Barbara Kiesenhofer: Toolbox zur analytischen Beschreibung von Exponentialpolynomen, 2011

Abstract: This bachelor thesis deals with the implementation of a toolbox for an analytic description of exponential polynomials in Matlab. An exponential polynomial is a function that takes the form of polynomials in a variable multiplied by an exponential function. This class of functions is very common in technical systems. For example the impulse response can be described. In addition signals of linear, time-invariant systems can be characterized. Furthermore the description of memoryless nonlinear systems with polynmial characteristic is possible. 

The essential parameters and coefficients of the exponential polynomials are saved as matrices in Matlab, so little memory is needed. The aim of the toolbox is to facilitate analytic computation with exponential polynomials, instead of working with vectors of sampled data, as usual in Matlab. Signals and systems are represented as matrices in Matlab. 

The toolbox includes several Matlab-functions that are partly based on previous work. Within this bachelor thesis the Matlab-functions for integration and summation, convolution, time extension, sampling and periodic extension have been implemented. Special emphasis was placed on the derivation of formulas and mathematical relationships.

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