Discrete Wiener¿Lee transforms

The use of Wiener–Lee transforms to construct one of the frequency characteristics, magnitude or phase of a network function, when the other characteristic is given graphically, is indicated. This application is useful in finding a realisable network function whose magnitude or phase curve is given. A discrete version of the transform is presented, so that a digital computer can be employed for the computation.

Numerical Analyses of Discrete Gust Response for an Aircraft

Based on Navier-Stokes equations and structural and flight dynamic equations of motion, dynamic responses in vertical discrete gust flow perturbation are investigated for a supersonic transport model. A tightly coupled method was developed by subiterations between aerodynamic equations and dynamic equations of motion. First, under the assumption of rigid-body and single freedom of motion in the vertical plunging, the results of a direct-coupling method are compared with the results of quasi-steady model method. Then, gust responses for the one-minus-cosine gust profile arc analyzed with two freedoms of motion in plunging and pitching for the airplane configurations with and without the consideration of structural deformation.

Rapid design of discrete orthonormal wavelet transforms

A methodology which allows a non-specialist to rapidly design silicon wavelet transform cores has been developed. This methodology is based on a generic architecture utilizing time-interleaved coefficients for the wavelet transform filters. The architecture is scaleable and it has been parameterized in terms of wavelet family, wavelet type, data word length and coefficient word length. The control circuit is designed in such a way that the cores can also be cascaded without any interface glue logic for any desired level of decomposition. This parameterization allows the use of any orthonormal wavelet family thereby extending the design space for improved transformation from algorithm to silicon. Case studies for stand alone and cascaded silicon cores for single and multi-stage analysis respectively are reported. The typical design time to produce silicon layout of a wavelet based system has been reduced by an order of magnitude. The cores are comparable in area and performance to hand-crafted designs. The designs have been captured in VHDL so they are portable across a range of foundries and are also applicable to FPGA and PLD implementations.

Rapid silicon design of discrete orthonormal wavelet transforms based algorithms

A methodology has been developed which allows a non-specialist to rapidly design silicon wavelet transform cores for a variety of specifications. The cores include both forward and inverse orthonormal wavelet transforms. This methodology is based on efficient, modular and scaleable architectures utilising time-interleaved coefficients for the wavelet transform filters. The cores are parameterized in terms of wavelet type and data and coefficient word lengths. The designs have been captured in VHDL and are hence portable across a range of silicon foundries as well as FPGA and PLD implementations.

Rapid design of discrete orthonormal wavelet transforms using silicon IP components

A rapid design methodology for orthonormal wavelet transform cores has been developed. This methodology is based on a generic, scaleable architecture utilising time-interleaved coefficients for the wavelet transform filters. The architecture has been captured in VHDL and parameterised in terms of wavelet family, wavelet type, data word length and coefficient word length. The control circuit is embedded within the cores and allows them to be cascaded without any interface glue logic for any desired level of decomposition. Case studies for stand alone and cascaded silicon cores for single and multi-stage wavelet analysis respectively are reported. The design time to produce silicon layout of a wavelet based system has been reduced to typically less than a day. The cores are comparable in area and performance to handcrafted designs. The designs are portable across a range of foundries and are also applicable to FPGA and PLD implementations.

Special functions of Weyl groups and their continuous and discrete orthogonality

Cette thèse s'intéresse à l'étude des propriétés et applications de quatre familles des fonctions spéciales associées aux groupes de Weyl et dénotées $C$, $S$, $S^s$ et $S^l$. Ces fonctions peuvent être vues comme des généralisations des polynômes de Tchebyshev. Elles sont en lien avec des polynômes orthogonaux à plusieurs variables associés aux algèbres de Lie simples, par exemple les polynômes de Jacobi et de Macdonald. Elles ont plusieurs propriétés remarquables, dont l'orthogonalité continue et discrète. En particulier, il est prouvé dans la présente thèse que les fonctions $S^s$ et $S^l$ caractérisées par certains paramètres sont mutuellement orthogonales par rapport à une mesure discrète. Leur orthogonalité discrète permet de déduire deux types de transformées discrètes analogues aux transformées de Fourier pour chaque algèbre de Lie simple avec racines des longueurs différentes. Comme les polynômes de Tchebyshev, ces quatre familles des fonctions ont des applications en analyse numérique. On obtient dans cette thèse quelques formules de <>, pour des fonctions de plusieurs variables, en liaison avec les fonctions $C$, $S^s$ et $S^l$. On fournit également une description complète des transformées en cosinus discrètes de types V--VIII à $n$ dimensions en employant les fonctions spéciales associées aux algèbres de Lie simples $B_n$ et $C_n$, appelées cosinus antisymétriques et symétriques. Enfin, on étudie quatre familles de polynômes orthogonaux à plusieurs variables, analogues aux polynômes de Tchebyshev, introduits en utilisant les cosinus (anti)symétriques.

