A complex Fourier transformation study of the contactless electroreflectance of an undoped-n(+) GaAs structure

Complex Fourier transformation (CFT) has been employed to analyse contactless electroreflectance (CER) spectra from an undoped-n(+) GaAs structure with various ac modulations and dc bias voltages. The CFT spectra of CER have been compared with those of photoreflectance (PR). It has been found that the CER non-flat modulation is between the built-in electric field and a larger electric field which increases with the modulation voltage. The result has been explained by the screening of the applied modulation electric field in one of the two half modulation cycles and the trapping of electrons in surface states in the other half modulation cycle. The dc bias does not change the CER spectra, hence their CFT spectra. This is because of the screening of the applied dc bias electric field.

Theoretical analysis and experimental study of Fourier transformation of Franz-Keldysh oscillations in GaAs

Fourier transformation (FT) has been used in the theoretical line shape analysis of Franz-Keldysh oscillations (FKOs) in detail by numerical simulations. FKOs from the surface-intrinsic-n(+) GaAs structure were obtained in photoreflectance (PR) measurements with various modulation light intensities and with different strengths of bias light illumination, which were used to change the static electric field in the intrinsic layer of the sample. The FT spectra of the PR spectra, including the real part, imaginary part, and the modulus, were very consistent with the theoretical line shapes. The ratio of the square root of the reduced mass (root mu (L)/root mu (H)) and the ratio of transition strength of the electron heavy hole to the electron light hole were obtained from the PT spectra. In addition, the electric field in the intrinsic layer of the sample without and with bias illumination and the modulation field induced by photomodulation were also obtained. (C) 2000 American Institute of Physics. [S0021-8979(00)02123-X].

Fourier transformation study of the Franz-Keldysh Oscillation in SIN+ GaAs structures

Fourier transformation (FT) method has been used in the theoretical lineshape analysis of the Franz-Keldysh Oscillation (FKO) in detail by numerical simulation. The FKO of a set of GaAs SIN+ samples was obtained in photoreflectance measurements. The FT spectra of a part of the samples,including of the real part,imaginary part, and mode of the FT,are well consistent with the theoretical lineshapes. The ratio of the square root of the reduced mass of the light hole (LH) to the heavy hole (HH), root mu(1)/root mu(h), obtained in the analysis was in the range of 0.805 to 0.816 for different samples. In addition,the built-in electric field F-1, and the modulation field delta F = F-1 - F-2 induced by photo-modulation were also obtained in the analysis. However,for a few samples great difference was found in the lineshape of the real part and imaginary part of their FT spectra from the theoretical lineshape. In this case the mode of the FT spectra still can be used to obtain useful information.

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.

Character recognition systems using Fourier transformation in incoherent light

Many attempts have been made to overcome problems involved in character recognition which have resulted in the manufacture of character reading machines. An investigation into a new approach to character recognition is described. Features for recognition are Fourier coefficients. These are generated optically by convolving characters with periodic gratings. The development of hardware to enable automatic measurement of contrast and position of periodic shadows produced by the convolution is described. Fourier coefficients of character sets were measured, many of which are tabulated. Their analysis revealed that a few low frequency sampling points could be selected to recognise sets of numerals. Limited treatment is given to show the effect of type face variations on the values of coefficients which culminated in the location of six sampling frequencies used as features to recognise numerals in two type fonts. Finally, the construction of two character recognition machines is compared and contrasted. The first is a pilot plant based on a test bed optical Fourier analyser, while the second is a more streamlined machine d(3signed for high speed reading. Reasons to indicate that the latter machine would be the most suitable to adapt for industrial and commercial applications are discussed.

Regenerative Fourier transformation for dual-quadrature regeneration of multilevel rectangular QAM

We propose a new nonlinear optical loop mirror based configuration capable of regenerating regular rectangular quadrature amplitude modulated (QAM) signals. The scheme achieves suppression of noise distortion on both signal quadratures through the realization of two orthogonal regenerative Fourier transformations. Numerical simulations show the performance of the scheme for high constellation complexities (including 256-QAM formats).

Full-range parallel Fourier-domain optical coherence tomography using sinusoidal phase-modulating interferometry

We demonstrate a full-range parallel Fourier-domain optical coherence tomography (FD-OCT) in which a tomogram free of mirror images as well as DC and autocorrelation terms is obtained in parallel. The phase and amplitude of two-dimensional spectral interferograms are accurately detected by using sinusoidal phase-modulating interferometry and a two-dimensional CCD camera, which allows for the reconstruction of two-dimensional complex spectral interferograms. By line-by-line inverse Fourier transformation of the two-dimensional complex spectral interferogram, a full-range parallel FD-OCT is realized. Tomographic images of two separated glass coverslips obtained with our method are presented as a proof-of-principle experiment.

