<p>A large amount of today’s telecommunication consists of mobile and short distance wireless applications, where the effect of the channel is unknown and changing over time, and thus needs to be described statistically. Therefore the received signal can not be accurately predicted and has to be estimated. Since telecom systems are implemented in real-time, the hardware in the receiver for estimating the sent signal can for example be based on a DSP where the statistic calculations are performed. A fixed-point DSP with a limited number of bits and a fixed binary point causes larger quantization errors compared to floating point operations with higher accuracy.</p><p>The focus on this thesis has been to build a library of functions for handling fixed-point data. A class that can handle the most common arithmetic operations and a least squares solver for fixed-point have been implemented in MATLAB code.</p><p>The MATLAB Fixed-Point Toolbox could have been used to solve this task, but in order to have full control of the algorithms and the fixed-point handling an independent library was created.</p><p>The conclusion of the simulation made in this thesis is that the least squares result are depending more on the number of integer bits then the number of fractional bits.</p> / <p>En stor del av dagens telekommunikation består av mobila trådlösa kortdistanstillämpningar där kanalens påverkan är okänd och förändras över tid. Signalen måste därför beskrivas statistiskt, vilket gör att den inte kan bestämmas exakt, utan måste estimeras. Eftersom telekomsystem arbetar i realtid består hårdvaran i mottagaren av t.ex. en DSP där de statistiska beräkningarna görs. En fixtals DSP har ett bestämt antal bitar och fast binärpunkt, vilket introducerar ett större kvantiseringsbrus jämfört med flyttalsoperationer som har en större noggrannhet.</p><p>Tyngdpunkten på det här arbetet har varit att skapa ett bibliotek av funktioner för att hantera fixtal. En klass har skapats i MATLAB-kod som kan hantera de vanligaste aritmetiska operationerna och lösa minsta-kvadrat-problem.</p><p>MATLAB:s Fixed-Point Toolbox skulle kunna användas för att lösa den här uppgiften men för att ha full kontroll över algoritmerna och fixtalshanteringen behövs ett eget bibliotek av funktioner som är oberoende av MATLAB:s Fixed-Point Toolbox.</p><p>Slutsatsen av simuleringen gjord i detta examensarbete är att resultatet av minsta-kvadrat-metoden är mer beroende av antalet heltalsbitar än antalet binaler.</p> / fixtal, telekommunikation, DSP, MATLAB, Fixed-Point Toolbox, minsta-kvadrat-lösning, flyttal, Householder QR faktorisering, saturering, kvantiseringsbrus

A common problem to all applications of linear finite dynamical systems is analyzing the dynamics without enumerating every possible state transition. Of particular interest is the long term dynamical behaviour, and if every element eventually converges on fixed points. In this paper, we study the number of iterations needed for a system to settle on a fixed set of elements. As our main result, we present two upper bounds on iterations needed, and each one may be readily applied to a fixed point system test. The bounds are based on submodule properties of iterated images and reduced systems modulo a prime.

Neste trabalho tem por objetivo a construção de conjugações suaves de pontos fixos hiperbólicos com condições de não ressonância. Por tanto, inicialmente são apresentados alguns conceitos básicos sobre espaços de Banach e alguns resultados de equações diferenciais ordinárias em espaços de Banach e sistemas dinâmicos, apresentamos o teorema de Hartman Grobman como motivação inicial de Linearização. Apresentamos também vários exemplos como motivação para estudar o Teorema de Sternberg para contrações hiperbólicas, o principal resultado estudado nesta dissertação para contrações hiperbólicas / This work has the objetive of building smooth conjugations of hyperbolic fixed points with non-resonance conditions. So, first we present some basics of Banach spaces and some results of ordinary differential equations in Banach spaces and dynamical systems, we present the theorem of Hartman Grobman as original motivation for linearization . We also present several examples as motivation to study the Sternberg theorem for hyperbolic contractions, as main result studied in this dissertation

In this thesis, we provide constructive proofs of serveral generalizations of Sperner's Lemma, a combinatorial result which is equivalent to the Brouwer Fixed Point Theorem. This lemma makes a statement about the number of a certain type of simplices in the triangulation of a simplex with a special labeling. We prove generalizations for polytopes with simplicial facets, for arbitrary 3-polytopes, and for polygons. We introduce a labeled graph which we call a nerve graph to prove these results. We also suggest a possible non-constructive proof for a polytopal generalization.

In a recent paper with N. Tarkhanov, the Lefschetz number for endomorphisms (modulo trace class operators) of sequences of trace class curvature was introduced. We show that this is a well defined, canonical extension of the classical Lefschetz number and establish the homotopy invariance of this number. Moreover, we apply the results to show that the Lefschetz fixed point formula holds for geometric quasiendomorphisms of elliptic quasicomplexes.

