In this thesis, an efficiency method for reducing the rotation ROM size in table-based architecture is proposed. The original rotation can be divided into two stages, coarse stage and fine stage. Our approach modifies the previous two-stage rotation method and proposes a multi-stage architecture and discuses three-stage phase calculation. The effect of table reduction is more apparently for higher accuracy requirement in the three-stage architecture. The total area of the previous two-stage architecture is larger than the proposed table-reduced three-stage architecture because the table size takes a significant ratio of the total area especially when the required bit accuracy is large. In the proposed three-stage design, there are two different types of architectures, depending on the rotation angles in the first and second rotation stages. Comparison of different types of architecture with the previous method shows that our designs indeed reduce the table size and the total area significantly.

<p>The target of this master thesis is to evaluate the Image Warping technique and propose a possible design for an implementation in FPGA. The Image Warping is widely used in the image processing for image correction and rectification. A DSP is a usual choice for implantation of the image processing algorithms, but to decrease a cost of the target system it was proposed to use an FPGA for implementation.</p><p>In this work a different Image Warping methods was evaluated in terms of performance, produced image quality, complexity and design size. Also, considering that it is not only Image Warping algorithm which will be implemented on the target system, it was important to estimate a possible memory bandwidth used by the proposed design. The evaluation was done by implemented a C-model of the proposed design with a finite datapath to simulate hardware implementation as close as possible.</p>

Zugl.: Hannover, University, Diss.

Reproduction de : Thèse de doctorat : Dynamique des fluides : Toulouse, INPT : 2005. / Titre provenant de l'écran-titre. Bibliogr. 182 réf.

In this thesis we propose a new class of Linearly Constrained Convex Optimization methods based on the use of a generalization of Shepard's interpolation formula. We prove the properties of the surface such as the interpolation property at the boundary of the feasible region and the convergence of the gradient to the null space of the constraints at the boundary. We explore several descent techniques such as steepest descent, two quasi-Newton methods and the Newton's method. Moreover, we implement in the Matlab language several versions of the method, particularly for the case of Quadratic Programming with bounded variables. Finally, we carry out performance tests against Matab Optimization Toolbox methods for convex optimization and implementations of the standard log-barrier and active-set methods. We conclude that the steepest descent technique seems to be the best choice so far for our method and that it is competitive with other standard methods both in performance and empirical growth order.

The present introduces fractal interpolation functions; reveals advantages of fractal interpolation of real world objects and presents organisational procedures of fractal interpolation process...The author tries to analyse and solve the problem of selection of interpolation points (general case). also, a new attitude on selection of oblique affined transformations that make IFS is suggested in the work.

The pseudospectral method is a family of numerical methods for the solution of differential equations based on the expansion of basis functions defined on a set of grid points. In this thesis, the relationship between the distribution of grid points and the accuracy and convergence of the solution is emphasized. The polynomial and sinc pseudospectral methods are extensively studied along with many applications to quantum and statistical mechanics involving the Fokker-Planck and Schroedinger equations. The grid points used in the polynomial methods coincide with the points of quadrature, which are defined by a set of polynomials orthogonal with respect to a weight function. The choice of the weight function plays an important role in the convergence of the solution. It is observed that rapid convergence is usually achieved when the weight function is chosen to be the square of the ground-state eigenfunction of the problem. The sinc method usually provides a slow convergence as the grid points are uniformly distributed regardless of the behaviour of the solution. For both polynomial and sinc methods, the convergence rate can be improved by redistributing the grid points to more appropriate positions through a transformation of coordinates. The transformation method discussed in this thesis preserves the orthogonality of the basis functions and provides simple expressions for the construction of discretized matrix operators. The convergence rate can be improved by several times in the evaluation of loosely bound eigenstates with an exponential or hyperbolic sine transformation. The transformation can be defined explicitly or implicitly. An explicit transformation is based on a predefined mapping function, while an implicit transformation is constructed by an appropriate set of grid points determined by the behaviour of the solution. The methodologies of these transformations are discussed with some applications to 1D and 2D problems. The implicit transformation is also used as a moving mesh method for the time-dependent Smoluchowski equation when a function with localized behaviour is used as the initial condition.

The Pixel Router was developed at the University of Kentucky with the intent of supporting multi-projector displays by combining the scalability of commercial software solutions with the flexibility of commercial hardware solutions. This custom hardware solution uses a Look Up Table for an arbitrary input to output pixel mapping, but suffers from high memory latencies due to random SDRAM accesses. In order for this device to achieve marketability, the image interpolation method needed improvement as well. The previous design used the nearest neighbor interpolation method, which produces poor looking results but requires the least amount of memory accesses. A cache was implemented to support bilinear interpolation to simultaneously increase the output frame rate and image quality. A number of software simulations were conducted to test and refine the cache design, and these results were verified by testing the implementation on hardware. The frame rate was improved by a factor of 6 versus bilinear interpolation on the previous design, and by as much as 50% versus nearest neighbor on the previous design. The Pixel Router was also certified for FCC conducted and radiated emissions compliance, and potential commercial market areas were explored.

Although one significant method of interpolation is that of the cubic spline, it has the drawback of occasionally producing undesired inflections in a curve. As a remedy, the spline can mathematically be "stretched" (so to speak) in much the same way that a draftsman's spline could be pulled at its ends while still being anchored at certain points throughout.This thesis will make use of FORTRAN subroutines given in the April, 1974 issue of Communications of the ACM, which have the capability of applying this tension factor to a cublic spline in a graphics package. It will also discuss the necessary modifications which are required before compatibility can be achieved between these subroutines and the Tektronix terminal which is coupled to the DEC-10 here at Ball State University.

The pseudospectral method is a family of numerical methods for the solution of differential equations based on the expansion of basis functions defined on a set of grid points. In this thesis, the relationship between the distribution of grid points and the accuracy and convergence of the solution is emphasized. The polynomial and sinc pseudospectral methods are extensively studied along with many applications to quantum and statistical mechanics involving the Fokker-Planck and Schroedinger equations. The grid points used in the polynomial methods coincide with the points of quadrature, which are defined by a set of polynomials orthogonal with respect to a weight function. The choice of the weight function plays an important role in the convergence of the solution. It is observed that rapid convergence is usually achieved when the weight function is chosen to be the square of the ground-state eigenfunction of the problem. The sinc method usually provides a slow convergence as the grid points are uniformly distributed regardless of the behaviour of the solution. For both polynomial and sinc methods, the convergence rate can be improved by redistributing the grid points to more appropriate positions through a transformation of coordinates. The transformation method discussed in this thesis preserves the orthogonality of the basis functions and provides simple expressions for the construction of discretized matrix operators. The convergence rate can be improved by several times in the evaluation of loosely bound eigenstates with an exponential or hyperbolic sine transformation. The transformation can be defined explicitly or implicitly. An explicit transformation is based on a predefined mapping function, while an implicit transformation is constructed by an appropriate set of grid points determined by the behaviour of the solution. The methodologies of these transformations are discussed with some applications to 1D and 2D problems. The implicit transformation is also used as a moving mesh method for the time-dependent Smoluchowski equation when a function with localized behaviour is used as the initial condition.