Fourier-Matrizen und Ringe mit Basis

Bei der Bestimmung der irreduziblen Charaktere einer Gruppe vom Lie-Typ entwickelte Lusztig eine Theorie, in der eine sogenannte Fourier-Transformation auftaucht. Dies ist eine Matrix, die nur von der Weylgruppe der Gruppe vom Lie-Typ abhängt. Anhand der Eigenschaften, die eine solche Fourier- Matrix erfüllen muß, haben Geck und Malle ein Axiomensystem aufgestellt. Dieses ermöglichte es Broue, Malle und Michel füur die Spetses, über die noch vieles unbekannt ist, Fourier-Matrizen zu bestimmen. Das Ziel dieser Arbeit ist eine Untersuchung und neue Interpretation dieser Fourier-Matrizen, die hoffentlich weitere Informationen zu den Spetses liefert. Die Werkzeuge, die dabei entstehen, sind sehr vielseitig verwendbar, denn diese Matrizen entsprechen gewissen Z-Algebren, die im Wesentlichen die Eigenschaften von Tafelalgebren besitzen. Diese spielen in der Darstellungstheorie eine wichtige Rolle, weil z.B. Darstellungsringe Tafelalgebren sind. In der Theorie der Kac-Moody-Algebren gibt es die sogenannte Kac-Peterson-Matrix, die auch die Eigenschaften unserer Fourier-Matrizen besitzt. Ein wichtiges Resultat dieser Arbeit ist, daß die Fourier-Matrizen, die G. Malle zu den imprimitiven komplexen Spiegelungsgruppen definiert, die Eigenschaft besitzen, daß die Strukturkonstanten der zugehörigen Algebren ganze Zahlen sind. Dazu müssen äußere Produkte von Gruppenringen von zyklischen Gruppen untersucht werden. Außerdem gibt es einen Zusammenhang zu den Kac-Peterson-Matrizen: Wir beweisen, daß wir durch Bildung äußerer Produkte von den Matrizen vom Typ A(1)1 zu denen vom Typ C(1) l gelangen. Lusztig erkannte, daß manche seiner Fourier-Matrizen zum Darstellungsring des Quantendoppels einer endlichen Gruppe gehören. Deswegen ist es naheliegend zu versuchen, die noch ungeklärten Matrizen als solche zu identifizieren. Coste, Gannon und Ruelle untersuchen diesen Darstellungsring. Sie stellen eine Reihe von wichtigen Fragen. Eine dieser Fragen beantworten wir, nämlich inwieweit rekonstruiert werden kann, zu welcher endlichen Gruppe gegebene Matrizen gehören. Den Darstellungsring des getwisteten Quantendoppels berechnen wir für viele Beispiele am Computer. Dazu müssen unter anderem Elemente aus der dritten Kohomologie-Gruppe H3(G,C×) explizit berechnet werden, was bisher anscheinend in noch keinem Computeralgebra-System implementiert wurde. Leider ergibt sich hierbei kein Zusammenhang zu den von Spetses herrührenden Matrizen. Die Werkzeuge, die in der Arbeit entwickelt werden, ermöglichen eine strukturelle Zerlegung der Z-Ringe mit Basis in bekannte Anteile. So können wir für die meisten Matrizen der Spetses Konstruktionen angeben: Die zugehörigen Z-Algebren sind Faktorringe von Tensorprodukten von affinen Ringe Charakterringen und von Darstellungsringen von Quantendoppeln.