The aim of this work is to propose viscosity-like methods for finding a specific common fixed point of a finite family T={ T_{i} }_{i=1}^{N} of nonexpansive self-mappings of a closed convex subset C of a Hilbert space H.We propose two schemes: one implicit and the other explicit.The implicit scheme determines a set {x_{t} : 0 < t < 1} through the fixed point equation x_{t}= tf (x_{t} ) + (1− t)Tx_{t}, where f : C¡÷C is a contraction.The explicit scheme is the discretization of the implicit scheme and de defines a sequence {x_{n} } by the recursion x_{n+1}=£\\_{n}f(x_{n}) +(1−£\\_{n})Tx_{n} for n ≥ 0, where {£\\_{n} }⊂ (0,1) It has been shown in the literature that both implicit and explicit schemes converge in norm to a fixed point of T (with additional conditions imposed on the sequence {£\ _{n} } in the explicit scheme).We will extend both schemes to the case of a finite family of nonexpansive mappings. Our proposed schemes converge in norm to a common fixed point of the family which in addition solves a variational inequality.

Multimedia workloads have always held an important role in embedded applications. Products are multifarious, such as various modeling mobile phone, MP3 player which is deft and convenient to carry and PDA which is popular with workers. We touch them all the time in our life. So these kinds of products are usually not high price. If their design cost and production cost are lower than others, then they can earn profits in this competition market. In so much multimedia applications, the most popular MP3 is our research goal. The design methods of multimedia audio application are using high performance CPU or combining general purpose processor with a DSP. Their performance satisfied the demand of multimedia application really, but the system hardware cost will increase at the same time. It is not the best solution in embedded products which emphasizing that low cost is better than high performance. So, my thesis will focus on MP3 algorithm optimization. We analyzed MP3 decoder algorithms, and found out the key operation. Using the SIMD operation feature of low cost multimedia processor development from our lab (It¡¦s named ME-MCU) to accelerate the processor speed. Then, I don¡¦t need a strong CPU or DSP, and I also can complete the MP3 decode operations as well. When I optimized the MP3 algorithm, I hope to provide some suggestion for ME-MCU modification. And the multimedia application will more agree with ME-MCU.

Thesis (B.S.)--Haverford College, Dept. of Mathematics, 2002. / Includes bibliographical references.

The ePUMA architecture is a novel master-multi-SIMD DSP platform aimed at low-power computing, like for embedded or hand-held devices for example. It is both a configurable and scalable platform, designed for multimedia and communications. Numbers with both integer and fractional parts are often used in computers because many important algorithms make use of them, like signal and image processing for example. A good way of representing these types of numbers is with a floating-point representation. The ePUMA platform currently supports a fixed-point representation, so the goal of this thesis will be to implement twelve basic floating-point arithmetic operations and two conversion operations onto an already existing datapath, conforming as much as possible to the IEEE 754-2008 standard for floating-point representation. The implementation should be done at a low hardware and power consumption cost. The target frequency will be 500MHz. The implementation will be compared with dedicated DesignWare components and the implementation will also be compared with floating-point done in software in ePUMA. This thesis presents a solution that on average increases the VPE datapath hardware cost by 15% and the power consumption increases by 15% on average. Highest clock frequency with the solution is 473MHz. The target clock frequency of 500MHz is thus not achieved but considering the lack of register retiming in the synthesis step, 500MHz can most likely be reached with this design.

In recent decades, significant interest, based on physics and engineering applications, has developed on so-called anomalous diffusion processes that possess different spread functions with classical ones. The resulting differential equation whose fundamental solution matches this decay process is best modeled by an equation containing a fractional order derivative. This dissertation mainly focuses on some inverse problems for fractional diffusion equations. After some background introductions and preliminaries in Section 1 and 2, in the third section we consider our first inverse boundary problem. This is where an unknown boundary condition is to be determined from overposed data in a time- fractional diffusion equation. Based upon the fundamental solution in free space, we derive a representation for the unknown parameters as the solution of a nonlinear Volterra integral equation of second kind with a weakly singular kernel. We are able to make physically reasonable assumptions on our constraining functions (initial and given boundary values) to be able to prove a uniqueness and reconstruction result. This is achieved by an iterative process and is an immediate result of applying a certain fixed point theorem. Numerical examples are presented to illustrate the validity and effectiveness of the proposed method. In the fourth section a reaction-diffusion problem with an unknown nonlinear source function, which has to be determined from overposed data, is considered. A uniqueness result is proved and a numerical algorithm including convergence analysis under some physically reasonable assumptions is presented in the one-dimensional case. To show effectiveness of the proposed method, some results of numerical simulations are presented. In Section 5, we also attempted to reconstruct a nonlinear source in a heat equation from a number of known input sources. This represents a new research even for the case of classical diffusion and would be the first step in a solution method for the fractional diffusion case. While analytic work is still in progress on this problem, Newton and Quasi-Newton method are applied to show the feasibility of numerical reconstructions. In conclusion, the fractional diffusion equations have some different properties with the classical ones but there are some similarities between them. The classical tools like integral equations and fixed point theory still hold under slightly different assumptions. Inverse problems for fractional diffusion equations have applications in many engineering and physics areas such as material design, porous media. They are trickier than classical ones but there are also some advantages due to the mildly ill-conditioned singularity caused by the new kernel functions.