospheric gases, and water vapor in particular, are dependent on the quality of databases of spectral line parameters. There has been increasing scrutiny of databases such as HITRAN in recent years, but this has mostly been performed on a band-by-band basis. We report nine high-spectral-resolution (0.03 cm(-1)) measurements of the solar radiation reaching the surface in southern England over the wave number range 2000 to 12,500 cm(-1) (0.8 to 5 mm) that allow a unique assessment of the consistency of the spectral line databases over this entire spectral region. The data are assessed in terms of the modeled water vapor column that is required to bring calculations and observations into agreement; for an entirely consistent database, this water vapor column should be constant with frequency. For the HITRAN01 database, the spread in water vapor column is about 11%, with distinct shifts between different spectral regions. The HITRAN04 database is in significantly better agreement (about 5% spread) in the completely updated 3000 to 8000 cm(-1) spectral region, but inconsistencies between individual spectral regions remain: for example, in the 8000 to 9500 cm(-1) spectral region, the results indicate an 18% (+/- 1%) underestimate in line intensities with respect to the 3000 to 8000 cm(-1) region. These measurements also indicate the impact of isotopic fractionation of water vapor in the 2500 to 2900 cm(-1) range, where HDO lines dominate over the lines of the most abundant isotope of H2O.

Fourier transform infrared spectra of H2CS and D2CS

Infrared spectra of thoformaldehyde, H2CS and D2CS, were observed in the gas phase at a resolution of better than 0.1 cm−1 from 4000 to 400 cm−1 using a Nicolet FTIR system. Vibrational band origins and rotational constants were determined for ν2, ν3, ν4, and ν6 of H2CS and for ν1, ν2, ν3, ν4, and ν6 of D2CS. The ν3, ν4, and ν6 bands of H2CS were analyzed as a set of three Coriolis interacting bands, and three Coriolis constants were determined; similarly the ν4 and ν6 bands of D2CS were analyzed as a pair of interacting bands and one Coriolis constant was determined. A general harmonic force field was determined, without constraints, to fit the vibrational wavenumbers, Coriolis constants, and centrifugal distortion constants. A zero-point (rz) structure was determined from the ground-state rotational constants, and the equilibrium (re) bond lengths were estimated.

Remote gas detection and quantitative analysis from infrared emission spectra obtained by Fourier transform infrared spectroscopy

Techniques for obtaining quantitative values of the temperatures and concentrations of remote hot gaseous effluents from their measured passive emission spectra have been examined in laboratory experiments. The high sensitivity of the spectrometer in the vicinity of the 2397 cm-1 band head region of CO2 has allowed the gas temperature to be calculated from the relative intensity of the observed rotational lines. The spatial distribution of the CO2 in a methane flame has been reconstructed tomographically using a matrix inversion technique. The spectrometer has been calibrated against a black body source at different temperatures and a self absorption correction has been applied to the data avoiding the need to measure the transmission directly. Reconstruction artifacts have been reduced by applying a smoothing routine to the inversion matrix.

Automatic internal calibration in liquid chromatography/Fourier transform ion cyclotron resonance mass spectrometry of protein digests

Accurately measured peptide masses can be used for large-scale protein identification from bacterial whole-cell digests as an alternative to tandem mass spectrometry (MS/MS) provided mass measurement errors of a few parts-per-million (ppm) are obtained. Fourier transform ion cyclotron resonance (FTICR) mass spectrometry (MS) routinely achieves such mass accuracy either with internal calibration or by regulating the charge in the analyzer cell. We have developed a novel and automated method for internal calibration of liquid chromatography (LC)/FTICR data from whole-cell digests using peptides in the sample identified by concurrent MS/MS together with ambient polydimethyl-cyclosiloxanes as internal calibrants in the mass spectra. The method reduced mass measurement error from 4.3 +/- 3.7 ppm to 0.3 +/- 2.3 ppm in an E. coli LC/FTICR dataset of 1000 MS and MS/MS spectra and is applicable to all analyses of complex protein digests by FTICRMS. Copyright (c) 2006 John Wiley & Sons, Ltd.

Use of thermography and fibre optics microscopy for the evaluation of railway structures in the Athens Metro in Greece (Invited Paper)

Rolling Contact Fatigue (RCF) is one of the main issues that concern, at least initially, the head of the railway; progressively they can be of very high importance as they can propagate inside the material with the risk of damaging the railway. In this work, two different non-destructive techniques, infrared thermography (IRT) and fibre optics microscopy (FOM), were used in the inspection of railways for the tracing of defects and deterioration signs. In the first instance, two different approaches (dynamic and pulsed thermography) were used, whilst in the case of FOM, microscopic characterisation of the railway heads and classification of the deterioration -- damage on the railways according to the UIC (International Union of Railways) code, took place. Results from both techniques are presented and discussed.

Integrated optics for nulling interferometry in the thermal infrared

Modal filtering is based on the capability of single-mode waveguides to transmit only one complex amplitude function to eliminate virtually any perturbation of the interfering wavefronts, thus making very high rejection ratios possible in a nulling interferometer. In the present paper we focus on the progress of Integrated Optics in the thermal infrared [6-20 mu m] range, one of the two candidate technologies for the fabrication of Modal Filters, together with fiber optics. In conclusion of the European Space Agency's (ESA) "Integrated Optics for Darwin" activity, etched layers of clialcogenide material deposited on chalcogenide glass substrates was selected among four candidates as the technology with the best potential to simultaneously meet the filtering efficiency, absolute and spectral transmission, and beam coupling requirements. ESA's new "Integrated Optics" activity started at mid-2007 with the purpose of improving the technology until compliant prototypes can be manufactured and validated, expectedly by the end of 2009. The present paper aims at introducing the project and the components requirements and functions. The selected materials and preliminary designs, as well as the experimental validation logic and test benches are presented. More details are provided on the progress of the main technology: vacuum deposition in the co-evaporation mode and subsequent etching of chalcogenide layers. In addition., preliminary investigations of an alternative technology based on burying a chalcogenide optical fiber core into a chalcogenide substrate are presented. Specific developments of anti-reflective solutions designed for the mitigation of Fresnel losses at the input and output surface of the components are also introduced.

An analysis of real time implementation of Fourier transform-based frequency recognition algorithms

Frequency recognition is an important task in many engineering fields such as audio signal processing and telecommunications engineering, for example in applications like Dual-Tone Multi-Frequency (DTMF) detection or the recognition of the carrier frequency of a Global Positioning, System (GPS) signal. This paper will present results of investigations on several common Fourier Transform-based frequency recognition algorithms implemented in real time on a Texas Instruments (TI) TMS320C6713 Digital Signal Processor (DSP) core. In addition, suitable metrics are going to be evaluated in order to ascertain which of these selected algorithms is appropriate for audio signal processing(1).

Optimal discrimination and classification of THz spectra in the wavelet domain

In rapid scan Fourier transform spectrometry, we show that the noise in the wavelet coefficients resulting from the filter bank decomposition of the complex insertion loss function is linearly related to the noise power in the sample interferogram by a noise amplification factor. By maximizing an objective function composed of the power of the wavelet coefficients divided by the noise amplification factor, optimal feature extraction in the wavelet domain is performed. The performance of a classifier based on the output of a filter bank is shown to be considerably better than that of an Euclidean distance classifier in the original spectral domain. An optimization procedure results in a further improvement of the wavelet classifier. The procedure is suitable for enhancing the contrast or classifying spectra acquired by either continuous wave or THz transient spectrometers as well as for increasing the dynamic range of THz imaging systems. (C) 2003 Optical Society of America.