Transformada de Fourier: teoria como base para aplicações em mecânica celeste

Pós-graduação em Matemática Universitária - IGCE

La trasformata veloce di Fourier (FFT): analisi e implementazione in C++

La trasformata di Fourier (FT) è uno strumento molto potente implementato, oggi, in un enorme numero di tecnologie. Il suo primo esempio di applicazione fu proprio il campionamento e la digitalizzazione di segnali analogici. Nel tempo l'utilizzo della FT è stato ampliato a più orizzonti in ambito digitale, basti pensare che il formato di compressione '.jpg' utilizza una FT bidimensionale, mentre uno degli ultimi esempi di applicazione si ha nell'imaging digitale in ambito medico (risonanza magnetica nucleare, tomografia assiale computerizzata TAC ecc...). Nonostante gli utilizzi della FT siano molto diversificati il suo basilare funzionamento non è mai cambiato: essa non fa altro che modificare il dominio di una funzione del tempo (un segnale) in un dominio delle frequenze, permettendo così lo studio della composizione in termini di frequenza, ampiezza e fase del segnale stesso. Parallelamente all'evoluzione in termini di applicazioni si è sviluppato uno studio volto a migliorare e ottimizzare la computazione della stessa, data l'esponenziale crescita del suo utilizzo. In questa trattazione si vuole analizzare uno degli algoritmi di ottimizzazione più celebri e utilizzati in tal senso: la trasformata veloce di Fourier (Fast Fourier Transformation o FFT). Si delineeranno quindi le caratteristiche salienti della FT, e verrà introdotto l'algoritmo di computazione tramite linguaggio C++ dedicando particolare attenzione ai limiti di applicazione di tale algoritmo e a come poter modificare opportunamente la nostra funzione in modo da ricondurci entro i limiti di validità.

Application of Discrete Fourier Inter-Coefficient Difference for Assessing Genetic Sequence Similarity

Digital signal processing (DSP) techniques for biological sequence analysis continue to grow in popularity due to the inherent digital nature of these sequences. DSP methods have demonstrated early success for detection of coding regions in a gene. Recently, these methods are being used to establish DNA gene similarity. We present the inter-coefficient difference (ICD) transformation, a novel extension of the discrete Fourier transformation, which can be applied to any DNA sequence. The ICD method is a mathematical, alignment-free DNA comparison method that generates a genetic signature for any DNA sequence that is used to generate relative measures of similarity among DNA sequences. We demonstrate our method on a set of insulin genes obtained from an evolutionarily wide range of species, and on a set of avian influenza viral sequences, which represents a set of highly similar sequences. We compare phylogenetic trees generated using our technique against trees generated using traditional alignment techniques for similarity and demonstrate that the ICD method produces a highly accurate tree without requiring an alignment prior to establishing sequence similarity.

Electronic band dispersion of graphene nanoribbons via Fourier-transformed scanning tunneling spectroscopy

The electronic structure of atomically precise armchair graphene nanoribbons of width N=7 (7-AGNRs) are investigated by scanning tunneling spectroscopy (STS) on Au(111). We record the standing waves in the local density of states of finite ribbons as a function of sample bias and extract the dispersion relation of frontier electronic states by Fourier transformation. The wave-vector-dependent contributions from these states agree with density functional theory calculations, thus enabling the unambiguous assignment of the states to the valence band, the conduction band, and the next empty band with effective masses of 0.41±0.08me,0.40±0.18me, and 0.20±0.03me, respectively. By comparing the extracted dispersion relation for the conduction band to corresponding height-dependent tunneling spectra, we find that the conduction band edge can be resolved only at small tip-sample separations and has not been observed before. As a result, we report a band gap of 2.37±0.06 eV for 7-AGNRs adsorbed on Au(111).

Image reconstruction in full-field Fourier-domain optical coherence tomography

Full-field Fourier-domain optical coherence tomography (3F-OCT) is a full-field version of spectral domain/swept source optical coherence tomography. A set of two-dimensional Fourier holograms is recorded at discrete wavenumbers spanning the swept source tuning range. The resultant three-dimensional data cube contains comprehensive information on the three-dimensional spatial properties of the sample, including its morphological layout and optical scatter. The morphological layout can be reconstructed in software via three-dimensional discrete Fourier transformation. The spatial resolution of the 3F-OCT reconstructed image, however, is degraded due to the presence of a phase cross-term, whose origin and effects are addressed in this paper. We present a theoretical and experimental study of the imaging performance of 3F-OCT, with particular emphasis on elimination of the deleterious effects of the phase cross-term.

Processing and rendering of Fourier domain optical coherence tomography images at a line rate over 524 kHz using a graphics processing unit

In Fourier domain optical coherence tomography (FD-OCT), a large amount of interference data needs to be resampled from the wavelength domain to the wavenumber domain prior to Fourier transformation. We present an approach to optimize this data processing, using a graphics processing unit (GPU) and parallel processing algorithms. We demonstrate an increased processing and rendering rate over that previously reported by using GPU paged memory to render data in the GPU rather than copying back to the CPU. This avoids unnecessary and slow data transfer, enabling a processing and display rate of well over 524,000 A-scan/s for a single frame. To the best of our knowledge this is the fastest processing demonstrated to date and the first time that FD-OCT processing and rendering has been demonstrated entirely on a GPU.

Effect of dental tissue conditioners and matrix metalloproteinase inhibitors on type I collagen microstructure analyzed by Fourier transform infrared spectroscopy

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)