A continuous wavelet transform and classification method for delirium motoric subtyping

The usefulness of motor subtypes of delirium is unclear due to inconsistency in subtyping methods and a lack of validation with objective measures of activity. The activity of 40 patients was measured over 24 h with a discrete accelerometer-based activity monitor. The continuous wavelet transform (CWT) with various mother wavelets were applied to accelerometry data from three randomly selected patients with DSM-IV delirium that were readily divided into hyperactive, hypoactive, and mixed motor subtypes. A classification tree used the periods of overall movement as measured by the discrete accelerometer-based monitor as determining factors for which to classify these delirious patients. This data used to create the classification tree were based upon the minimum, maximum, standard deviation, and number of coefficient values, generated over a range of scales by the CWT. The classification tree was subsequently used to define the remaining motoric subtypes. The use of a classification system shows how delirium subtypes can be categorized in relation to overall motoric behavior. The classification system was also implemented to successfully define other patient motoric subtypes. Motor subtypes of delirium defined by observed ward behavior differ in electronically measured activity levels.

Use of the statistical properties of the wavelet-transform coefficients for optimization of integration time in Fourier transform spectrometry

We show that an analysis of the mean and variance of discrete wavelet coefficients of coaveraged time-domain interferograms can be used as a specification for determining when to stop coaveraging. We also show that, if a prediction model built in the wavelet domain is used to determine the composition of unknown samples, a stopping criterion for the coaveraging process can be developed with respect to the uncertainty tolerated in the prediction.

A nonparametric ensemble transform method for Bayesian inference

Many applications, such as intermittent data assimilation, lead to a recursive application of Bayesian inference within a Monte Carlo context. Popular data assimilation algorithms include sequential Monte Carlo methods and ensemble Kalman filters (EnKFs). These methods differ in the way Bayesian inference is implemented. Sequential Monte Carlo methods rely on importance sampling combined with a resampling step, while EnKFs utilize a linear transformation of Monte Carlo samples based on the classic Kalman filter. While EnKFs have proven to be quite robust even for small ensemble sizes, they are not consistent since their derivation relies on a linear regression ansatz. In this paper, we propose another transform method, which does not rely on any a priori assumptions on the underlying prior and posterior distributions. The new method is based on solving an optimal transportation problem for discrete random variables. © 2013, Society for Industrial and Applied Mathematics

Disparity estimation using TI multi-wavelet transform

A multi-resolution image matching technique based on translation invariant discrete multi-wavelet transform followed by a coarse to fine matching strategy is presented. The technique addresses the estimation of optimal corresponding points and the corresponding disparity maps in the presence of occlusion, ambiguity and illuminative variations in the two perspective views taken by two different cameras or at different lighting conditions. The problem of occlusion and ambiguity is addressed explicitly by a geometric optimization approach along with the uniqueness constraint whereas the illuminative variation is dealt with by using windowed normalized correlation on the discrete multi-wavelet coefficients.

Mineraly of oceanic crust from the Kane Transform, Mid-Atlantic Ridge

Gabbroic cumulates drilled south of the Kane Transform Fault on the slow-spread Mid-Atlantic Ridge preserve up to three discrete magnetization components. Here we use absolute age constraints derived from the paleomagnetic data to develop a model for the magmatic construction of this section of the lower oceanic crust. By comparing the paleomagnetic data with mineral compositions, and based on thermal models of local reheating, we infer that magmas that began crystallizing in the upper mantle intruded into the lower oceanic crust and formed meter-scale sills. Some of these magmas were crystal-laden and the subsequent expulsion of interstitial liquid from them produced '"cumulus" sills. These small-scale magmatic injections took place over at least 210 000 years and at distances of ~3 km from the ridge axis and may have formed much of the lower crust. This model explains many of the complexities described in this area and can be used to help understand the general formation of oceanic crust at slow-spread ridges.

Smoothing a Discrete Hazard Function for the Number of Patients Colonized with Methicillin-Resistance Staphylococcus Aureus in an Intensive Care Unit

A new method for estimating the time to colonization of Methicillin-resistant Staphylococcus Aureus (MRSA) patients is developed in this paper. The time to colonization of MRSA is modelled using a Bayesian smoothing approach for the hazard function. There are two prior models discussed in this paper: the first difference prior and the second difference prior. The second difference prior model gives smoother estimates of the hazard functions and, when applied to data from an intensive care unit (ICU), clearly shows increasing hazard up to day 13, then a decreasing hazard. The results clearly demonstrate that the hazard is not constant and provide a useful quantification of the effect of length of stay on the risk of MRSA colonization which provides useful insight.