Zugl.: Marburg, Univ., Diss., 2006

University, Diss., 2006--Marburg.

Thesis--Giessen. / Without thesis statement. Vita. Bibliography: leaf [40-41].

Thesis (Ph. D.)--University of Wisconsin--Madison, 1984. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 54-57).

Proefschrift--Groningen. / Lijst van de voornaamste, geraadpleegde werken: p. [85]-86.

This thesis concerns the absolute convergence of the Fourier series of functions belonging to certain Lipschitz classes on totally disconnected groups. The technique used is one of interpolating between certain endpoint results which are proven directly. These results are shown to be best possible and a counterexample in interpolation theory is given. / Science, Faculty of / Mathematics, Department of / Graduate

This thesis is devoted to a study about Fractals and Fractal Polynomial Interpolation. Fractal Interpolation is a great topic with many interesting applications, some of which are used in everyday lives such as television, camera, and radio. The thesis is comprised of eight chapters. Chapter one contains a brief introduction and a historical account of fractals. Chapter two is about polynomial interpolation processes such as Newton s, Hermite, and Lagrange. Chapter three focuses on iterated function systems. In this chapter I report results contained in Barnsley s paper, Fractal Functions and Interpolation. I also mention results on iterated function system for fractal polynomial interpolation. Chapters four and five cover fractal polynomial interpolation and fractal interpolation of functions studied by Navascués. Chapter five and six are the generalization of Hermite and Lagrange functions using fractal interpolation. As a concluding chapter we look at the current applications of fractals in various walks of life such as physics and finance and its prospects for the future.

No description available.

No description available.

The aim of this thesis is to implement flexible interpolators and decimators onField Programmable Gate Array (FPGA). Interpolators and decimators of differentwordlengths (WL) are implemented in VHDL. The Farrow structure is usedfor the realization of the polyphase components of the interpolation/decimationfilters. A fixed set of subfilters and adjustable fractional-delay multiplier valuesof the Farrow structure give different linear-phase finite-length impulse response(FIR) lowpass filters. An FIR filter is designed in such a way that it can be implementedfor different wordlengths (8-bit, 12-bit, 16-bit). Fixed-point representationis used for representing the fractional-delay multiplier values in the Farrow structure. To perform the fixed-point operations in VHDL, a package called fixed pointpackage [1] is used. A 8-bit, 12-bit, and 16-bit interpolator are implemented and their performancesare verified. The designs are compiled in Quartus-II CAD tool for timing analysisand for logical registers usage. The designs are synthesised by selecting Cyclone IVGX family and EP4X30CF23C6 device. The wordlength issues while implementingthe interpolators and decimators are discussed. Truncation of bits is required inorder to reduce the output wordlength of the interpolator and decimator.