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. 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. 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. 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. / 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. 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. 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. Slutsatsen av simuleringen gjord i detta examensarbete är att resultatet av minsta-kvadrat-metoden är mer beroende av antalet heltalsbitar än antalet binaler. / fixtal, telekommunikation, DSP, MATLAB, Fixed-Point Toolbox, minsta-kvadrat-lösning, flyttal, Householder QR faktorisering, saturering, kvantiseringsbrus

<p>The question about how to determine the rank of a tensor has been widely studied in the literature. However the analytical methods to compute the decomposition of tensors have not been so much developed even for low-rank tensors.</p><p>In this report we present analytical methods for finding real and complex PARAFAC decompositions of 2 x 2 x 2 tensors before computing the actual rank of the tensor.</p><p>These methods are also implemented in MATLAB.</p><p>We also consider the question of how best lower-rank approximation gives rise to problems of degeneracy, and give some analytical explanations for these issues.</p>

<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

The question about how to determine the rank of a tensor has been widely studied in the literature. However the analytical methods to compute the decomposition of tensors have not been so much developed even for low-rank tensors. In this report we present analytical methods for finding real and complex PARAFAC decompositions of 2 x 2 x 2 tensors before computing the actual rank of the tensor. These methods are also implemented in MATLAB. We also consider the question of how best lower-rank approximation gives rise to problems of degeneracy, and give some analytical explanations for these issues.

This dissertation addresses the development and use of novel software tools and environments for the computation and visualization of canonical information as well as stratification hierarchies for matrices and matrix pencils. The simplest standard shape to which a matrix pencil with a given set of eigenvalues can be reduced is called the Kronecker canonical form (KCF). The KCF of a matrix pencil is unique, and all pencils in the manifold of strictly equivalent pencils - collectively termed the orbit - can be reduced to the same canonical form and so have the same canonical structure. For a problem with fixed input size, all orbits are related under small perturbations. These relationships can be represented in a closure hierarchy with a corresponding graph depicting the stratification of these orbits. Since degenerate canonical structures are common in many applications, software tools to determine canonical information, especially under small perturbations, are central to understanding the behavior of these problems. The focus in this dissertation is the development of a software tool called StratiGraph. Its purpose is the computation and visualization of stratification graphs of orbits and bundles (i.e., union of orbits in which the eigenvalues may change) for matrices and matrix pencils. It also supports matrix pairs, which are common in control systems. StratiGraph is extensible by design, and a well documented plug-in feature enables it, for example, to communicate with Matlab(TM). The use and associated benefits of StratiGraph are illustrated via numerous examples. Implementation considerations such as flexible software design, suitable data representations, and good and efficient graph layout algorithms are also discussed. A way to estimate upper and lower bounds on the distance between an input S and other orbits is presented. The lower bounds are of Eckhart-Young type, based on the matrix representation of the associated tangent spaces. The upper bounds are computed as the Frobenius norm F of a perturbation such that S + F is in the manifold defining a specified orbit. Using associated plug-ins to StratiGraph this information can be computed in Matlab, while visualization alongside other canonical information remains within StratiGraph itself. Also, a proposal of functionality and structure of a framework for computation of matrix canonical structure is presented. Robust, well-known algorithms, as well algorithms improved and developed in this work, are used. The framework is implemented as a prototype Matlab toolbox. The intention is to collect software for computing canonical structures as well as for computing bounds and to integrate it with the theory of stratification into a powerful new environment called the MCS toolbox. Finally, a set of utilities for generating web computing environments related to mathematical and engineering library software is presented. The web interface can be accessed from a standard web browser with no need for additional software installation on the local machine. Integration with the control and systems library SLICOT further demonstrates the efficacy of this approach.

No description available.

Master Thesis deals with supplier rating with usage of fuzzy logic as an advanced decision-making method. There was made a model for selection of the optimal technologies supplier for a self-service vehicle wash. The main solution is realized with support of programs MS Excel and MATLAB.

This diploma thesis deals with the design of fuzzy models to support decision making for selecting the most suitable suppliers for PSL, a.s. Describes methods and procedures for modeling in MS Excel and MATLAB. The goal is to create a decision-making system that will evaluate suppliers to optimize the choice of the most suitable supplier based on the requirements of the selected company.

This thesis deal with an analysis of network traffic and its properties. In this thesis are discussed possibilities of prediction network traffic by FARIMA model, theory of chaos with Lyapunov exponent and by neural networks. The biggest attention was dedicated to prediction network traffic by neural networks. In Matlab with using Neural Network Toolbox were created, trained and tested recurrent networks for prediction specific types of network traffics, which was captured on local network. There were choosed Elman network, LRN and NARX network to test the prediction of network traffic, results were discussed. Thesis also introduce area of application ability prediction of network traffic, there is introduce design of system for dynamic allocation bandwidth with particular description of its prediction part. Thesis also states possible use designed system for dynamic allocation of bandwidth.

The aim of this thesis was to study problems of prediction of data in computer networks. Furthermore, this work deals with network traffic and analyzing its properties. In this study were analyzed the possibilities of network traffic prediction using Farima model, the theory of chaos with Lyapunov exponents and neural networks. Possibilities of prediction with the focus on neural network were discussed in detail here, mainly on recurrent neural networks. Prediction was performed in Matlab development environment in Neural Network Toolbox, where they were created, trained and evaluated neural network to predict specific types of network traffic. For testing were selected Elman network NARX network and general LRN recurrent network. The results were clearly organized into tables and plotted in graphical relationships before and after the use of predictive techniques designed to final evaluation.