Hilbert transform

The Hilbert transform is an important tool in both pure and applied mathematics. It is largely used in the field of signal processing. Lately has been used in mathematical finance as the fast Hilbert transform method is an efficient and accurate algorithm for pricing discretely monitored barrier and Bermudan style options. The purpose of this report is to show the basic properties of the Hilbert transform and to check the domain of definition of this operator.

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.

Integração da equação de movimento através da Transformada de Fourier com o uso de ponderadores de ordem elevada

Baseando-se em um sistema com um grau de liberdade, é apresentada neste trabalho a equação de movimento, bem como a sua resolução através das Transformadas de Fourier e da Transformada Rápida de Fourier (FFT). Através da análise da forma como são feitas as integrações nas transformadas, foram estudados e aplicados os ponderadores de Newton-Cotes na resolução da equação de movimento, de forma a aumentar substancialmente a precisão dos resultados em comparação com a forma convencional da Transformada de Fourier.

Removal of antibiotic compounds by adsorption using glycerol-based carbon materials

This study is focused on the synthesis and application of glycerol-based carbon materials (GBCM200, GBCM300 and GBCM350) as adsorbents for the removal of the antibiotic compounds flumequine and tetracycline from aqueous solution. The synthesis enrolled the partial carbonization of a glycerol-sulfuric acid mixture, followed by thermal treatments under inert conditions and further thermal activation under oxidative atmosphere. The textural properties were investigated through N2 adsorption–desorption isotherms, and the presence of oxygenated groups was discussed based on zeta potential and Fourier transform infrared (FTIR) data. The kinetic data revealed that the equilibrium time for flumequine adsorption was achieved within 96 h, while for tetracycline, it was reached after 120 h. Several kinetic models, i.e., pseudo-first order, pseudo-second order, fractional power, Elovich and Weber–Morris models, were applied, finding that the pseudo-second order model was the most suitable for the fitting of the experimental kinetic data. The estimated surface diffusion coefficient values, Ds, of 3.88 and 5.06 10 14 m2 s 1, suggests that the pore diffusion is the rate limiting step of the adsorption process. Finally, as it is based on SSE values, Sips model well-fitted the experimental FLQ and TCN adsorption isotherm data, followed by Freundlich equation. The maximum adsorption capacities for flumequine and tetracycline was of 41.5 and 58.2 mg g 1 by GBCM350 activated carbon.

Full-field Fourier-domain optical coherence tomography

Full-field Fourier-domain optical coherence tomography (3F-OCT) is a full-field version of spectraldomain/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 morphological layout of the sample that can be reconstructed in software via three-dimensional discrete Fourier-transform. This method of recording of the OCT signal confers signal-to-noise ratio improvement in comparison with "flying-spot" time-domain OCT. 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 theoretical and experimental study of imaging performance of 3F-OCT, with particular emphasis on elimination of the deleterious effects of the phase cross-term.

An Lp − Lq - Version of Morgan's Theorem Associated with Partial Differential Operators

2000 Mathematics Subject Classification: 42B10, 43A32.

Polynomial Expansions for Solutions of Higher-Order Bessel Heat Equation in Quantum Calculus

Mathematics Subject Class.: 33C10,33D60,26D15,33D05,33D15,33D90

A Note on Multipliers for Integrable Boehmians

2000 Mathematics Subject Classification: 44A40, 42A38, 46F05

Hermite Polynomials and the Zero-Distribution of Riemann's Zeta Function

AMS Subject Classification 2010: 11M26, 33C45, 42A38.

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.

Double Fourier analysis for Emotion Identification in Voiced Speech

We propose a novel analysis alternative, based on two Fourier Transforms for emotion recognition from speech -- Fourier analysis allows for display and synthesizes different signals, in terms of power spectral density distributions -- A spectrogram of the voice signal is obtained performing a short time Fourier Transform with Gaussian windows, this spectrogram portraits frequency related features, such as vocal tract resonances and quasi-periodic excitations during voiced sounds -- Emotions induce such characteristics in speech, which become apparent in spectrogram time-frequency distributions -- Later, the signal time-frequency representation from spectrogram is considered an image, and processed through a 2-dimensional Fourier Transform in order to perform the spatial Fourier analysis from it -- Finally features related with emotions in voiced speech are extracted and presented

Desenvolvimento e validação de metodologia analítica para quantificação de urânio em compostos do ciclo do combustível nuclear por espectroscopia no infravermelho com transformada de Fourier (FTIR)

Tese (Doutorado em Tecnologia Nuclear)

Development and testing of a Fourier trasform based experimental system for Dynamic Mechanical Thermal Analysis tests

Altough nowadays DMTA is one of the most used techniques to characterize polymers thermo-mechanical behaviour, it is only effective for small amplitude oscillatory tests and limited to a single frequency analysis (linear regime). In this thesis work a Fourier transform based experimental system has proven to give hint on structural and chemical changes in specimens during large amplitude oscillatory tests exploiting multi frequency spectral analysis turning out in a more sensitive tool than classical linear approach. The test campaign has been focused on three test typologies: Strain sweep tests, Damage investigation and temperature sweep tests.

Graphene And Carbon Nanotube Nanocomposite For Gene Transfection.

Graphene and carbon nanotube nanocomposite (GCN) was synthesised and applied in gene transfection of pIRES plasmid conjugated with green fluorescent protein (GFP) in NIH-3T3 and NG97 cell lines. The tips of the multi-walled carbon nanotubes (MWCNTs) were exfoliated by oxygen plasma etching, which is also known to attach oxygen content groups on the MWCNT surfaces, changing their hydrophobicity. The nanocomposite was characterised by high resolution scanning electron microscopy; energy-dispersive X-ray, Fourier transform infrared and Raman spectroscopies, as well as zeta potential and particle size analyses using dynamic light scattering. BET adsorption isotherms showed the GCN to have an effective surface area of 38.5m(2)/g. The GCN and pIRES plasmid conjugated with the GFP gene, forming π-stacking when dispersed in water by magnetic stirring, resulting in a helical wrap. The measured zeta potential confirmed that the plasmid was connected to the nanocomposite. The NIH-3T3 and NG97 cell lines could phagocytize this wrap. The gene transfection was characterised by fluorescent protein produced in the cells and pictured by fluorescent microscopy. Before application, we studied GCN cell viability in NIH-3T3 and NG97 line cells using both MTT and Neutral Red uptake assays. Our results suggest that GCN has moderate stability behaviour as colloid solution and has great potential as a gene carrier agent in non-viral based therapy, with low cytotoxicity and good transfection efficiency.